"Contextual Epistemic Logic"

The Routledge Handbook of Epistemic Contextualism, 2017

1991

Under "epistemic-doxastic logic"-EDL for short-we undersland a logic system in which both concepLs, knowledge and belief, are contemplated.) So, to begin this work, and to set its main and more importam goal, I will follow their suggestion an d try to characterize "minimal epistemic statcs" in different EDL-calculi. In other words, I'll be looking for ways of describing Angela's epistemic (i.e., knowledge or belief-we'll decide it laler) stale under lhe supposition that she knows or believes only some formula a. In doing this I won't stay resiricted to the only EDL-system proposed by HM (since this logic's "knowledge branch" is S5, and I am not lhat convinced that S5 is lhe best option in formalizing knowledge), but 1*11 ralher try to work with several calculi of different strength. Thus, in Chapter I, we ll have an overview of some epistemic-doxastic logics. I will introduce several systems which we'll be working with, giving for each one an axiomatic presentalion. This will be accompanied by a small discussion about lhe tenability of the various epistemic-doxastical principies involved. Also in the syntactical part are includcd some results about lhe number of modalilies and the

Contextualism in …, 2005

A very simple contextualist treatment of a sentence containing an epistemic modal, e.g. a might be F, is that it is true iff for all the contextually salient community knows, a is F. It is widely agreed that the simple theory will not work in some cases, but the counterexamples produced so far seem amenable to a more complicated contextualist theory. We argue, however, that no contextualist theory can capture the evaluations * Thanks to Keith DeRose, Kai von Fintel, Ernie Lepore, Jason Stanley and especially Tamar Szabó Gendler and John MacFarlane for helpful discussions and suggestions for improvement. re knowledge about other possible worlds. It's not clear this is a huge problem though. Remember that a sentence containing an epistemic modal is meant to determine a function from centred worlds to functions from worlds to truth values. Provided we have a semantics that allows for semantic indeterminacy, we can just say that the functions from worlds to truth values are partial functions, and they simply aren't determined when it's unclear what the people in c know about w. Or we can say there's a default semantic rule such that w is not in f(c) (where f is the function determined by the sentence) whenever this is unclear. Since the sentences whose meanings are determined by these values of the function, like Possibly Granger might be in Prague are similarly vague, it is no harm if the function is a little vague.

Logic-Based Program Synthesis and Transformation, 2021

We propose a mechanism for automating discovery of definitions, that, when added to a logic system for which we have a theorem prover, extends it to support an embedding of a new logic system into it. As a result, the synthesized definitions, when added to the prover, implement a prover for the new logic. As an instance of the proposed mechanism, we derive a Prolog theorem prover for an interesting but unconventional epistemic Logic by starting from the sequent calculus G4IP that we extend with operator definitions to obtain an embedding in intuitionistic propositional logic (IPC). With help of a candidate definition formula generator, we discover epistemic operators for which axioms and theorems of Artemov and Protopopescu's Intuitionistic Epistemic Logic (IEL) hold and formulas expected to be non-theorems fail. We compare the embedding of IEL in IPC with a similarly discovered successful embedding of Dosen's double negation modality, judged inadequate as an epistemic operator. Finally, we discuss the failure of the necessitation rule for an otherwise successful S4 embedding and share our thoughts about the intuitions explaining these differences between epistemic and alethic modalities in the context of the Brouwer-Heyting-Kolmogorov semantics of intuitionistic reasoning and knowledge acquisition.

