When Do Introspection Axioms Matter for Multi-Agent Epistemic Reasoning?

Berkeley); Cedegao Zhang (University of California; Wesley H. Holliday (University of California; Yifeng Ding (University of California

arxiv: 1907.09101 · v1 · pith:ADB566ZAnew · submitted 2019-07-22 · 💻 cs.LO · cs.MA

When Do Introspection Axioms Matter for Multi-Agent Epistemic Reasoning?

Yifeng Ding (University of California , Berkeley) , Wesley H. Holliday (University of California , Cedegao Zhang (University of California This is my paper

Pith reviewed 2026-05-24 18:04 UTC · model grok-4.3

classification 💻 cs.LO cs.MA

keywords multi-agent epistemic logicintrospection axiomsagent-alternating formulasconservativitybelief logicknowledge logicmodal logic

0 comments

The pith

In multi-agent belief logics K and KD, adding the 4 and 5 axioms (or the B axiom) yields no new agent-alternating formulas.

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

The paper asks whether single-agent introspection axioms matter once epistemic logic moves to multiple agents, where reasoning often involves alternating beliefs such as what A believes about B's beliefs about A's beliefs. It defines agent-alternating formulas to capture exactly those patterns and proves that, for belief systems based on K or KD, the addition of 4 and 5 together, or of B alone, is conservative over the alternating fragment. The same conservativity fails when the base system is KT for knowledge, although it holds for the smaller class of agent-nonrepeating formulas. The result isolates the precise sense in which introspection can be set aside without changing the multi-agent alternating consequences.

Core claim

If one starts with multi-agent K or KD, then adding both the 4 and 5 axioms (or adding the B axiom) does not allow the derivation of any new agent-alternating formulas; by contrast, such conservativity results fail for knowledge and multi-agent KT, though they hold with respect to a smaller class of agent-nonrepeating formulas.

What carries the argument

Agent-alternating formulas (formulas such as Box_a Box_b Box_a p, which switch agents at each modal step, but not Box_a Box_a p).

If this is right

Multi-agent belief reasoning about alternating perspectives can proceed without assuming positive or negative introspection.
The choice between KD4 and KD45 (or between KD and KB) makes no difference to the set of provable alternating formulas.
For knowledge logics based on KT the same insulation does not hold, so introspection axioms can affect alternating conclusions.
Restricting attention to agent-nonrepeating formulas restores conservativity even for KT.

Where Pith is reading between the lines

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

If alternating formulas suffice for most game-theoretic or distributed-computing applications, then model-checking or proof-search tools for those domains can safely omit the introspection axioms.
The failure for KT suggests that any attempt to combine knowledge and belief in a single multi-agent language may need to track which modalities are introspective.
One could test whether the conservativity extends to other base logics, such as those with common knowledge operators or with mixed knowledge and belief.

Load-bearing premise

The multi-agent epistemic scenarios of interest are exactly those captured by agent-alternating formulas.

What would settle it

A concrete derivation, inside K or KD plus 4 and 5, of an agent-alternating formula that is not already a theorem of plain multi-agent K or KD.

Figures

Figures reproduced from arXiv: 1907.09101 by Berkeley), Cedegao Zhang (University of California, Wesley H. Holliday (University of California, Yifeng Ding (University of California.

**Figure 2.** Figure 2: Systems when restricted to Lalt Proposition 3.7 (Collapsing 4 and 5). K|alt = K45|alt and KD|alt = KD45|alt Proof. The right-to-left direction of both equations is trivial. For the left-to-right direction, by completeness, we need only show that for every ϕ ∈ Lalt, if ϕ is satisfied by a pointed model, then it is also satisfied by a pointed model based on a transitive and Euclidean frame. Further, if the … view at source ↗

