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arxiv: 2604.17346 · v1 · submitted 2026-04-19 · 💻 cs.CL

Logical Computational Linguistics

Glyn V. Morrill , Oriol Valent\'in This is my paper

Pith reviewed 2026-05-10 06:27 UTC · model grok-4.3

classification 💻 cs.CL
keywords logical computational linguisticstype logical grammarlogical semantic interfacedependency chainsconfidence preservationlife-critical NLP
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The pith

Type logical grammar enables chains of dependencies that retain complete confidence regardless of length.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper advocates for logical computational linguistics based on type logical grammar instead of statistical approaches. It argues that while chains of statistical dependencies with less than perfect confidence degrade to zero, logical chains maintain full confidence end to end. The work compiles over twenty years of research on type logical grammar and introduces a logical semantic interface. The goal is to achieve perfect syntactic and semantic processing suitable for life-critical applications in natural language processing.

Core claim

Chains of logical dependencies of any length maintain one hundred per cent confidence end to end, in contrast to statistical dependencies that tend monotonically to zero.

What carries the argument

Type logical grammar supplying a logical semantic interface for complete syntactic and semantic coverage of natural language.

If this is right

  • Perfect syntactic and semantic processing is possible in life-critical NLP applications.
  • Arbitrary-length chains of logical dependencies can be used with no loss of certainty.
  • Statistical fallback becomes unnecessary once complete coverage is achieved.
  • More than twenty years of type logical grammar research can be unified into one framework.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • High-stakes domains such as medical or legal text processing could use deterministic logical pipelines instead of probabilistic models.
  • The framework could support formal verification of entire NLP systems for safety certification.
  • Empirical testing of the grammar on large real-world corpora would reveal whether coverage gaps exist in practice.

Load-bearing premise

Type logical grammar supplies complete coverage of natural-language syntax and semantics without requiring statistical fallback or introducing coverage gaps in real text.

What would settle it

A sentence or construction in natural language that type logical grammar cannot fully parse and semantically interpret, or any logical dependency chain that fails to maintain 100% end-to-end confidence.

Figures

Figures reproduced from arXiv: 2604.17346 by Glyn V. Morrill, Oriol Valent\'in.

