Epistemic Logics

2019 ◽  
pp. 107-124
Author(s):  
Francesco Berto ◽  
Mark Jago
Keyword(s):  
Epistemic Logic ◽  
Classical Logic ◽  
Possible Worlds ◽  
Impossible Worlds ◽  
Logical Omniscience ◽  
Epistemic States ◽  
Deep Problem

Standard possible-worlds epistemic logic gives rise to the problem of logical omniscience. There are attempts to deal with the problem without using impossible worlds. A number of these approaches are discussed in this chapter and all are found wanting. The impossible worlds approach is immediately more successful, but faces a deep problem: how should impossible worlds be constrained, so as to give adequate models of knowledge and belief? One option is to take impossible worlds to be closed under some weaker-than-classical logic. But this approach does not genuinely solve the problem of logical omniscience. A different approach is the dynamic one, whereby epistemic states are not closed at any one time, but nevertheless evolve towards closure in a dynamic way.

scholarly journals QUANTIFIED LOGIC OF AWARENESS AND IMPOSSIBLE POSSIBLE WORLDS

2008 ◽  
Vol 1 (4) ◽  
pp. 514-529 ◽  
Author(s):  
GIACOMO SILLARI
Keyword(s):  
Possible Worlds ◽  
Explicit Knowledge ◽  
Impossible Worlds ◽  
Kripke Semantics ◽  
Logical Omniscience ◽  
Neighborhood Semantics ◽  
Two Systems ◽  
The Many ◽  
Implicit And Explicit

Among the many possible approaches to dealing with logical omniscience, I consider here awareness and impossible worlds structures. The former approach, pioneered by Fagin and Halpern, distinguishes between implicit and explicit knowledge, and avoids logical omniscience with respect to explicit knowledge. The latter, developed by Rantala and by Hintikka, allows for the existence of logically impossible worlds to which the agents are taken to have “epistemological” access; since such worlds need not behave consistently, the agents’ knowledge is fallible relative to logical omniscience. The two approaches are known to be equally expressive in propositional systems interpreted over Kripke semantics. In this paper I show that the two approaches are equally expressive in propositional systems interpreted over Montague-Scott (neighborhood) semantics. Furthermore, I provide predicate systems of both awareness and impossible worlds structures interpreted on neighborhood semantics and prove the two systems to be equally expressive.

From Possible to Impossible Worlds

2019 ◽  
pp. 11-40 ◽  
Author(s):  
Francesco Berto ◽  
Mark Jago
Keyword(s):  
Possible Worlds ◽  
Information Overload ◽  
Impossible Worlds ◽  
Logical Omniscience ◽  
Possible Worlds Semantics ◽  
Counterfactual Conditionals ◽  
General Issue

Possible worlds are ways things might have been. They find applications in analysing possibility and necessity; propositions; knowledge and belief; information; and indicative and counterfactual conditionals. But possible worlds semantics faces the issue of hyperintensionality, generated by concepts that require distinctions between logical or necessary equivalents. The problems of distinguishing equivalent propositions, of logical omniscience, of information overload, of irrelevant conditionals, and of counterpossible conditionals, are all instances of the general issue. Adding impossible worlds promises to help with these puzzles. But can we genuinely think about the impossible? It is argued that we can.

Principles of epistemic logic I: Knowledge

2021 ◽  
pp. 18-36
Author(s):  
Sven Rosenkranz
Keyword(s):  
Epistemic Logic ◽  
Possible Worlds ◽  
Large Family ◽  
Coarse Grained ◽  
Logical Omniscience ◽  
Fine Grained ◽  
Logic Of Knowledge ◽  
Knowledge Ascriptions ◽  
Objects Of Knowledge ◽  
Untoward Consequence

All epistemic logics come with some idealizations. Not all such idealizations seem acceptable. A large family of epistemic logics assume that if ⌜φ‎⌝ and ⌜ψ‎⌝ are logically equivalent, so are ⌜One knows that φ‎⌝ and ⌜One knows that ψ‎⌝. This assumption, characteristic of normal epistemic logics but also of many non-normal ones, is acceptable only if the objects of knowledge can be construed as sets of possible worlds known under some mode of presentation or other, where knowledge-ascriptions do not yet make those modes explicit. Unlike fine-grained conceptions that reject the assumption, such coarse-grained conceptions of the objects of knowledge have the untoward consequence that failures of logical omniscience are no longer expressible in the logic. But even on coarse-grained conceptions, epistemic logic cannot be expected to be normal. Fine-grained conceptions allow for failures of logical omniscience to be expressible in the logic. On balance, fine-grained conceptions are to be preferred. Against this backdrop, candidate principles for inclusion in the logic of knowledge are critically reviewed in the light of general epistemological considerations. Very few survive closer scrutiny.