**Figure 3.** Figure 3: Systems when restricted to LA Theorem 4.7. Among the systems displayed in [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗

read the original abstract

The early literature on epistemic logic in philosophy focused on reasoning about the knowledge or belief of a single agent, especially on controversies about "introspection axioms" such as the 4 and 5 axioms. By contrast, the later literature on epistemic logic in computer science and game theory has focused on multi-agent epistemic reasoning, with the single-agent 4 and 5 axioms largely taken for granted. In the relevant multi-agent scenarios, it is often important to reason about what agent A believes about what agent B believes about what agent A believes; but it is rarely important to reason just about what agent A believes about what agent A believes. This raises the question of the extent to which single-agent introspection axioms actually matter for multi-agent epistemic reasoning. In this paper, we formalize and answer this question. To formalize the question, we first define a set of multi-agent formulas that we call agent-alternating formulas, including formulas like Box_a Box_b Box_a p but not formulas like Box_a Box_a p. We then prove, for the case of belief, that if one starts with multi-agent K or KD, then adding both the 4 and 5 axioms (or adding the B axiom) does not allow the derivation of any new agent-alternating formulas -- in this sense, introspection axioms do not matter. By contrast, we show that such conservativity results fail for knowledge and multi-agent KT, though they hold with respect to a smaller class of agent-nonrepeating formulas.

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.

Desk Editor's Note private letter to a colleague

The paper proves conservativity of 4+5 and B over multi-agent K/KD in the agent-alternating fragment but shows failure for KT, with the practical takeaway scoped to that fragment.

read the letter

The central result is that adding 4 and 5 (or B) to multi-agent K or KD produces no new theorems among agent-alternating formulas, while the same fails for KT though it holds on the smaller nonrepeating class. This directly addresses the single-agent versus multi-agent gap noted in the abstract. The new element is the definition of agent-alternating formulas together with the specific conservativity theorems that make the difference between belief and knowledge logics precise. The work is useful for pinning down when introspection axioms change deductive power in the multi-agent setting. The proofs appear to be standard modal-logic arguments, and the contrast between the belief and knowledge cases is cleanly drawn. The main limitation is that the claim introspection axioms do not matter is explicitly limited to the alternating fragment. The abstract motivates this choice by appeal to typical CS and game-theory patterns, but if repeated-agent formulas matter in some applications the scope of the takeaway narrows. That is a modeling choice rather than a flaw in the formal results themselves. The paper is aimed at researchers already working in epistemic logic who want a technical handle on why single-agent introspection debates may not transfer directly to multi-agent systems. A reader looking for concrete theorems that separate belief from knowledge in this way will get value from it. It deserves peer review because the conservativity statements are sharp and falsifiable.

Referee Report

2 major / 2 minor

Summary. The paper claims that for multi-agent belief logics based on K or KD, adding the single-agent introspection axioms 4 and 5 (or the B axiom) yields no new theorems within the fragment of agent-alternating formulas (e.g., □_a □_b □_a p but excluding same-agent iterations like □_a □_a p). By contrast, the corresponding conservativity fails for knowledge logics based on KT, though it holds relative to the smaller class of agent-nonrepeating formulas. The results are used to conclude that introspection axioms do not matter for multi-agent epistemic reasoning in the relevant sense.

Significance. If the agent-alternating fragment adequately captures the multi-agent scenarios of interest in computer science and game theory, the conservativity theorems supply a precise technical basis for omitting introspection axioms without loss of deductive power over alternating formulas. The contrast between the belief (K/KD) and knowledge (KT) cases is a substantive finding that clarifies how axiom choice interacts with multi-agent structure. The explicit definition of the formula class and the provision of formal conservativity proofs are strengths that allow the question to be posed and answered rigorously rather than informally.

major comments (2)

[Introduction] Introduction (motivation for agent-alternating formulas): The claim that introspection axioms 'do not matter' for multi-agent reasoning is derived from conservativity over the agent-alternating class, which is motivated by the informal observation that alternating-agent formulas (□_a □_b □_a p) arise in typical CS/game-theory scenarios while same-agent iterations do not. No reference, empirical check, or formal argument is supplied showing that non-alternating formulas can be safely ignored in the intended applications; if such formulas remain relevant, the interpretive step from the technical result to the title question does not follow.
[Definition and conservativity (around §3–4)] Definition of agent-alternating formulas and conservativity statement (likely §3–4): The conservativity is stated only for the newly defined agent-alternating class; the manuscript does not address whether this class is closed under logical consequence in the base systems or whether there exist formulas outside the class that are provably equivalent (modulo the base axioms) to alternating ones, which would affect whether the result fully captures the deductive closure relevant to applications.

