nLab S5 modal logic as epistemic logic -- references

S5 modal logic as epistemic logic

Discussion of S5 modal logic as epistemic logic:

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

$[$Ditmarsch, Hoek & Kooi (2008):$]$ “in Aumann’s survey paper on interactive epistemology the reader will immediately recognise the system S5.”

• Joseph Y. Halpern, Yoram Moses, §2.3 in: A guide to completeness and complexity for modal logics of knowledge and belief, Artificial Intelligence 54 3 (1992) 319-379 $[$doi:10.1016/0004-3702(92)90049-4$]$

• Ronald Fagin, Joseph Y. Halpern, Yoram Moses, Moshe Y. Vardi, Reasoning About Knowledge, The MIT Press (1995) $[$ISBN:9780262562003$]$

p. 35: “in a precise sense the S5 properties completely characterize our definition of knowledge”

• Joseph Y. Halpern, Should knowledge entail belief?, Journal of Philosophical Logic 25 5 (1996) 483-494 $[$jstor:30226583, philpapers:HALSKE$]$

• Melvin Fitting, Logics of Knowlege, Sec. 9 in: Modal proof theory, Ch. 2 in: The Handbook of Modal Logic, Studies in Logic and Practical Reasoning 3 (2007) 85-183 $[$doi:10.1016/S1570-2464(07)80005-X, book webpage$]$

pp. 121: “What standard logics of knowledge capture is not actual knowledge, but potential knowledge — what one is entitled to know. The switch to potential knowledge means we drop all considerations of complexity $[...]$ It is easy to see that, under such an assumption, a knowledge modality should be a normal modal operator. But, what else should be required? $[...]$ All these together make a knowledge operator obey the S5 conditions.”

• Wiebe van der Hoek, Marc Pauly, Epistemic Logic, Sec 4 in: Modal logic for games and information, Ch. 20 in: The Handbook of Modal Logic, Studies in Logic and Practical Reasoning 3 (2007) 85-183 $[$doi:10.1016/S1570-2464(07)80023-1, book webpage$]$

p. 198: “Modal epistemic logic, the logic of knowledge, provides a very natural interpretation to the accessibility relation in Kripke models. For an agent $i$, two worlds $w$ and $v$ are connected (written $R_i w v$), if the agent cannot (epistemically) distinguish them. In other words, we have $R_i v w$ if, according to $i$’s information at $w$, the world might as well be in state $v$, or that $v$ is compatible with i’s information at w. Using this interpretation of access, $R_i$ is obviously an equivalence relation. $[...]$ Thus, we are in the realm of the multi-modal logic $S5_m$.”

• Hans Ditmarsch, Wiebe Hoek, Barteld Kooi, Epistemic Logic, chapter 2 in: Dynamic Epistemic Logic, Studies In Epistemology, Logic, Methodology, And Philosophy Of Science (SYLI) 337, Springer (2008) $[$doi:10.1007/978-1-4020-5839-4_2, pdf$]$

p. 11: “The logical system S5 is by far the most popular and accepted epistemic logic”

• Dov Samet, S5 knowledge without partitions, Synthese 172 (2010) 145–155 $[$doi:10.1007/s11229-009-9469-0$]$

• Meghyn Bienvenu, Hélène Fargier, Pierre Marquis, Knowledge Compilation in the Modal Logic S5, Proceedings of the AAAI Conference on Artificial Intelligence 24 1 (2010) $[$doi:10.1609/aaai.v24i1.7587, pdf$]$

  p. 1: “Propositional epistemic logic S5 is a well-known modal logic which is suitable for representing and reasoning about the knowledge of a single agent”

• Rasmus Rendsvig, John Symons, Epistemic Logic, The Stanford Encyclopedia of Philosophy (2011) $[$web$]$

“Fagin, Halpern, Moses, and Vardi (1995) and many others use S5 for knowledge”

• Rachel Boddy, Epistemic Issues and Group Knowledge, Amsterdam (2014) $[$pdf$]$

p. 13: “Formal approaches to epistemology – such as game theory and computer science – typically assume the S5 conditions for knowledge, which is (partly) explained by the convenient formal properties of the logic. Philosophers typically opt for a weaker notion. Hintikka (1962), for instance, argues that the proper logic for knowledge is the modal system S4”

• Yakoub Salhi and Michael Sioutis, A Resolution Method for Modal Logic S5, EPiC Series in Computer Science 36 (2015) 252–262 $[$pdf$]$

• Ronald de Haan, Iris van de Pol, On the Computational Complexity of Model Checking for Dynamic Epistemic Logic with S5 Models $[$arXiv:1805.09880$]$