Figure 2
Figure 2. Figure 2: , and the structure preserving prosodic type map [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
Figure 2.1
Figure 2.1. Figure 2.1: , and the structure preserving prosodic type map s associates these with sorts. The sort s(A) (sA) of a type A is the i ∈ N such that A ∈ Tpi . For example, if s(N) = s(S) = 0, we have s((S↑1N)↑0N) = s((S↑0N)↑1N) = 2, and if s(VP) = 1, s((J\(N\VP))↑0N) = 2. 0. Tpi ::= Pt1 . . . tn s(A) = σ 1. Tpi ::= Tpi+j/Tpj s(C/B) = s(C) − s(B) over [46] 2. Tpj ::= Tpi\Tpi+j s(A\C) = s(C) − s(A) over [46] 3. Tpi+j ::=… view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: Continuous multiplicative rules Notice how in the multiplicative rules the conclusion stoup is partitioned between premises in binary rules, copied to the premise in unary rules, and is empty in the axiomatic IR rule. When stoups are empty, both the empty stoup and ‘; ’ may be omitted in derivations. The directional divisions “over”, /, and “under”, \, are exemplified by assignments such as the: N/CN for… view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Discontinuous multiplicative rules Notice how the discontinuous multiplicative rules have exactly the same form as the continuous multi￾plicative rules but with metalinguistic intercalation “ |k ” in place of the metalinguistic concatenation “,”; the stoups distribute as before. When the value of the k subscript is one it may be omitted, i.e. it defaults to one. “Circumfixation”, ↑, is exemplified by a p… view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: Additive rules Notice how the stoup is shared between premises and conclusion in the additive rules. By way of example of the additives, the additive conjunction “with”, &, can be used for the polymorphism of a mass noun rice: N&CN as in rice grows: S and the rice grows: S: (19) N ⇒ N &L1 N&CN ⇒ N S ⇒ S \L N&CN, N\S ⇒ S N/CN, CN, N\S ⇒ S &L2 N/CN, N&CN, N\S ⇒ S The additive disjunction “plus”, ⊕, can be … view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: Quantifier rules, where † indicates that there is no a in the conclusion Notice how the stoup is identical on premises and conclusions in the quantifier rules. By way of example of the quantifiers, we can generalise over singular and plural number in sheep: V nCNn for the sheep grazes: S and the sheep graze: S: (21) CNsg ⇒ CNsg V ^ L nCNn ⇒ CNsg CNpl ⇒ CNpl V ^ L nCNn ⇒ CNpl And we can express a past, pr… view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: Normal modality rules; 2×/+3marks a structure all the types of which have principal connective a box/diamond Note how the stoup is identical in premises and conclusions in the normal modality rules. With respect to the (S4) normal modalities the universal (Morrill 1990[59]) has application to intensionality. For exam￾ple, for a propositional attitude verb such as believes we can assign type 2((N\S)/2S) w… view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: Bracket modality rules Notice how the stoup is identical in conclusions and premises of bracket modality rules. By way of example of bracket modalities, we may assign walks:⟨⟩N\S for the subject condition (Chomsky 1973[13]), and before: [ ]−1 (VP\VP)/VP for the adverbial island constraint, which are weak islands, and can contain parasitic gaps; for a strong island such as a coordinate structure, which ca… view at source ↗
Figure 3.7
Figure 3.7. Figure 3.7: Subexponential rules Using the universal subexponential, !, we can assign a relative pronoun type that: (CN\CN)/(S/!N) allowing both medial extraction (via the permutation rule) and parasitic extraction (via the contraction rule), Morrill (2011[81]), Morrill and Valent´ın (2015[73]), and Morrill (2017[66]), such as paper that John filed without reading: CN, where parasitic gaps can appear only in (weak) … view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: The types of Generalised Displacement Logic [PITH_FULL_IMAGE:figures/full_fig_p030_4_1.png] view at source ↗
Figure 4
Figure 4. Figure 4: and the semantically inactive discontinuous multiplicative rules are as given in Figure 4.3. [PITH_FULL_IMAGE:figures/full_fig_p031_4.png] view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Semantically inactive continuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p032_4_2.png] view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: Semantically inactive discontinuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p032_4_3.png] view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: Semantically inactive additive rules 33. Ξ⟨ −−−−→ A[t/v]⟩ ⇒ B ∀L Ξ⟨ −−−→∀vA⟩ ⇒ B Ξ ⇒ A[a/v] ∀R † Ξ ⇒ ∀vA 34. Ξ⟨ −−−−−→ A[a/v]⟩ ⇒ B ∃L † Ξ⟨ −−−→∃vA⟩ ⇒ B Ξ ⇒ A[t/v] ∃R Ξ ⇒ ∃vA [PITH_FULL_IMAGE:figures/full_fig_p033_4_4.png] view at source ↗
Figure 4.5
Figure 4.5. Figure 4.5: Semantically inactive quantifier rules, where [PITH_FULL_IMAGE:figures/full_fig_p033_4_5.png] view at source ↗
Figure 4.6
Figure 4.6. Figure 4.6: Semantically inactive normal modality rules; [PITH_FULL_IMAGE:figures/full_fig_p033_4_6.png] view at source ↗
Figure 4.7
Figure 4.7. Figure 4.7: Unary synthetic multiplicatives Rules for unary synthetic multiplicatives 37. Ξ⟨ −→A⟩ ⇒ B ◁ −1L Ξ⟨ −−−→◁ −1A, 1⟩ ⇒ B ζ; Γ, 1 ⇒ A ◁ −1R ζ; Γ ⇒ ◁ −1A 38. Ξ⟨ −→A⟩ ⇒ B ▷ −1L Ξ⟨1, −−−→▷ −1A⟩ ⇒ B ζ; 1, Γ ⇒ A ▷ −1R ζ; Γ ⇒ ▷ −1A 39. Ξ⟨ −→A, 1⟩ ⇒ B ◁L Ξ⟨ −→◁A⟩ ⇒ B ζ; Γ ⇒ A ◁R ζ; Γ, 1 ⇒ ◁A 40. Ξ⟨1, −→A⟩ ⇒ B ▷L Ξ⟨ −→▷A⟩ ⇒ B ζ; Γ ⇒ A ▷R ζ; 1, Γ ⇒ ▷A 41, k. Ξ⟨ −→B⟩ ⇒ C ˇ kL Ξ⟨ −→ˇ kB |k Λ⟩ ⇒ C ζ;∆|k Λ ⇒ B ˇ kR ζ;∆ ⇒ … view at source ↗
Figure 4.8
Figure 4.8. Figure 4.8: Unary synthetic multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p034_4_8.png] view at source ↗
Figure 4.9
Figure 4.9. Figure 4.9: Binary synthetic multiplicatives Rules for binary synthetic multiplicatives 43. ζ1; Γ ⇒ A Ξ(ζ2;∆1,⟨ −→C⟩,∆2) ⇒ D ÷L1 Ξ(ζ1 ⊎ζ2;∆1,⟨Γ, −−−→C÷A⟩,∆2) ⇒ D ζ1; Γ ⇒ A Ξ(ζ2;∆1,⟨ −→C⟩,∆2) ⇒ D ÷L2 Ξ(ζ1 ⊎ζ2;∆1,⟨ −−−→C÷A, Γ⟩,∆2) ⇒ D ζ; −→A, Γ ⇒ C ζ; Γ, −→A ⇒ C ÷R ζ; Γ ⇒ C÷A 44. Ξ⟨ −→A, −→B⟩ ⇒ D Ξ⟨ −→B, −→A⟩ ⇒ D ◦L Ξ⟨ −−−→A◦B⟩ ⇒ D: ζ1;∆ ⇒ A ζ2; Γ ⇒ B ◦R1 ζ1 ⊎ζ2;∆, Γ ⇒ A◦B ζ1;∆ ⇒ B ζ2; Γ ⇒ A ◦R2 ζ1 ⊎ζ2;∆, Γ ⇒ A◦B 45. … view at source ↗
Figure 4.10
Figure 4.10. Figure 4.10: Binary synthetic multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p035_4_10.png] view at source ↗
Figure 4.11
Figure 4.11. Figure 4.11: Limited contraction and limited expansion [PITH_FULL_IMAGE:figures/full_fig_p036_4_11.png] view at source ↗
Figure 4.12
Figure 4.12. Figure 4.12: Difference rules The difference operator is a means to define exceptions. For example, to avoid generation of* the extremely man with an intensifier type (CN/CN)/(CN/CN) applying to the empty string of type CN/CN, we can instead assign an intensifier type (CN/CN)/((CN/CN) − I) excluding the empty string [PITH_FULL_IMAGE:figures/full_fig_p036_4_12.png] view at source ↗
Figure 6.1
Figure 6.1. Figure 6.1: Types of GDL [PITH_FULL_IMAGE:figures/full_fig_p045_6_1.png] view at source ↗
Figure 7.1
Figure 7.1. Figure 7.1: Interpretation of the semantic representation language [PITH_FULL_IMAGE:figures/full_fig_p048_7_1.png] view at source ↗
Figure 7.2
Figure 7.2. Figure 7.2: Semantic conversion laws [PITH_FULL_IMAGE:figures/full_fig_p049_7_2.png] view at source ↗
Figure 7.3
Figure 7.3. Figure 7.3: Semantic commuting conversion laws [PITH_FULL_IMAGE:figures/full_fig_p050_7_3.png] view at source ↗
Figure 8.1
Figure 8.1. Figure 8.1: Continuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p053_8_1.png] view at source ↗
Figure 8.2
Figure 8.2. Figure 8.2: Discontinuous multiplicative rules When the value of the k subscript is one it may be omitted, i.e. it defaults to one. Circumfixation, ↑, is exemplified by a discontinuous idiom assignment gives+1+the+cold+shoulder: (N\S)↑N:shun for Mary gives the man the cold shoulder: S: ((shun (ι man)) m): (39) CN ⇒ CN N ⇒ N /L N/CN, CN ⇒ N N ⇒ N S ⇒ S \L N, N\S ⇒ S ↑L N, (N\S)↑N{N/CN,CN} ⇒ S Infixation, ↓, and extra… view at source ↗
Figure 8.3
Figure 8.3. Figure 8.3: Additive rules For example the additive conjunction & can be used for rice: N&CN: ((gen rice),rice) as in rice grows: S: (grow (gen rice)) and the rice grows: S: (grow (ι rice)): (43) N ⇒ N &L1 N&CN ⇒ N S ⇒ S \L N&CN, N\S ⇒ S N/CN, CN, N\S ⇒ S &L2 N/CN, N&CN, N\S ⇒ S The additive disjunction ⊕ can be used for is: (N\S)/(N⊕(CN/CN)): λxλyx → z.[z = y]; w.((w λu[y = u]) y) as in Tully is Cicero: S: [t = c] … view at source ↗
Figure 8.4
Figure 8.4. Figure 8.4: Quantifier rules; † indicates that there is no a in the conclusion For example, we can generalise over singular and plural number in sheep: V nCNn: λn(n sheep) for the sheep grazes: S: (graze (ι (sg sheep))) and the sheep graze: S: (graze (ι (pl sheep))): (45) CNsg ⇒ CNsg V ^ L nCNn ⇒ CNsg CNpl ⇒ CNpl V ^ L nCNn ⇒ CNpl And we can express a past, present or future tense finite sentence complement: said: (… view at source ↗