minor comments (2)

The abstract and introduction use 'Box' notation; ensure consistent use of modal operators (□ or K) throughout the formal sections and that the definition of agent-alternating formulas is given with a precise inductive clause.
Related-work discussion should cite prior results on multi-agent epistemic logics and conservativity (e.g., work on alternating bisimulations or fragments in dynamic epistemic logic) to situate the contribution.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We respond point by point to the major comments below.

read point-by-point responses

Referee: [Introduction] Introduction (motivation for agent-alternating formulas): The claim that introspection axioms 'do not matter' for multi-agent reasoning is derived from conservativity over the agent-alternating class, which is motivated by the informal observation that alternating-agent formulas (□_a □_b □_a p) arise in typical CS/game-theory scenarios while same-agent iterations do not. No reference, empirical check, or formal argument is supplied showing that non-alternating formulas can be safely ignored in the intended applications; if such formulas remain relevant, the interpretive step from the technical result to the title question does not follow.

Authors: We agree that the motivation for the agent-alternating fragment is presented informally, relying on the observation that typical multi-agent scenarios in computer science and game theory involve alternating agents. To address this, we will revise the introduction to include specific references to works in epistemic game theory and multi-agent systems (e.g., papers on common knowledge and belief in games) that illustrate the prevalence of alternating formulas. This provides a more concrete grounding without altering the technical results. revision: yes
Referee: [Definition and conservativity (around §3–4)] Definition of agent-alternating formulas and conservativity statement (likely §3–4): The conservativity is stated only for the newly defined agent-alternating class; the manuscript does not address whether this class is closed under logical consequence in the base systems or whether there exist formulas outside the class that are provably equivalent (modulo the base axioms) to alternating ones, which would affect whether the result fully captures the deductive closure relevant to applications.

Authors: The conservativity result shows that the introspection axioms add no new theorems within the syntactically defined agent-alternating class. While the class is not necessarily closed under consequence in the base logic, and equivalences to non-alternating formulas could exist in the base systems, such equivalences would not affect the statement that no additional alternating formulas become derivable. We will add a clarifying remark in §3 noting this distinction and confirming that the conservativity statement remains unaffected. This is a partial revision focused on exposition. revision: partial

Circularity Check

0 steps flagged

No circularity: conservativity is a direct syntactic proof over an explicitly defined formula class

full rationale

The paper defines agent-alternating formulas by a clear syntactic criterion (sequences of distinct agents in nested modalities) and proves that K/KD plus 4+5 or B yields no new theorems in that fragment. This is a standard modal-logic conservativity argument with no fitted parameters, no self-referential definitions, and no load-bearing self-citations. The interpretive gloss that introspection axioms 'do not matter' for multi-agent reasoning is presented as a consequence of the modeling choice, not as a premise that feeds back into the proof. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on the standard axioms of multi-agent epistemic logic (K, KD, KT) as base systems and introduces the new syntactic class of agent-alternating formulas; no free parameters or invented entities are mentioned.

axioms (2)

domain assumption Multi-agent K or KD as the base logic for belief
The conservativity claims are stated relative to these standard base systems.
domain assumption Multi-agent KT as the base logic for knowledge
The contrasting result for knowledge is stated relative to this base system.

pith-pipeline@v0.9.0 · 5823 in / 1315 out tokens · 39715 ms · 2026-05-24T18:04:41.167490+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

27 extracted references · 27 canonical work pages · 2 internal anchors

[1]

Aumann (1976): Agreeing to Disagree

Robert J. Aumann (1976): Agreeing to disagree . The Annals of Statistics 4(6), pp. 1236–1239, doi:10.1214/aos/1176343654

work page doi:10.1214/aos/1176343654 1976
[2]

Aumann (1999): Interactive Epistemology I, II

Robert J. Aumann (1999): Interactive epistemology I: Knowledge . International Journal of Game Theory 28(3), pp. 263–300, doi:10.1007/s001820050111

work page doi:10.1007/s001820050111 1999
[3]