Journal of Philosophical Logic, 2015

Epistemic closure has been a central issue in epistemology over the last forty years. According to versions of the relevant alternatives and subjunctivist theories of knowledge, epistemic closure can fail: an agent who knows some propositions can fail to know a logical consequence of those propositions, even if the agent explicitly believes the consequence (having “competently deduced” it from the known propositions). In this sense, the claim that epistemic closure can fail must be distinguished from the fact that agents do not always believe, let alone know, the consequences of what they know—a fact that raises the “problem of logical omniscience” that has been central in epistemic logic. This paper, part I of II, is a study of epistemic closure from the perspective of epistemic logic. First, I introduce models for epistemic logic, based on Lewis’s models for counterfactuals, that correspond closely to the pictures of the relevant alternatives and subjunctivist theories of knowledge in epistemology. Second, I give an exact characterization of the closure properties of knowl edge according to these theories, as formalized. Finally, I consider the relation between closure and higher-order knowledge. The philosophical repercussions of these results and results from part II, which prompt a reassessment of the issue of closure in epistemology, are discussed further in companion papers. As a contribution to modal logic, this paper demonstrates an alternative approach to proving modal completeness theorems, without the standard canonical model construction. By “modal decomposition” I obtain completeness and other results for two non-normal modal logics with respect to new semantics. One of these logics, dubbed the logic of ranked relevant alternatives, appears not to have been previously identified in the modal logic literature. More broadly, the paper presents epistemology as a rich area for logical study.

Computational Intelligence, 1989

In the past, Kripke structures have been used to specify the semantic theory of various modal logics. More recently, modal structures have been developed as an alternative to Kripke structures for providing the semantics of such logics. While these approaches are equivalent in a certain sense, it has been argued that modal structures provide a more appropriate basis for representing the modal notions of knowledge and belief. Since these notions, rather than the traditional notions of necessity and possibility, are of particular interest to artificial intelligence, it is of interest to examine the applicability and versatility of these structures. This paper presents an investigation of modal structures by examining how they may be extended to account for generalizations of Kripke structures. To begin with, we present an alternative formulation of modal structures in terms of trees; this formulation emphasizes the relation between Kripke structures and modal structures, by showing how the latter may be obtained from the former by means of a three-step transformation. Following this, we show how modal structures may be extended to represent generalizations of possible worlds, and to represent generalizations of accessibility between possible worlds. Lastly, we show how modal structures may be used in the case of a full first-order system. In all cases, the extensions are shown to be equivalent to the corresponding extension of Kripke structures.

Acts of Knowledge: History, Philosophy and Logic, 2009

Fundamenta Informaticae, 2009

An important question in modal nonmonotonic logics concerns the limits of propositional definability for logics of the McDermott-Doyle family. Inspired by this technical question we define a variant of autoepistemic logic which provably corresponds to the logic of the McDermott-Doyle family that is based on the modal axiom p5 : 3ϕ ⊃ (¬2ϕ ⊃ 2¬2ϕ). This axiom is a natural weakening of classical negative introspection restricting its scope to possible facts. It closely resembles the axiom w5 : ϕ ⊃ (¬2ϕ ⊃ 2¬2ϕ) which restricts the effect of negative introspection to true facts. We examine p5 in the context of classical possibleworlds Kripke models, providing results for correspondence, completeness and the finite model property. We also identify the corresponding condition for p5 in the context of neighbourhood semantics. Although rather natural epistemically, this axiom has not been investigated in classical modal epistemic reasoning, probably because its addition to S4 gives the well-known strong modal system S5.

The Review of Symbolic Logic, 2009

The question of whether knowledge is definable in terms of belief, which has played an important role in epistemology for the last fifty years, is studied here in the framework of epistemic and doxastic logics. Three notions of definability are considered: explicit definability, implicit definability, and reducibility, where explicit definability is equivalent to the combination of implicit definability and reducibility. It is shown that if knowledge satisfies any set of axioms contained in S5, then it cannot be explicitly defined in terms of belief. S5 knowledge can be implicitly defined by belief, but not reduced to it. On the other hand, S4.4 knowledge and weaker notions of knowledge cannot be implicitly defined by belief, but can be reduced to it by defining knowledge as true belief. It is also shown that S5 knowledge cannot be reduced to belief and justification, provided that there are no axioms that involve both belief and justification.