Figure 8.5
Figure 8.5. Figure 8.5: Normal modality rules; 2×/+3marks a structure all the types of which have principal connective a box/diamond an assignment believes: 2((N\S)/2S): believe with a modality outermost since the word, like all words, has a sense, and its sentential complement is an intensional domain, but its subject is not.4 8.8 Bracket modalities The bracket modalities {[ ]−1 , ⟨⟩} of [PITH_FULL_IMAGE:figures/full_fig_p057… view at source ↗
Figure 8.6
Figure 8.6. Figure 8.6: Bracket modality rules walk for the sentential subject condition, and before: [ ]−1 (VP\VP)/VP: λxλyλz((before (x z)) (y z)) for the adverbial island constraint, which are weak islands, and can contain parasitic gaps, see the next section; for a strong island such as a coordinate structure, which cannot contain a parasitic gap, we define doubly bracketed strong islands — and: (S\[ ]−1 [ ]−1S)/S: λxλy[y ∧… view at source ↗
Figure 8.7
Figure 8.7. Figure 8.7: Exponential rules 8.10 Semantically inactive connectives The semantically inactive multiplicatives {, ⊸, , , G#, H#, , ⊸ , ⊸,  , G# , H# } of Figures 8.8 and 8.9, Morrill and Valent´ın (2014[72]), can be used for the subcategorization without vacuous lambda abstraction of semantically void elements. For example: (48) a. rains: it⊸S:rain for it rains: S:rain b. give: (N\S)/(NH#the + cold+shoulder):sh… view at source ↗
Figure 8.8
Figure 8.8. Figure 8.8: Semantically inactive continuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p060_8_8.png] view at source ↗
Figure 8.9
Figure 8.9. Figure 8.9: Semantically inactive discontinuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p061_8_9.png] view at source ↗
Figure 8.10
Figure 8.10. Figure 8.10: Semantically inactive additive rules 33. Ξ⟨ −−−−→ A[t/v]: x⟩ ⇒ B:ψ ∀L Ξ⟨ −−−→∀vA: x⟩ ⇒ B:ψ Ξ ⇒ A[a/v]: ϕ ∀R † Ξ ⇒ ∀vA: ϕ 34. Ξ⟨ −−−−−→ A[a/v]: x⟩ ⇒ B:ψ ∃L † Ξ⟨ −−−→∃vA: x⟩ ⇒ B:ψ Ξ ⇒ A[t/v]: ϕ ∃R Ξ ⇒ ∃vA: ϕ [PITH_FULL_IMAGE:figures/full_fig_p061_8_10.png] view at source ↗
Figure 8.11
Figure 8.11. Figure 8.11: Semantically inactive quantifier rules; † indicates that there is no a in the conclusion [PITH_FULL_IMAGE:figures/full_fig_p061_8_11.png] view at source ↗
Figure 8.12
Figure 8.12. Figure 8.12: Semantically inactive normal modality rules; [PITH_FULL_IMAGE:figures/full_fig_p062_8_12.png] view at source ↗
Figure 8.13
Figure 8.13. Figure 8.13: Deterministic synthetic multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p062_8_13.png] view at source ↗
Figure 8.14
Figure 8.14. Figure 8.14: Non-deterministic synthetic multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p063_8_14.png] view at source ↗
Figure 8.15
Figure 8.15. Figure 8.15: Limited contraction and limited expansion rules [PITH_FULL_IMAGE:figures/full_fig_p064_8_15.png] view at source ↗
Figure 9.1
Figure 9.1. Figure 9.1: Spurious ambiguity 9.1.2 Spurious ambiguity in CFG and CG Consider the following production rules: (53) S → Q VP Q → Det CN VP → TV N These generate the following sequential rewriting derivations: (54) S → Q VP → Det CN VP → Det CN TV N S → Q VP → Q TV N → Det CN TV N These sequential rewriting derivations correspond to the same parellelised parse structure: (55) S Q VP Det CN TV N And they correspond to… view at source ↗
Figure 9.2
Figure 9.2. Figure 9.2: Proof net 9.2 Focalisation for FDL The discipline of focalisation depends fundamentally on the distinction between invertible and noninvert￾ible rules. A rule is invertible (or reversable) if its premises are derivable from its conclusion — for example \R and ⊕L — otherwise it is noninvertible. In focalisation situated (antecedent, input, • / succedent, output, ◦ ) connectives are classified as of negati… view at source ↗
Figure 9.3
Figure 9.3. Figure 9.3: Asynchronous multiplicative rules 9. Ξ ⇒ A: ϕ Ξ ⇒ B:ψ &R Ξ ⇒ A&B: (ϕ, ψ) 10. Ξ⟨ −→A: x⟩ ⇒ C: χ1 Ξ⟨ −→B: y⟩ ⇒ C: χ2 ⊕L Ξ⟨ −−−→A⊕B: z⟩ ⇒ C: z−>x.χ1; y.χ2 [PITH_FULL_IMAGE:figures/full_fig_p072_9_3.png] view at source ↗
Figure 9.4
Figure 9.4. Figure 9.4: Asynchronous additive rules 11. Ξ ⇒ A[a/v]: ϕ V R † Ξ ⇒ ^ vA: λvϕ 12. Ξ⟨ −−−−−→ A[a/v]: x⟩ ⇒ B:ψ W L † Ξ⟨ −−−−−→ _ vA: z⟩ ⇒ B:ψ{π2z/x} [PITH_FULL_IMAGE:figures/full_fig_p072_9_4.png] view at source ↗
Figure 9.5
Figure 9.5. Figure 9.5: Asynchronous quantifier rules, where † indicates that there is no a in the conclusion [PITH_FULL_IMAGE:figures/full_fig_p072_9_5.png] view at source ↗
Figure 9.6
Figure 9.6. Figure 9.6: Asynchronous normal modality rules; 2×/+3 marks a structure all the types of which have principal connective a box/diamond 15. [Ξ] ⇒ A: ϕ [ ]−1R Ξ ⇒ [ ]−1A: ϕ 16. Ξ⟨[ −→A: x]⟩ ⇒ B:ψ ⟨⟩L Ξ⟨ −−→⟨⟩A: x⟩ ⇒ B:ψ [PITH_FULL_IMAGE:figures/full_fig_p073_9_6.png] view at source ↗
Figure 9.7
Figure 9.7. Figure 9.7: Asynchronous bracket modality rules 17. ζ; Λ ⇒ A:ϕ !R ζ; Λ ⇒ !A:ϕ Ξ(ζ⊎ {A: x}; Γ1, Γ2) ⇒ B:ψ !P Ξ(ζ; Γ1, !A: x, Γ2) ⇒ B:ψ [PITH_FULL_IMAGE:figures/full_fig_p073_9_7.png] view at source ↗
Figure 9.8
Figure 9.8. Figure 9.8: Asynchronous subexponential rules [PITH_FULL_IMAGE:figures/full_fig_p073_9_8.png] view at source ↗
Figure 9.9
Figure 9.9. Figure 9.9: Asynchronous semantically inactive continuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p074_9_9.png] view at source ↗
Figure 9.10
Figure 9.10. Figure 9.10: Asynchronous semantically inactive discontinuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p074_9_10.png] view at source ↗
Figure 9.11
Figure 9.11. Figure 9.11: Asynchronous semantically inactive additive rules [PITH_FULL_IMAGE:figures/full_fig_p075_9_11.png] view at source ↗
Figure 9.12
Figure 9.12. Figure 9.12: Asynchronous semantically inactive quantifier rules, where [PITH_FULL_IMAGE:figures/full_fig_p075_9_12.png] view at source ↗
Figure 9.13
Figure 9.13. Figure 9.13: Asynchronous semantically inactive normal modality rules; [PITH_FULL_IMAGE:figures/full_fig_p075_9_13.png] view at source ↗
Figure 9.14
Figure 9.14. Figure 9.14: Asynchronous deterministic synthetic multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p076_9_14.png] view at source ↗
Figure 9.15
Figure 9.15. Figure 9.15: Asynchronous non-deterministic synthetic multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p076_9_15.png] view at source ↗
Figure 9.16
Figure 9.16. Figure 9.16: Left synchronous continuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p077_9_16.png] view at source ↗
Figure 9.17
Figure 9.17. Figure 9.17: Left synchronous discontinuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p077_9_17.png] view at source ↗
Figure 9.18
Figure 9.18. Figure 9.18: Left synchronous additive rules 11. Ξ⟨ −−−−−−→ Q[t/v] : x⟩ ⇒ B:ψ V L Ξ⟨ −−−−−→ V vQ : z⟩ ⇒ B:ψ{(z t)/x} Ξ⟨ −−−−−→ M[t/v]: x⟩ ⇒ B:ψ V L Ξ⟨ −−−−−−→ V vM : z⟩ ⇒ B:ψ{(z t)/x} [PITH_FULL_IMAGE:figures/full_fig_p078_9_18.png] view at source ↗
Figure 9.19
Figure 9.19. Figure 9.19: Left synchronous quantifier rules 13. Ξ⟨ −−→ Q : x⟩ ⇒ B:ψ 2L Ξ⟨ −−−→ 2Q : z⟩ ⇒ B:ψ{ ∨ z/x} Ξ⟨ −→M: x⟩ ⇒ B:ψ 2L Ξ⟨ −−−−→ 2M : z⟩ ⇒ B:ψ{ ∨ z/x} [PITH_FULL_IMAGE:figures/full_fig_p078_9_19.png] view at source ↗
Figure 9.20
Figure 9.20. Figure 9.20: Left synchronous normal modality rules 15. Ξ⟨ −−→ Q : x⟩ ⇒ B:ψ [ ]−1L Ξ⟨[ −−−−−−→ [ ]−1Q : x]⟩ ⇒ B:ψ Ξ⟨ −→M: x⟩ ⇒ B:ψ [ ]−1L Ξ⟨[ −−−−−−→ [ ]−1M : x]⟩ ⇒ B:ψ [PITH_FULL_IMAGE:figures/full_fig_p078_9_20.png] view at source ↗
Figure 9.21
Figure 9.21. Figure 9.21: Left synchronous bracket modality rules [PITH_FULL_IMAGE:figures/full_fig_p078_9_21.png] view at source ↗
Figure 9.22
Figure 9.22. Figure 9.22: Left synchronous semantically inactive continuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p079_9_22.png] view at source ↗
Figure 9.23
Figure 9.23. Figure 9.23: Left synchronous semantically inactive discontinuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p080_9_23.png] view at source ↗
Figure 9.24
Figure 9.24. Figure 9.24: Semantically inactive additives [PITH_FULL_IMAGE:figures/full_fig_p080_9_24.png] view at source ↗
Figure 9.25
Figure 9.25. Figure 9.25: Left synchronous semantically inactive quantifier rules [PITH_FULL_IMAGE:figures/full_fig_p081_9_25.png] view at source ↗
Figure 9.26
Figure 9.26. Figure 9.26: Left synchronous semantically inactive normal modality rules [PITH_FULL_IMAGE:figures/full_fig_p081_9_26.png] view at source ↗
Figure 9.27
Figure 9.27. Figure 9.27: Left synchronous deterministic synthetic multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p082_9_27.png] view at source ↗
Figure 9.28
Figure 9.28. Figure 9.28: Left synchronous continuous non-deterministic synthetic multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p082_9_28.png] view at source ↗
Figure 9.29
Figure 9.29. Figure 9.29: Left synchronous discontinuous non-deterministic synthetic multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p083_9_29.png] view at source ↗
Figure 9.30