Douglas Bernheim (1984): Rationalizable strategic behavior

B. Douglas Bernheim (1984): Rationalizable strategic behavior . Econometrica 52(4), pp. 1007–1028, doi:10.2307/1911196

work page doi:10.2307/1911196 1984
[4]

Risk, Decision and Policy 7(3), pp

Giacomo Bonanno (2002): Modal logic and game theory: two alternative approaches . Risk, Decision and Policy 7(3), pp. 309–324, doi:10.1017/s1357530902000704

work page doi:10.1017/s1357530902000704 2002
[5]

Halpern, Yoram Moses & Moshe Y

Ronald Fagin, Joseph Y . Halpern, Yoram Moses & Moshe Y . Vardi (2003): Reasoning About Knowledge . MIT Press

work page 2003
[6]

Knowledge Compilation in Multi-Agent Epistemic Logics

Liangda Fang, Kewen Wang, Zhe Wang & Ximing Wen (2018): Knowledge compilation in multi-agent epistemic logics. arXiv: 1806.10561v2

work page internal anchor Pith review Pith/arXiv arXiv 2018
[7]

In Edward N

James Garson (2018): Modal Logic. In Edward N. Zalta, editor: The Stanford Encyclopedia of Philosophy, fall 2018 edition, Metaphysics Research Lab, Stanford University

work page 2018
[8]

Cowles Foundation Discussion Papers 914, Cowles Foundation for Research in Economics, Yale University

John Geanakoplos (1989): Game theory without partitions, and applications to speculation and consensus . Cowles Foundation Discussion Papers 914, Cowles Foundation for Research in Economics, Yale University

work page 1989
[9]

James Hales (2016): Quantifying over epistemic updates. Ph.D. thesis, The University of Western Australia. Y . Ding, W. H. Holliday, & C. Zhang 135

work page 2016
[10]

In: Advances in Modal Logic, V olume 9, pp

James Hales, Tim French & Rowan Davies (2012): Reﬁnement quantiﬁed logics of knowledge and belief for multiple agents. In: Advances in Modal Logic, V olume 9, pp. 317–338

work page 2012
[11]

Journal of Logic and Computa- tion 11(1), pp

Joseph Y Halpern & Gerhard Lakemeyer (2001): Multi-agent only knowing. Journal of Logic and Computa- tion 11(1), pp. 41–70, doi:10.1093/logcom/11.1.41

work page doi:10.1093/logcom/11.1.41 2001
[12]

Halpern & Richard A

Joseph Y . Halpern & Richard A. Shore (2004): Reasoning about common knowledge with inﬁnitely many agents. Information and Computation 191(1), pp. 1–40, doi:10.1016/j.ic.2004.01.003

work page doi:10.1016/j.ic.2004.01.003 2004
[13]

Cornell University Press

Jaakko Hintikka (1962): Knowledge and Belief: An Introduction to the Logic of the Two Notions . Cornell University Press

work page 1962
[14]

A General Multi-agent Epistemic Planner Based on Higher-order Belief Change

Xiao Huang, Biqing Fang, Hai Wan & Yongmei Liu (2018): A general multi-agent epistemic planner based on higher-order belief change. arXiv: 1806.11298v2

work page internal anchor Pith review Pith/arXiv arXiv 2018
[15]

Economic Theory 19(1), pp

Mamoru Kaneko (2002): Epistemic logics and their game theoretic applications: Introduction . Economic Theory 19(1), pp. 7–62, doi:10.1007/s001990100202

work page doi:10.1007/s001990100202 2002
[16]

In: Proceedings of the 20th European Conference on Artiﬁcial Intelligence , ECAI’12, pp

Gerhard Lakemeyer & Yves Lesp ´erance (2012): Efﬁcient reasoning in multiagent epistemic logics . In: Proceedings of the 20th European Conference on Artiﬁcial Intelligence , ECAI’12, pp. 498–503, doi:10.3233/978-1-61499-098-7-498

work page doi:10.3233/978-1-61499-098-7-498 2012
[17]

In Jon Doyle, Erik Sandewall & Pietro Torasso, editors: Principles of Knowledge Repre- sentation and Reasoning , The Morgan Kaufmann Series in Representation and Reasoning, pp