A First-Order Logic of Limited Belief Based on Possible Worlds

2020 ◽  
Author(s):  
Gerhard Lakemeyer ◽  
Hector J. Levesque
Keyword(s):  
Knowledge Base ◽  
Epistemic Logic ◽  
Possible Worlds ◽  
Order Logic ◽  
First Order Logic ◽  
Possible World ◽  
Possible World Semantics ◽  
First Order ◽  
Epistemic States

In a recent paper Lakemeyer and Levesque proposed a first-order logic of limited belief to characterize the beliefs of a knowledge base (\KB). Among other things, they show that their model of belief is expressive, eventually complete, and tractable. This means, roughly, that a \KB\ may consist of arbitrary first-order sentences, that any sentence which is logically entailed by the \KB\ is eventually believed, given enough reasoning effort, and that reasoning is tractable under reasonable assumptions. One downside of the proposal is that epistemic states are defined in terms of sets of clauses, possibly containing variables, giving the logic a distinct syntactic flavour compared to the more traditional possible-world semantics found in the literature on epistemic logic. In this paper we show that the same properties as above can be obtained by defining epistemic states as sets of three-valued possible worlds. This way we are able to shed new light on those properties by recasting them using the more familiar notion of truth over possible worlds.

scholarly journals The Dynamic Epistemic Logic for Actual Knowledge

2020 ◽  
Vol 49 (1) ◽  
Author(s):  
Arkadiusz Wójcik
Keyword(s):  
Epistemic Logic ◽  
Dynamic Epistemic Logic ◽  
Logical Omniscience ◽  
Actual Knowledge ◽  
Knowledge Change ◽  
The Past ◽  
Knowledge Models ◽  
Complete Axiomatization ◽  
New Information

The dynamic epistemic logic for actual knowledge models the phenomenon of actual knowledge change when new information is received. In contrast to the systems of dynamic epistemic logic which have been discussed in the past literature, our system is not burdened with the problem of logical omniscience, that is, an idealized assumption that the agent explicitly knows all classical tautologies and all logical consequences of his or her knowledge. We provide a sound and complete axiomatization for this logic.

Constructing the Impossible

2021 ◽  
pp. 141-163
Author(s):  
Kit Fine
Keyword(s):  
Natural Language ◽  
Possible Worlds ◽  
Formal Languages ◽  
Impossible Worlds ◽  
Possible World ◽  
Limited Role ◽  
Wide Range ◽  
Degree Of Acceptance ◽  
Broad Role ◽  
Natural Way

Please keep the original abstract. A number of philosophers have flirted with the idea of impossible worlds and some have even become enamored of it. But it has not met with the same degree of acceptance as the more familiar idea of a possible world. Whereas possible worlds have played a broad role in specifying the semantics for natural language and for a wide range of formal languages, impossible worlds have had a much more limited role; and there has not even been general agreement as to how a reasonable theory of impossible worlds is to be developed or applied. This chapter provides a natural way of introducing impossible states into the framework of truthmaker semantics and shows how their introduction permits a number of useful applications.

scholarly journals EVERYONE KNOWS THAT SOMEONE KNOWS: QUANTIFIERS OVER EPISTEMIC AGENTS

2019 ◽  
Vol 12 (2) ◽  
pp. 255-270 ◽  
Author(s):  
PAVEL NAUMOV ◽  
JIA TAO
Keyword(s):  
Modal Logic ◽  
Epistemic Logic ◽  
Possible Worlds ◽  
Completeness Theorem ◽  
Kripke Semantics ◽  
Possible Worlds Semantics ◽  
Distributed Knowledge ◽  
First Order ◽  
Soundness And Completeness ◽  
First Order Modal Logic

AbstractModal logic S5 is commonly viewed as an epistemic logic that captures the most basic properties of knowledge. Kripke proved a completeness theorem for the first-order modal logic S5 with respect to a possible worlds semantics. A multiagent version of the propositional S5 as well as a version of the propositional S5 that describes properties of distributed knowledge in multiagent systems has also been previously studied. This article proposes a version of S5-like epistemic logic of distributed knowledge with quantifiers ranging over the set of agents, and proves its soundness and completeness with respect to a Kripke semantics.

scholarly journals Intensional models for the theory of types

2007 ◽  
Vol 72 (1) ◽  
pp. 98-118 ◽  
Author(s):  
Reinhard Muskens
Keyword(s):  
Type Theory ◽  
Possible Worlds ◽  
Sequent Calculus ◽  
Propositional Attitude ◽  
Essential Elements ◽  
Classical Type ◽  
Logical Omniscience ◽  
Small Fragment ◽  
Model Existence ◽  
Model Existence Theorem

AbstractIn this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up.

scholarly journals An Epistemic Event Calculus for ASP-based Reasoning About Knowledge of the Past, Present and Future

10.29007/zswj ◽  
2018 ◽  
Author(s):  
Jiefei Ma ◽  
Rob Miller ◽  
Leora Morgenstern ◽  
Theodore Patkos
Keyword(s):  
Classical Logic ◽  
Causal Reasoning ◽  
Possible Worlds ◽  
Event Calculus ◽  
The Past ◽  
Sensing Actions ◽  
Reasoning About Knowledge

We present a generalisation of the Event Calculus, specified in classical logic and implemented in ASP, that facilitates reasoning about non-binary-valued fluents in domains with non-deterministic, triggered, concurrent, and possibly conflicting actions. We show via a case study how this framework may be used as a basis for a "possible-worlds" style approach to epistemic and causal reasoning in a narrative setting. In this framework an agent may gain knowledge about both fluent values and action occurrences through sensing actions, lose knowledge via non-deterministic actions, and represent plans that include conditional actions whose conditions may be initially unknown.

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