Figure 9.30. Figure 9.30: Synchronous exponential stoup rules 9.6 Synchronous right rules (63) −→ id, if atomic focus(out, P) P: x ⇒ P : x 9.6.1 Primary connectives 3. ζ; Γ1 ⇒ P1 : ϕ ζ′ ; Γ2 ⇒ P2 :ψ •R ζ⊎ζ ′ ; Γ1, Γ2 ⇒ P1•P2 : (ϕ, ψ) ζ; Γ1 ⇒ P : ϕ ζ′ ; Γ2 ⇒ N:ψ •R ζ⊎ζ ′ ; Γ1, Γ2 ⇒ P•N : (ϕ, ψ) ζ; Γ1 ⇒ N: ϕ ζ′ ; Γ2 ⇒ P :ψ •R ζ⊎ζ ′ ; Γ1, Γ2 ⇒ N•P : (ϕ, ψ) ζ; Γ1 ⇒ N1: ϕ ζ′ ; Γ2 ⇒ N2:ψ •R ζ⊎ζ ′ ; Γ1, Γ2 ⇒ N1•N2 : (ϕ, ψ) 4. IR Λ ⇒ I … view at source ↗
Figure 9.31
Figure 9.31. Figure 9.31: Right synchronous continuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p084_9_31.png] view at source ↗
Figure 9.32
Figure 9.32. Figure 9.32: Right synchronous discontinuous multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p084_9_32.png] view at source ↗
Figure 9.33
Figure 9.33. Figure 9.33: Right synchronous additive rules 12. Ξ ⇒ P[t/v] : ϕ W R Ξ ⇒ W vP : (t, ϕ) Ξ ⇒ N[t/v]: ϕ W R Ξ ⇒ W vN : (t, ϕ) [PITH_FULL_IMAGE:figures/full_fig_p085_9_33.png] view at source ↗
Figure 9.34
Figure 9.34. Figure 9.34: Right synchronous quantifier rules 14. Ξ ⇒ P : ϕ 3R Ξ ⇒ 3P : ∩ϕ Ξ ⇒ N: ϕ 3R Ξ ⇒ 3N : ∩ϕ [PITH_FULL_IMAGE:figures/full_fig_p085_9_34.png] view at source ↗
Figure 9.35
Figure 9.35. Figure 9.35: Right synchronous normal modality rules 16. Ξ ⇒ P : ϕ ⟨⟩R [Ξ] ⇒ ⟨⟩P : ϕ Ξ ⇒ N: ϕ ⟨⟩R [Ξ] ⇒ ⟨⟩N : ϕ [PITH_FULL_IMAGE:figures/full_fig_p085_9_35.png] view at source ↗
Figure 9.36
Figure 9.36. Figure 9.36: Right synchronous bracket modality rules [PITH_FULL_IMAGE:figures/full_fig_p085_9_36.png] view at source ↗
Figure 9.37
Figure 9.37. Figure 9.37: Right synchronous subexponential rules [PITH_FULL_IMAGE:figures/full_fig_p085_9_37.png] view at source ↗
Figure 9.38
Figure 9.38. Figure 9.38: Right synchronous rules for semantically inactive continuous multiplicatives [PITH_FULL_IMAGE:figures/full_fig_p086_9_38.png] view at source ↗
Figure 9.39
Figure 9.39. Figure 9.39: Right synchronous rules for semantically inactive discontinuous multiplicatives [PITH_FULL_IMAGE:figures/full_fig_p086_9_39.png] view at source ↗
Figure 9.40
Figure 9.40. Figure 9.40: Right synchronous semantically inactive additive rules [PITH_FULL_IMAGE:figures/full_fig_p087_9_40.png] view at source ↗
Figure 9.41
Figure 9.41. Figure 9.41: Right synchronous semantically inactive quantifier rules [PITH_FULL_IMAGE:figures/full_fig_p087_9_41.png] view at source ↗
Figure 9.42
Figure 9.42. Figure 9.42: Right synchronous semantically inactive normal modality rules [PITH_FULL_IMAGE:figures/full_fig_p087_9_42.png] view at source ↗
Figure 9.43
Figure 9.43. Figure 9.43: Right synchronous deterministic synthetic multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p088_9_43.png] view at source ↗
Figure 9.44
Figure 9.44. Figure 9.44: Right synchronous continuous non-deterministic derived multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p088_9_44.png] view at source ↗
Figure 9.45
Figure 9.45. Figure 9.45: Right synchronous discontinuous non-deterministic synthetic multiplicative rules [PITH_FULL_IMAGE:figures/full_fig_p088_9_45.png] view at source ↗
Figure 9.46
Figure 9.46. Figure 9.46: Right synchronous rules for limited contraction [PITH_FULL_IMAGE:figures/full_fig_p089_9_46.png] view at source ↗
Figure 9.47
Figure 9.47. Figure 9.47: Right synchronous rules for limited expansion [PITH_FULL_IMAGE:figures/full_fig_p089_9_47.png] view at source ↗
Figure 9.48
Figure 9.48. Figure 9.48: Right synchronous rules for difference 9.7 Completeness of focalisation for DA We shall be dealing with three systems: the displacement calculus DA with sequents notated ∆ ⇒ A, the weakly focalised displacement calculus with additives DAfoc with sequents notated ∆=⇒wA, and the strongly focalised displacement calculus with additives DAFoc with sequents notated ∆=⇒A. Sequents of both DAfoc and DAFoc may c… view at source ↗
Figure 10.1
Figure 10.1. Figure 10.1: Rules for the categorial logic fragment [PITH_FULL_IMAGE:figures/full_fig_p104_10_1.png] view at source ↗
Figure 12.1
Figure 12.1. Figure 12.1: Derivation for John loves Mary (As we have said, this elucidation is not exactly how CatLog2 extracts semantics; CatLog2 uses unification and instantiation of metavariables to deliver in a single pass the unevaluated semantics of the upwards and downward phases, and then normalises.) By way of a second example, the following is a simple transitive sentence: (136) [john]+loves+mary : S f Lexical lookup y… view at source ↗
Figure 12.2
Figure 12.2. Figure 12.2: Derivation for John thinks Mary walks Nt(s(m)) ⇒ Nt(s(m)) ■L ■Nt(s(m)) ⇒ Nt(s(m)) ∃R ■Nt(s(m)) ⇒ ∃aNa Nt(s(n)) ⇒ Nt(s(n)) &L Nt(s(n))&CNs(n) ⇒ Nt(s(n)) 2L □(Nt(s(n))&CNs(n)) ⇒ Nt(s(n)) ∃R □(Nt(s(n))&CNs(n)) ⇒ ∃aNa •R ■Nt(s(m)),□(Nt(s(n))&CNs(n)) ⇒ ∃aNa•∃aNa Nt(s(f)) ⇒ Nt(s(f)) ■L ■Nt(s(f)) ⇒ Nt(s(f)) ∃R ■Nt(s(f)) ⇒ ∃gNt(s(g)) ⟨⟩R [■Nt(s(f))] ⇒ ⟨⟩∃gNt(s(g)) S f ⇒ S f \L [■Nt(s(f))], ⟨⟩∃gNt(s(g))\S f ⇒ S … view at source ↗
Figure 12.3
Figure 12.3. Figure 12.3: Derivation for Mary buys John coffee Lexical lookup is as follows; note the use of product (multiplicative conjunction) for the ditransitive verb, and the use of additive conjunction for the polymorphism of the mass noun coffee which can appear either as a bare nominal or with an article: (143) [■Nt(s(f)) : m],□((⟨⟩∃gNt(s(g))\S f)/(∃aNa•∃aNa)) : ˆλAλB(Pres (((ˇbuy π1A) π2A) B)), ■Nt(s(m)) : j,□(Nt(s(n))… view at source ↗
Figure 12.4
Figure 12.4. Figure 12.4: Derivation for The man walks (146) [■∀n(Nt(n)/CNn) : ι,□CNs(m) : man],□(⟨⟩∃gNt(s(g))\S f) : ˆλA(Pres (ˇwalk A)) ⇒ S f There is the derivation given in [PITH_FULL_IMAGE:figures/full_fig_p128_12_4.png] view at source ↗
Figure 12.5
Figure 12.5. Figure 12.5: Derivation for John walks from Edinburgh [PITH_FULL_IMAGE:figures/full_fig_p129_12_5.png] view at source ↗
Figure 12.6
Figure 12.6. Figure 12.6: Derivation for The man from Edinburgh walks [PITH_FULL_IMAGE:figures/full_fig_p130_12_6.png] view at source ↗
Figure 12.7
Figure 12.7. Figure 12.7: Derivation for Bond is 007 (153) (Pres (ˇwalk (ι ((ˇfromadn e) ˇman)))) The last two initial examples involve the copula with nominal and (intersective) adjectival complemen￾tation respectively. We consider first the nominal case: (154) [bond]+is+007 : S f Lexical lookup inserts a single argument-polymorphic copula type, which uses both semantically active and semantically inactive additive disjunction:… view at source ↗
Figure 12.8
Figure 12.8. Figure 12.8: Derivation for Bond is teetotal , [PITH_FULL_IMAGE:figures/full_fig_p132_12_8.png] view at source ↗
Figure 13.1
Figure 13.1. Figure 13.1: The mini-corpus of the Montague test (164) [■∀g(∀f((S f ↑Nt(s(g)))↓S f)/CNs(g)) : λAλB∀C[(A C) → (B C)],□CNs(m) : man], □(⟨⟩∃gNt(s(g))\ S f) : ˆλD(Pres (ˇtalk D)) ⇒ S f The semantic modality of the quantifier is inactive since its semantics is purely logical. Within its modality the type for the quantifier is a functor seeking a count noun to its right; the feature variable g transmits gender from the c… view at source ↗
Figure 13.2
Figure 13.2. Figure 13.2: Lexicon for the Montague test [PITH_FULL_IMAGE:figures/full_fig_p135_13_2.png] view at source ↗
Figure 16.1
Figure 16.1. Figure 16.1: Derivation for man that walks (339) [■∀n(Nt(n)/CNn) : ι,□CNs(m) : man,[[■∀n([]−1 []−1 (CNn\CNn)/ ■((⟨⟩Nt(n)⊓!■Nt(n))\S f)) : λAλBλC[(B C) ∧ (A C)],[■Nt(s(f)) : m], □((⟨⟩∃gNt(s(g))\S f)/∃aNa) : ˆλDλE(Pres ((ˇlove D) E))]]],□(⟨⟩∃gNt(s(g))\S f) : ˆλF(Pres (ˇwalk F)) ⇒ S f There is the derivation given in [PITH_FULL_IMAGE:figures/full_fig_p219_16_1.png] view at source ↗
Figure 16.2
Figure 16.2. Figure 16.2: Derivation for The man that Mary loves walks , [PITH_FULL_IMAGE:figures/full_fig_p220_16_2.png] view at source ↗
Figure 16.3
Figure 16.3. Figure 16.3: Derivation for The man that John thinks Mary loves walks [PITH_FULL_IMAGE:figures/full_fig_p222_16_3.png] view at source ↗
Figure 16.4
Figure 16.4. Figure 16.4: Derivation of medial relativisation: man that Mary likes today [PITH_FULL_IMAGE:figures/full_fig_p223_16_4.png] view at source ↗
Figure 16.5
Figure 16.5. Figure 16.5: Derivation of [PITH_FULL_IMAGE:figures/full_fig_p225_16_5.png] view at source ↗
Figure 16.6
Figure 16.6. Figure 16.6: Derivation for paper that John filed without reading , [PITH_FULL_IMAGE:figures/full_fig_p227_16_6.png] view at source ↗
Figure 16.7
Figure 16.7. Figure 16.7: Auxiliary derivations for paper that the editor of filed without reading , [PITH_FULL_IMAGE:figures/full_fig_p228_16_7.png] view at source ↗
Figure 16.8
Figure 16.8. Figure 16.8: Main derivation for paper that the editor of filed without reading [PITH_FULL_IMAGE:figures/full_fig_p229_16_8.png] view at source ↗
Figure 17.1
Figure 17.1. Figure 17.1: Determiner gapping [PITH_FULL_IMAGE:figures/full_fig_p244_17_1.png] view at source ↗
Figure 17.2
Figure 17.2. Figure 17.2: Discontinuous determiner gapping [PITH_FULL_IMAGE:figures/full_fig_p246_17_2.png] view at source ↗
read the original abstract