Philippe Lamarre & Yoav Shoham (1994): Knowledge, certainty, belief, and conditionalisation (abbrevi- ated version). In Jon Doyle, Erik Sandewall & Pietro Torasso, editors: Principles of Knowledge Repre- sentation and Reasoning , The Morgan Kaufmann Series in Representation and Reasoning, pp. 415–424, doi:10.1016/b978-1-4832-1452-8.50134-2

work page doi:10.1016/b978-1-4832-1452-8.50134-2 1994
[18]

Review of Symbolic Logic 8(1), pp

Harvey Lederman (2015): People with common priors can agree to disagree . Review of Symbolic Logic 8(1), pp. 11–45, doi:10.1017/s1755020314000380

work page doi:10.1017/s1755020314000380 2015
[19]

Acta Philosophica Fennica 30(2), pp

Wolfgang Lenzen (1978): Recent work in epistemic logic. Acta Philosophica Fennica 30(2), pp. 1–219

work page 1978
[20]

In: Pro- ceedings of the 27th International Joint Conference on Artiﬁcial Intelligence, IJCAI-18 , pp

Qiang Liu & Yongmei Liu (2018): Multi-agent epistemic planning with common knowledge. In: Pro- ceedings of the 27th International Joint Conference on Artiﬁcial Intelligence, IJCAI-18 , pp. 1912–1920, doi:10.24963/ijcai.2018/264

work page doi:10.24963/ijcai.2018/264 2018
[21]

[MvdH95] John-Jules Ch

John-Jules Ch Meyer & Wiebe van der Hoek (1995): Epistemic Logic for AI and Computer Science . Cam- bridge University Press, doi:10.1017/cbo9780511569852

work page doi:10.1017/cbo9780511569852 1995
[22]

Osborne & Ariel Rubinstein (1994): A Course in Game Theory

Martin J. Osborne & Ariel Rubinstein (1994): A Course in Game Theory. MIT Press

work page 1994
[23]

Sadhana 17(1), pp

Rohit Parikh & Paul Krasucki (1992): Levels of knowledge in distributed systems. Sadhana 17(1), pp. 167– 191, doi:10.1007/bf02811342

work page doi:10.1007/bf02811342 1992
[24]

Theory and Decision 37(1), pp

Robert Stalnaker (1994): On the evaluation of solution concepts . Theory and Decision 37(1), pp. 49–73, doi:10.1007/bf01079205

work page doi:10.1007/bf01079205 1994
[25]

Vardi (1985): A model-theoretic analysis of monotonic knowledge

Moshe Y . Vardi (1985): A model-theoretic analysis of monotonic knowledge . In: Proceedings of the 9th International Joint Conference on Artiﬁcial Intelligence, IJCAI-85, pp. 509–512

work page 1985
[26]

conjectures

Arnis Vilks (1999): Knowledge of the game, relative rationality, and backwards induction without counter- factuals. Working Paper no.25, Leipzig Graduate School of Management. A Rationalizability as agent-alternating common belief of rationality In this appendix, we sketch a proof that rationality plus agent-alternating common belief of rationality, in wh...

work page 1999
[27]

The following two models deal with the KD5 case

But of course M ,l1̸⇆2 N ,l′ 1 since M ,l1|= 3a3ap but N ,l′ 1̸|= 3a3ap. The following two models deal with the KD5 case. Y . Ding, W. H. Holliday, & C. Zhang 139 m1 m2 p m3M l1 r1 l2 r2 p l3 p r3N This case is easier. For each i∈{ 1,2,3}, mi⇆a li,ri and mi⇆b ri. Then connecting m1 with r1 by ⇆alt, we have an agent-alternating bisimulation family. Hence M...

work page

[1] [1]

Aumann (1976): Agreeing to Disagree

Robert J. Aumann (1976): Agreeing to disagree . The Annals of Statistics 4(6), pp. 1236–1239, doi:10.1214/aos/1176343654

work page doi:10.1214/aos/1176343654 1976

[2] [2]

