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A Denotational Semantics for First-Order Logic

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Krzysztof R. Apt

Programming Languages · Submitted 8 May 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The soundness result shows correctness of the semantics with respect to the notion of truth.

how it is stated · asserted 1.00 read the record →

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arXiv IDcs/0005008 (version 1)
Pith IDYRWY3DM3, Pith's permanent record of this paper and its review
CitationKrzysztof R. Apt. "A Denotational Semantics for First-Order Logic." arXiv:cs/0005008 (2000). https://pith.science/paper/YRWY3DM3
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,509 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.85 · mentions code or data availability 0.04.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic. Additionally, by allowing an assignment of a non-ground term to a variable we introduce in this framework logical variables. The semantics combines a number of well-known ideas from the areas of semantics of imperative programming languages and logic programming. In the resulting computational view conjunction corresponds to sequential composition, disjunction to ``don't know'' nondeterminism, existential quantification to declaration of a local variable, and negation to the ``negation as finite failure'' rule. The soundness result shows correctness of the semantics with respect to the notion of truth. The proof resembles in some aspects the proof of the soundness of the SLDNF-resolution.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. background 0.99 0.65 0.03 asserted 1.00
s1 Here we complement this work by introducing a denotational semantics for first-order logic. contribution 1.00 0.90 0.21 asserted 0.99
s2 Additionally, by allowing an assignment of a non-ground term to a variable we introduce in this framework logical variables. contribution 0.93 0.92 0.07 asserted 1.00
s3 The semantics combines a number of well-known ideas from the areas of semantics of imperative programming languages and logic programming. method 0.79 0.49 0.06 asserted 1.00
s4 In the resulting computational view conjunction corresponds to sequential composition, disjunction to ``don't know'' nondeterminism, existential quantification to declaration of a local variable, and negation to the ``negation as finite failure'' rule. interpretation 0.36 0.80 0.17 asserted 1.00
s5 The soundness result shows correctness of the semantics with respect to the notion of truth. result 0.97 0.91 0.36 asserted 1.00
s6 The proof resembles in some aspects the proof of the soundness of the SLDNF-resolution. method 0.38 0.81 0.06 asserted 0.86

What kind of paper the classifier reports this is: theoretical result 0.64 · evidence from proof or derivation 1.00.

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

In Apt and Bezem [AB99] (see cs.LO/9811017) we provided a computational interpretation of first-order formulas over arbitrary interpretations. Here we complement this work by introducing a denotational semantics for first-order logic. Additionally, by allowing an assignment of a non-ground term to a variable we introduce in this framework logical variables. The semantics combines a number of well-known ideas from the areas of semantics of imperative programming languages and logic programming. In the resulting computational view conjunction corresponds to sequential composition, disjunction to ``don't know'' nondeterminism, existential quantification to declaration of a local variable, and negation to the ``negation as finite failure'' rule. The soundness result shows correctness of the semantics with respect to the notion of truth. The proof resembles in some aspects the proof of the soundness of the SLDNF-resolution.

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