In this book we promote logical computational linguistics as opposed to statistical computational linguistics. In particular, we provide a logical semantic interface. This book assembles more than twenty years of research work on type logical grammar, and adds new ideas and material. Chains of statistical dependencies of less than one hundred per cent confidence tend monotonically to zero. Chains of logical dependencies of any length maintain one hundred per cent confidence end to end. We aspire to enable perfect syntactic and semantic processing in life-critical NLP applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript promotes logical computational linguistics, based on type-logical grammar, as an alternative to statistical methods. It assembles more than twenty years of prior research on type-logical grammar, introduces a logical semantic interface, and advances the claim that statistical dependency chains lose confidence monotonically while logical dependency chains of arbitrary length preserve 100% end-to-end confidence. The work expresses the goal of enabling perfect syntactic and semantic processing for life-critical NLP applications.

Significance. If the central claim of gap-free, 100% reliable logical processing were supported by completeness results and coverage evidence, the contribution would be substantial for high-stakes NLP domains by supplying a sound, non-probabilistic foundation. The compilation of extensive type-logical grammar literature is a clear strength and provides a useful reference point, but the absence of new formal derivations, completeness proofs, or empirical validation on unrestricted text limits the immediate significance.

major comments (2)
  1. [Abstract] Abstract: The assertion that logical dependency chains 'maintain one hundred per cent confidence end to end' is load-bearing for the central contrast with statistical methods, yet no derivation, completeness theorem, or coverage argument is supplied to establish that type-logical grammar achieves exhaustive, unambiguous analysis of arbitrary natural-language input without statistical fallback.
  2. [Abstract] Abstract and assembled research summary: The manuscript does not address or provide metrics for phenomena historically requiring extensions in categorial grammar (long-distance dependencies, coordination, scope ambiguities, idioms), which directly challenges the presupposition of gap-free coverage needed for the monotonic 100% confidence claim to transfer from deductive logic to real text.
minor comments (1)
  1. The distinction between previously published results and the 'new ideas and material' added in this compilation should be made explicit, for example by a dedicated section or table listing novel contributions.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the constructive review. We address each major comment below and will revise the manuscript to provide clearer references to foundational results and explicit discussion of linguistic phenomena.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The assertion that logical dependency chains 'maintain one hundred per cent confidence end to end' is load-bearing for the central contrast with statistical methods, yet no derivation, completeness theorem, or coverage argument is supplied to establish that type-logical grammar achieves exhaustive, unambiguous analysis of arbitrary natural-language input without statistical fallback.

    Authors: The 100% confidence claim derives from the soundness and completeness properties of the type-logical systems compiled in the book, which have been established in the referenced literature over twenty years. The logical semantic interface ensures that syntactic derivations map directly to semantic interpretations via deduction, without probabilistic degradation. We agree the abstract would be strengthened by explicit pointers to these results. In the revised version we will add citations to key completeness theorems for the Lambek calculus and its multimodal extensions, along with a brief clarification of the coverage scope for the fragments treated. revision: yes

  2. Referee: [Abstract] Abstract and assembled research summary: The manuscript does not address or provide metrics for phenomena historically requiring extensions in categorial grammar (long-distance dependencies, coordination, scope ambiguities, idioms), which directly challenges the presupposition of gap-free coverage needed for the monotonic 100% confidence claim to transfer from deductive logic to real text.

    Authors: The book assembles prior work on multimodal type-logical grammar that handles long-distance dependencies and coordination via structural modalities, scope ambiguities through higher-order types, and idioms as lexical logical entries. These treatments preserve deductive certainty rather than relying on statistical metrics. We acknowledge the summary sections would benefit from more explicit discussion. In revision we will expand the abstract and introductory summary to reference these mechanisms and how they maintain end-to-end logical confidence without fallback. revision: yes

Circularity Check

1 steps flagged

100% logical chain confidence reduces to definitional soundness once exhaustive type-logical coverage is presupposed

specific steps
  1. self definitional [Abstract]
    "Chains of logical dependencies of any length maintain one hundred per cent confidence end to end."