Aumann (1999): Interactive Epistemology I, II

Robert J. Aumann (1999): Interactive epistemology I: Knowledge . International Journal of Game Theory 28(3), pp. 263–300, doi:10.1007/s001820050111

work page doi:10.1007/s001820050111 1999

[3] [3]

Douglas Bernheim (1984): Rationalizable strategic behavior

B. Douglas Bernheim (1984): Rationalizable strategic behavior . Econometrica 52(4), pp. 1007–1028, doi:10.2307/1911196

work page doi:10.2307/1911196 1984

[4] [4]

Risk, Decision and Policy 7(3), pp

Giacomo Bonanno (2002): Modal logic and game theory: two alternative approaches . Risk, Decision and Policy 7(3), pp. 309–324, doi:10.1017/s1357530902000704

work page doi:10.1017/s1357530902000704 2002

[5] [5]

Halpern, Yoram Moses & Moshe Y

Ronald Fagin, Joseph Y . Halpern, Yoram Moses & Moshe Y . Vardi (2003): Reasoning About Knowledge . MIT Press

work page 2003

[6] [6]

Knowledge Compilation in Multi-Agent Epistemic Logics

Liangda Fang, Kewen Wang, Zhe Wang & Ximing Wen (2018): Knowledge compilation in multi-agent epistemic logics. arXiv: 1806.10561v2

work page internal anchor Pith review Pith/arXiv arXiv 2018

[7] [7]

In Edward N

James Garson (2018): Modal Logic. In Edward N. Zalta, editor: The Stanford Encyclopedia of Philosophy, fall 2018 edition, Metaphysics Research Lab, Stanford University

work page 2018

[8] [8]

Cowles Foundation Discussion Papers 914, Cowles Foundation for Research in Economics, Yale University

John Geanakoplos (1989): Game theory without partitions, and applications to speculation and consensus . Cowles Foundation Discussion Papers 914, Cowles Foundation for Research in Economics, Yale University

work page 1989

[9] [9]

James Hales (2016): Quantifying over epistemic updates. Ph.D. thesis, The University of Western Australia. Y . Ding, W. H. Holliday, & C. Zhang 135

work page 2016

[10] [10]

In: Advances in Modal Logic, V olume 9, pp

James Hales, Tim French & Rowan Davies (2012): Reﬁnement quantiﬁed logics of knowledge and belief for multiple agents. In: Advances in Modal Logic, V olume 9, pp. 317–338

work page 2012

[11] [11]

Journal of Logic and Computa- tion 11(1), pp

Joseph Y Halpern & Gerhard Lakemeyer (2001): Multi-agent only knowing. Journal of Logic and Computa- tion 11(1), pp. 41–70, doi:10.1093/logcom/11.1.41

work page doi:10.1093/logcom/11.1.41 2001

[12] [12]

Halpern & Richard A

Joseph Y . Halpern & Richard A. Shore (2004): Reasoning about common knowledge with inﬁnitely many agents. Information and Computation 191(1), pp. 1–40, doi:10.1016/j.ic.2004.01.003

work page doi:10.1016/j.ic.2004.01.003 2004

[13] [13]

Cornell University Press

Jaakko Hintikka (1962): Knowledge and Belief: An Introduction to the Logic of the Two Notions . Cornell University Press

work page 1962

[14] [14]

A General Multi-agent Epistemic Planner Based on Higher-order Belief Change

Xiao Huang, Biqing Fang, Hai Wan & Yongmei Liu (2018): A general multi-agent epistemic planner based on higher-order belief change. arXiv: 1806.11298v2

work page internal anchor Pith review Pith/arXiv arXiv 2018

[15] [15]

Economic Theory 19(1), pp

Mamoru Kaneko (2002): Epistemic logics and their game theoretic applications: Introduction . Economic Theory 19(1), pp. 7–62, doi:10.1007/s001990100202

work page doi:10.1007/s001990100202 2002

[16] [16]

In: Proceedings of the 20th European Conference on Artiﬁcial Intelligence , ECAI’12, pp

Gerhard Lakemeyer & Yves Lesp ´erance (2012): Efﬁcient reasoning in multiagent epistemic logics . In: Proceedings of the 20th European Conference on Artiﬁcial Intelligence , ECAI’12, pp. 498–503, doi:10.3233/978-1-61499-098-7-498

work page doi:10.3233/978-1-61499-098-7-498 2012

[17] [17]