    The sentence follows immediately from the definition of logical soundness. Its application to NLP requires that type-logical grammar supplies exhaustive, gap-free derivations for arbitrary natural-language input, an assumption the manuscript neither proves nor quantifies.

full rationale

The manuscript states the central contrast between statistical and logical dependency chains directly in the abstract and introduction. The logical claim holds by the standard definition of deductive soundness (truth preservation at each step implies truth preservation end-to-end) provided every input receives a complete, unambiguous type-logical derivation. The paper assembles two decades of prior type-logical grammar results but supplies no new completeness theorem, no coverage statistics on unrestricted text, and no treatment of known coverage gaps (long-distance dependencies, coordination, scope, idioms). Consequently the 100% end-to-end guarantee is true by construction once the coverage assumption is granted, rather than independently demonstrated.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that a type-logical interface can be made complete for natural language without statistical supplementation.

axioms (1)
  • domain assumption Type logical grammar supplies a sound and complete semantic interface for all natural-language constructions.
    Invoked when the authors assert that logical chains maintain 100% confidence end to end.

pith-pipeline@v0.9.0 · 5362 in / 1260 out tokens · 38313 ms · 2026-05-10T06:27:26.770550+00:00 · methodology

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Works this paper leans on

94 extracted references · 94 canonical work pages

  1. [1]

    V . M. Abrusci. Phase semantics and sequent calculus for pure noncommutative classical linear propo- sitional logic.The Journal of Symbolic logic, 56(4), 1991

    work page 1991

  2. [2]

    Michele Abrusci

    V . Michele Abrusci. A comparison between Lambek syntactic calculus and intuitionistic linear propo- sitional logic.Mathematical Logic Quarterly, 36(1):666–777, 1990

    work page 1990

  3. [3]

    Michele Abrusci

    V . Michele Abrusci. Non-commutative intuitionistic linear propositional logic.Zeitschrift f ¨ur Math- ematische Logik und Grundlagen der Mathematik, 36(4):297–318, 1990

    work page 1990

  4. [4]

    Die syntaktische Konnexit ¨at.Studia Philosphica, 1:1–27, 1935

    Kazimierz Ajdukiewicz. Die syntaktische Konnexit ¨at.Studia Philosphica, 1:1–27, 1935. Translated in Storrs McCall, editor, 1967,Polish Logic: 1920–1939, Oxford University Press, Oxford, 207–231

    work page 1935

  5. [5]

    J. M. Andreoli. Logic programming with focusing in linear logic.Journal of Logic and Computation, 2(3):297–347, 1992

    work page 1992

  6. [6]

    Bar-Hillel, C

    Y . Bar-Hillel, C. Gaifman, and E. Shamir. On categorial and phrase structure grammars.Bulletin of the Research Council of Israel, 9F:1–16, 1960. Also in Yehoshua Bar-Hillel (1964)Language and Information: Selected Essays on their Theory and Application, Addison-Wesley Publishing Company, Reading, Massachusetts, Ch. 8, 99–115

    work page 1960

  7. [7]

    A quasi-arithmetical notation for syntactic description.Language, 29:47–58, 1953

    Yehoshua Bar-Hillel. A quasi-arithmetical notation for syntactic description.Language, 29:47–58, 1953

    work page 1953

  8. [8]

    Oxford University Press, New York and Oxford, 2015

    Chris Barker and Chung-chieh Shan.Continuations and Natural Language. Oxford University Press, New York and Oxford, 2015

    work page 2015

  9. [9]

    Proof Figures and Structural Operators for Categorial Grammar

    Guy Barry, Mark Hepple, Neil Leslie, and Glyn Morrill. Proof Figures and Structural Operators for Categorial Grammar. InProceedings of the Fifth Conference of the European Chapter of the Association for Computational Linguistics, Berlin, 1991

    work page 1991

  10. [10]

    The Coordination of Unlike Categories.Language, 72(3):579–616, 1996

    Samuel Bayer. The Coordination of Unlike Categories.Language, 72(3):579–616, 1996

    work page 1996

  11. [11]

    MIT Press, Cambridge, MA, 1997

    Bob Carpenter.Type-Logical Semantics. MIT Press, Cambridge, MA, 1997

    work page 1997

  12. [12]

    PhD thesis, Carnegie Mellon University, Pittsburgh, PA, USA, 2006

    Kaustuv Chaudhuri.The Focused Inverse Method for Linear Logic. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, USA, 2006. AAI3248489

    work page 2006

  13. [13]

    N. Chomsky. Conditions on transformations. In S. Anderson and P. Kiparsky, editors,A Festschrift for Morris Halle, pages 232–286. Holt, Rinehart and Winston, New York, 1973

    work page 1973

  14. [14]

    Chomsky.The minimalist program

    N. Chomsky.The minimalist program. MIT Press, 1996

    work page 1996

  15. [15]

    Mouton, The Hague, 1957

    Noam Chomsky.Syntactic Structures. Mouton, The Hague, 1957

    work page 1957

  16. [16]

    Curry and Robert Feys.Combinatory Logic, volume I

    Haskell B. Curry and Robert Feys.Combinatory Logic, volume I. North-Holland, Amsterdam, 1958

    work page 1958

  17. [17]

    Limits to attention: A cognitive theory of island phenomena.Cognitive Linguistics, 2(1):1–63, 1991

    Paul Deane. Limits to attention: A cognitive theory of island phenomena.Cognitive Linguistics, 2(1):1–63, 1991. 253 254 BIBLIOGRAPHY

    work page 1991

  18. [18]

    Dowty, Robert E

    David R. Dowty, Robert E. Wall, and Stanley Peters.Introduction to Montague Semantics, volume 11 ofSynthese Language Library. D. Reidel, Dordrecht, 1981

    work page 1981

  19. [19]

    PhD thesis, Universitat Polit `ecnica de Catalunya, Barcelona, 2010

    Mario Fadda.Geometry of Grammar: Exercises in Lambek Style. PhD thesis, Universitat Polit `ecnica de Catalunya, Barcelona, 2010

    work page 2010

  20. [20]

    Optimality of syntactic dependency distances.Physical Review,105(014308), 2022

    Ferrer-i-Cancho, Ramon, Carlos G ´omez-Rodr´ıguez, Juan Luis Esteban, and Llu ´ıs Alemany-Puig. Optimality of syntactic dependency distances.Physical Review,105(014308), 2022

    work page 2022

  21. [21]

    Basil Blackwell, Oxford, 1985

    Gerald Gazdar, Ewan Klein, Geoffrey Pullum, and Ivan Sag.Generalized Phrase Structure Grammar. Basil Blackwell, Oxford, 1985

    work page 1985

  22. [22]

    Linear logic.Theoretical Computer Science, 50:1–102, 1987

    Jean-Yves Girard. Linear logic.Theoretical Computer Science, 50:1–102, 1987

    work page 1987

  23. [23]

    European Mathematical Society, Z ¨urich, 2011

    Jean-Yves Girard.The Blind Spot. European Mathematical Society, Z ¨urich, 2011

    work page 2011

  24. [24]

    Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, Cambridge, 1989

    Jean-Yves Girard, Paul Taylor, and Yves Lafont.Proofs and Types, volume 7. Cambridge Tracts in Theoretical Computer Science, Cambridge University Press, Cambridge, 1989

    work page 1989

  25. [25]

    Hendriks.Studied flexibility

    H. Hendriks.Studied flexibility. Categories and types in syntax and semantics. PhD thesis, Universiteit van Amsterdam, ILLC, Amsterdam, 1993

    work page 1993

  26. [26]

    PhD thesis, Rijksuniversiteit Groningen, Groningen, 1995

    Petra Hendriks.Comparatives and Categorial Grammar. PhD thesis, Rijksuniversiteit Groningen, Groningen, 1995

    work page 1995

  27. [27]

    PhD thesis, University of Edinburgh, 1990

    Mark Hepple.The Grammar and Processing of Order and Dependency. PhD thesis, University of Edinburgh, 1990

    work page 1990

  28. [28]

    Philip Hofmeister and Ivan A. Sag. Cognitive constraints and island effects.Language, 86(2):366– 415, 2010

    work page 2010

  29. [29]

    Springer, Dordrecht, 2005

    Gerhard J ¨ager.Anaphora and Type Logical Grammar, volume 24 ofTrends in Logic – Studia Logica Library. Springer, Dordrecht, 2005

    work page 2005

  30. [30]

    Review of Mark Steedman, The Syntactic Process.Journal of Linguistics, 38:684–690, 2002

    Martin Jansche and Shravan Vasishth. Review of Mark Steedman, The Syntactic Process.Journal of Linguistics, 38:684–690, 2002

    work page 2002

  31. [31]

    Johnson and S

    M. Johnson and S. Bayer. Features and Agreement in Lambek Categorial Grammar. In G. Morrill and R.T.E. Oehrle, editors,Proceedings of the 1995 Conference on Formal Grammar, Barcelona, 1995. ESSLLI

    work page 1995

  32. [32]

    Kanazawa

    M. Kanazawa. The Lambek calculus enriched with additional connectives.Journal of Logic, Lan- guage and Information, 1:141–171, 1992

    work page 1992

  33. [33]

    Kanovich, Stepan L

    Max I. Kanovich, Stepan L. Kuznetsov, Vivek Nigam, and Andre Scedrov. A logical framework with commutative and non-commutative subexponentials. In Didier Galmiche, Stephan Schulz, and Roberto Sebastiani, editors,Automated Reasoning - 9th International Joint Conference, IJCAR 2018, Held as Part of the Federated Logic Conference, FloC 2018, Oxford, UK, July...

    work page 2018

  34. [34]

    Foris, Dordrecht, 1984

    Richard Kayne.Connectedness and Binary Branching. Foris, Dordrecht, 1984

    work page 1984

  35. [35]

    CSLI Publicacions, Stanford, California, 2002

    Andrew Kehler.Coherence, Reference and the Theory of Grammar. CSLI Publicacions, Stanford, California, 2002

    work page 2002

  36. [36]

    Deriving island constraints from principles of predication

    Robert Kluender. Deriving island constraints from principles of predication. In H. Goodluck and M. Rochemont, editors,Island Constraints: Theory, Acquisition, and Processing, pages 223–258. Kluwer, Dordrecht, 1992. BIBLIOGRAPHY 255

    work page 1992

  37. [37]

    On the distinction between strong and weak islands: A processing perspective

    Robert Kluender. On the distinction between strong and weak islands: A processing perspective. In P. Culicover and L. McNally, editors,The Limits of Syntax, volume 29 ofSyntax and Semantics, pages 241–279. Academic Press, San Diego, 1998

    work page 1998

  38. [38]

    Gapping as like-category coordination

    Yusuke Kubota and Robert Levine. Gapping as like-category coordination. In Denis Bechet and Alexander Dikovsky, editors,Logical Aspects of Computational Linguistics, volume 7351 ofLecture Notes in Computer Science, pages 135–150. Springer Berlin Heidelberg, 2012

    work page 2012

  39. [39]

    Determiner Gapping as Higher-Order Discontinuous Con- stituency

    Yusuke Kubota and Robert Levine. Determiner Gapping as Higher-Order Discontinuous Con- stituency. In Glyn Morrill and Mark-Jan Nederhof, editors,Proceedings of Formal Grammar 2012 and 2013, volume 8036 ofSpringer LNCS, FoLLI Publications in Logic, Language and Information, pages 225–241, Berlin, 2013. Springer

    work page 2012

  40. [40]

    Against ellipsis: Arguments for the direct licensing of ‘non- canonical’ coordinations.Linguistics and Philosophy, 2015

    Yusuke Kubota and Robert Levine. Against ellipsis: Arguments for the direct licensing of ‘non- canonical’ coordinations.Linguistics and Philosophy, 2015. to appear

    work page 2015

  41. [41]

    Gapping as hypothetical reasoning.Natural Language and Lin- guistic Theory, 2015

    Yusuke Kubota and Robert Levine. Gapping as hypothetical reasoning.Natural Language and Lin- guistic Theory, 2015. in press

    work page 2015

  42. [42]

    Count-Invariance Including Exponentials

    Stepan Kuznetsov, Glyn Morrill, and Oriol Valent ´ın. Count-Invariance Including Exponentials. In M. Kanazawa, Ph. de Groote, and M. Sadrzadeh, editors,15th Meeting on Mathematics of Language, pages 128–139, London, 2017

    work page 2017

  43. [43]

    Frame semantic control of the Coordinate Structure Constraint

    George Lakoff. Frame semantic control of the Coordinate Structure Constraint. In A. M. Farley, P. T. Farley, and K.-E. McCullough, editors,CLS 22 PART 2: Papers from the Parasession on Pragmatics and Grammatical Theory, 152. Chicago Linguistics Society, Chicago, 1986

    work page 1986

  44. [44]

    J. Lambek. On the Calculus of Syntactic Types. In Roman Jakobson, editor,Structure of Language and its Mathematical Aspects, Proceedings of the Symposia in Applied Mathematics XII, pages 166–

    work page

  45. [45]

    American Mathematical Society, Providence, Rhode Island, 1961

    work page 1961

  46. [46]

    J. Lambek. Categorial and Categorical Grammars. In Richard T. Oehrle, Emmon Bach, and Deidre Wheeler, editors,Categorial Grammars and Natural Language Structures, volume 32 ofStudies in Linguistics and Philosophy, pages 297–317. D. Reidel, Dordrecht, 1988

    work page 1988

  47. [47]

    The mathematics of sentence structure.American Mathematical Monthly, 65:154– 170, 1958

    Joachim Lambek. The mathematics of sentence structure.American Mathematical Monthly, 65:154– 170, 1958. Reprinted in Buszkowski, Wojciech, Wojciech Marciszewski, and Johan van Benthem, editors, 1988,Categorial Grammar, Linguistic & Literary Studies in Eastern Europe volume 25, John Benjamins, Amsterdam, 153–172

    work page 1958

  48. [48]

    A proof of the Focalization property of Linear Logic

    Olivier Laurent. A proof of the Focalization property of Linear Logic. Unpublished manuscript, CNRS - Universit´e Paris VII, 2004

    work page 2004

  49. [49]

    Levine and Thomas E

    Robert D. Levine and Thomas E. Hukari.The Unity of Unbounded Dependency Constructions. CSLI Publications, Stanford, California, 2006

    work page 2006

  50. [50]

    Distinguishing phenogrammar from tectogrammar simplifies the analysis of interrogatives

    Vedrana Mihali ˇcek and Carl Pollard. Distinguishing phenogrammar from tectogrammar simplifies the analysis of interrogatives. In P. de Groote and M.-J. Nederhof, editors,Formal Grammar 2010/2011, pages 130–145, Heidelberg, 2012. Springer

    work page 2010

  51. [51]

    English as a Formal Language

    Richard Montague. English as a Formal Language. In B. Visentini et al., editor,Linguaggi nella So- ciet`a e nella Tecnica, pages 189–224. Edizioni di Comunit`a, Milan, 1970. Reprinted in R.H. Thoma- son, editor, 1974,Formal Philosophy: Selected Papers of Richard Montague, Yale University Press, New Haven, 188–221

    work page 1970

  52. [52]

    The Proper Treatment of Quantification in Ordinary English

    Richard Montague. The Proper Treatment of Quantification in Ordinary English. In J. Hintikka, J.M.E. Moravcsik, and P. Suppes, editors,Approaches to Natural Language: Proceedings of the 1970 Stanford Workshop on Grammar and Semantics, pages 189–224. D. Reidel, Dordrecht, 1973. Reprinted in R.H. Thomason, editor, 1974,Formal Philosophy: Selected Papers of ...

    work page 1970

  53. [53]

    Foris, Dordrecht, 1988

    Michael Moortgat.Categorial Investigations: Logical and Linguistic Aspects of the Lambek Calculus. Foris, Dordrecht, 1988. PhD thesis, Universiteit van Amsterdam

    work page 1988

  54. [54]

    Multimodal linguistic inference.Journal of Logic, Language and Information, 5(3, 4):349–385, 1996

    Michael Moortgat. Multimodal linguistic inference.Journal of Logic, Language and Information, 5(3, 4):349–385, 1996. Also inBulletin of the IGPL, 3(2,3):371–401, 1995

    work page 1996

  55. [55]

    Categorial Type Logics

    Michael Moortgat. Categorial Type Logics. In Johan van Benthem and Alice ter Meulen, editors, Handbook of Logic and Language, pages 93–177. Elsevier Science B.V . and the MIT Press, Amster- dam and Cambridge, Massachusetts, 1997

    work page 1997

  56. [56]

    Extended Lambek calculi and first-order linear logic

    Richard Moot. Extended Lambek calculi and first-order linear logic. In Claudia Casadio, Bob Coecke, Michael Moortgat, and Philip Scott, editors,Categories and Types in Logic, Language, and Physics, volume 8222 ofLecture Notes in Computer Science, pages 297–330. Springer Berlin Heidelberg, 2014

    work page 2014

  57. [57]

    Springer, Heidelberg, 2012

    Richard Moot and Christian Retor ´e.The Logic of Categorial Grammars: A Deductive Account of Natural Language Syntax and Semantics. Springer, Heidelberg, 2012

    work page 2012

  58. [58]