In Jon Doyle, Erik Sandewall & Pietro Torasso, editors: Principles of Knowledge Repre- sentation and Reasoning , The Morgan Kaufmann Series in Representation and Reasoning, pp

Philippe Lamarre & Yoav Shoham (1994): Knowledge, certainty, belief, and conditionalisation (abbrevi- ated version). In Jon Doyle, Erik Sandewall & Pietro Torasso, editors: Principles of Knowledge Repre- sentation and Reasoning , The Morgan Kaufmann Series in Representation and Reasoning, pp. 415–424, doi:10.1016/b978-1-4832-1452-8.50134-2

work page doi:10.1016/b978-1-4832-1452-8.50134-2 1994

[18] [18]

Review of Symbolic Logic 8(1), pp

Harvey Lederman (2015): People with common priors can agree to disagree . Review of Symbolic Logic 8(1), pp. 11–45, doi:10.1017/s1755020314000380

work page doi:10.1017/s1755020314000380 2015

[19] [19]

Acta Philosophica Fennica 30(2), pp

Wolfgang Lenzen (1978): Recent work in epistemic logic. Acta Philosophica Fennica 30(2), pp. 1–219

work page 1978

[20] [20]

In: Pro- ceedings of the 27th International Joint Conference on Artiﬁcial Intelligence, IJCAI-18 , pp

Qiang Liu & Yongmei Liu (2018): Multi-agent epistemic planning with common knowledge. In: Pro- ceedings of the 27th International Joint Conference on Artiﬁcial Intelligence, IJCAI-18 , pp. 1912–1920, doi:10.24963/ijcai.2018/264

work page doi:10.24963/ijcai.2018/264 2018

[21] [21]

[MvdH95] John-Jules Ch

John-Jules Ch Meyer & Wiebe van der Hoek (1995): Epistemic Logic for AI and Computer Science . Cam- bridge University Press, doi:10.1017/cbo9780511569852

work page doi:10.1017/cbo9780511569852 1995

[22] [22]

Osborne & Ariel Rubinstein (1994): A Course in Game Theory

Martin J. Osborne & Ariel Rubinstein (1994): A Course in Game Theory. MIT Press

work page 1994

[23] [23]

Sadhana 17(1), pp

Rohit Parikh & Paul Krasucki (1992): Levels of knowledge in distributed systems. Sadhana 17(1), pp. 167– 191, doi:10.1007/bf02811342

work page doi:10.1007/bf02811342 1992

[24] [24]

Theory and Decision 37(1), pp

Robert Stalnaker (1994): On the evaluation of solution concepts . Theory and Decision 37(1), pp. 49–73, doi:10.1007/bf01079205

work page doi:10.1007/bf01079205 1994

[25] [25]

Vardi (1985): A model-theoretic analysis of monotonic knowledge

Moshe Y . Vardi (1985): A model-theoretic analysis of monotonic knowledge . In: Proceedings of the 9th International Joint Conference on Artiﬁcial Intelligence, IJCAI-85, pp. 509–512

work page 1985

[26] [26]

conjectures

Arnis Vilks (1999): Knowledge of the game, relative rationality, and backwards induction without counter- factuals. Working Paper no.25, Leipzig Graduate School of Management. A Rationalizability as agent-alternating common belief of rationality In this appendix, we sketch a proof that rationality plus agent-alternating common belief of rationality, in wh...

work page 1999

[27] [27]

The following two models deal with the KD5 case

But of course M ,l1̸⇆2 N ,l′ 1 since M ,l1|= 3a3ap but N ,l′ 1̸|= 3a3ap. The following two models deal with the KD5 case. Y . Ding, W. H. Holliday, & C. Zhang 139 m1 m2 p m3M l1 r1 l2 r2 p l3 p r3N This case is easier. For each i∈{ 1,2,3}, mi⇆a li,ri and mi⇆b ri. Then connecting m1 with r1 by ⇆alt, we have an agent-alternating bisimulation family. Hence M...

work page