    G. Morrill. Grammar and Logical Types. In Martin Stockhof and Leen Torenvliet, editors,Proceed- ings of the Seventh Amsterdam Colloquium, pages 429–450, 1990

    work page 1990

  59. [59]

    G. Morrill. Grammar and Logical Types. In Martin Stockhof and Leen Torenvliet, editors,Proceed- ings of the Seventh Amsterdam Colloquium, pages 429–450, 1990. Also in G. Barry and G. Morrill, editors,Studies in Categorial Grammar, Edinburgh Working Papers in Cognitive Science, V olume 5, pages 127–148: 1990. Revised version published as Grammar and Logic,...

    work page 1990

  60. [60]

    Intensionality and Boundedness.Linguistics and Philosophy, 13(6):699–726, 1990

    Glyn Morrill. Intensionality and Boundedness.Linguistics and Philosophy, 13(6):699–726, 1990

    work page 1990

  61. [61]

    Categorial Formalisation of Relativisation: Pied Piping, Islands, and Extraction Sites

    Glyn Morrill. Categorial Formalisation of Relativisation: Pied Piping, Islands, and Extraction Sites. Technical Report LSI-92-23-R, Departament de Llenguatges i Sistemes Inform `atics, Universi- tat Polit`ecnica de Catalunya, 1992

    work page 1992

  62. [62]

    Incremental Processing and Acceptability.Computational Linguistics, 26(3):319–338, 2000

    Glyn Morrill. Incremental Processing and Acceptability.Computational Linguistics, 26(3):319–338, 2000

    work page 2000

  63. [63]

    Islands, Coordination and Parasitic Gaps

    Glyn Morrill. Islands, Coordination and Parasitic Gaps. In V .M. Abrusci and C. Casadio, editors, New Perspectives in Logic and Formal Linguistics, Proceedings Vth Roma Workshop. Bulzoni Edi- tore, Roma, 2002. Also Report de Recerca LSI–02–16–R, Departament de Llenguatges i Sistemes Inform`atics, Universitat Polit`ecnica de Catalunya

    work page 2002

  64. [64]

    Logic Programming of the Displacement Calculus

    Glyn Morrill. Logic Programming of the Displacement Calculus. In Sylvain Pogodalla and Jean- Philippe Prost, editors,Proceedings of Logical Aspects of Computational Linguistics 2011, LACL’11, Montpellier, number LNAI 6736 in Springer Lecture Notes in AI, pages 175–189, Berlin, 2011. Springer

    work page 2011

  65. [65]

    CatLog: A Categorial Parser/Theorem-Prover

    Glyn Morrill. CatLog: A Categorial Parser/Theorem-Prover. InLACL 2012 System Demonstrations, Logical Aspects of Computational Linguistics 2012, pages 13–16, Nantes, 2012

    work page 2012

  66. [66]

    Logical grammar

    Glyn Morrill. Logical grammar. In Ruth Kempson, Tim Fernando, and Nicholas Asher, editors,The Handbook of Philosophy of Linguistics, pages 63–92. Elsevier, Oxford and Amsterdam, 2012

    work page 2012

  67. [67]

    Grammar Logicised: Relativisation.Linguistics and Philosophy, 40(2):119–163, 2017

    Glyn Morrill. Grammar Logicised: Relativisation.Linguistics and Philosophy, 40(2):119–163, 2017. Doi 10.1007/s10988-016-9197-0

    work page doi:10.1007/s10988-016-9197-0 2017

  68. [68]

    Parsing/theorem-proving for logical grammar: CatLog3.Journal of Logic, Language and Information, 28(2):183–216, 2019

    Glyn Morrill. Parsing/theorem-proving for logical grammar: CatLog3.Journal of Logic, Language and Information, 28(2):183–216, 2019. BIBLIOGRAPHY 257

    work page 2019

  69. [69]

    Bracket induction for Lam- bek calculus with bracket modalities

    Glyn Morrill, Stepan Kuznetsov, Max Kanovich, and Andre Scedrov. Bracket induction for Lam- bek calculus with bracket modalities. In Anne Foret, Greg Kobele, and Sylvain Pogodalla, editors, Proceedings of Formal Grammar, Sofia, pages 84–101, Berlin, 2018. Springer

    work page 2018

  70. [70]

    Generalising discontinuity.Traitement automatique des langues, 37(2):119–143, 1996

    Glyn Morrill and Josep-Maria Merenciano. Generalising discontinuity.Traitement automatique des langues, 37(2):119–143, 1996

    work page 1996

  71. [71]

    Displacement Calculus.Linguistic Analysis, 36(1–4):167–192,

    Glyn Morrill and Oriol Valent ´ın. Displacement Calculus.Linguistic Analysis, 36(1–4):167–192,

    work page

  72. [72]

    Special issue Festschrift for Joachim Lambek, http://arxiv.org/abs/1004.4181

    work page arXiv

  73. [73]

    Displacement Logic for Anaphora.Journal of Computing and System Science, 80:390–409, 2014

    Glyn Morrill and Oriol Valent ´ın. Displacement Logic for Anaphora.Journal of Computing and System Science, 80:390–409, 2014. http://dx.doi.org/10.1016/j.jcss.2013.05.006

    work page doi:10.1016/j.jcss.2013.05.006 2014

  74. [74]

    Semantically Inactive Multiplicatives and Words as Types

    Glyn Morrill and Oriol Valent ´ın. Semantically Inactive Multiplicatives and Words as Types. In Nicholas Asher and Sergei Soloviev, editors,Proceedings of Logical Aspects of Computational Lin- guistics, LACL’14, Toulouse, number 8535 in LNCS, FoLLI Publications on Logic, Language and Information, pages 149–162, Berlin, 2014. Springer

    work page 2014

  75. [75]

    Computational Coverage of TLG: Nonlinearity

    Glyn Morrill and Oriol Valent ´ın. Computational Coverage of TLG: Nonlinearity. In M. Kanazawa, L.S. Moss, and V . de Paiva, editors,Proceedings of NLCS’15. Third Workshop on Natural Language and Computer Science, volume 32 ofEPiC, pages 51–63, Kyoto, 2015. Workshop affiliated with Automata, Languages and Programming (ICALP) and Logic in Computer Science (LICS)

    work page 2015

  76. [76]

    Computational Coverage of Type Logical Grammar: The Montague Test

    Glyn Morrill and Oriol Valent´ın. Computational Coverage of Type Logical Grammar: The Montague Test. In C. Pi˜ n´on, editor,Empirical Issues in Syntax and Semantics 11, pages 141–170. Colloque de Syntaxe et S´emantique `a Paris (CSSP), Paris, 2016. http://www.cssp.cnrs.fr/eiss11/

    work page 2016

  77. [77]

    On the logic of expansion in natural language

    Glyn Morrill and Oriol Valent´ın. On the logic of expansion in natural language. In Maxime Amblard, Phillipe de Groote, Sylvain Pogodalla, and Christian Retor´e, editors,Proceedings of Logical Aspects of Computational Linguistics, LACL’16, Nancy, LNCS, FoLLI Publications on Logic, Language and Information, Berlin, 2016. Springer

    work page 2016

  78. [78]

    A Reply to Kubota and Levine on Gapping.Natural Lan- guage and Linguistic Theory, 35(1):257–270, 2017

    Glyn Morrill and Oriol Valent ´ın. A Reply to Kubota and Levine on Gapping.Natural Lan- guage and Linguistic Theory, 35(1):257–270, 2017. Doi 10.1007/s11049-016-9336-x. SharedIt link: http://rdcu.be/nXnd

    work page doi:10.1007/s11049-016-9336-x 2017

  79. [79]

    Spurious Ambiguity and Focalization.Computational Linguistics, 44(2):285–327, 2018

    Glyn Morrill and Oriol Valent ´ın. Spurious Ambiguity and Focalization.Computational Linguistics, 44(2):285–327, 2018

    work page 2018

  80. [80]

    Dutch Grammar and Processing: A Case Study in TLG

    Glyn Morrill, Oriol Valent ´ın, and Mario Fadda. Dutch Grammar and Processing: A Case Study in TLG. In Peter Bosch, David Gabelaia, and J ´erˆome Lang, editors,Logic, Language, and Computa- tion: 7th International Tbilisi Symposium, Revised Selected Papers, number 5422 in Lecture Notes in Artificial Intelligence, pages 272–286, Berlin, 2009. Springer

    work page 2009

Showing first 80 references.