Epistemic Modalities

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.

Journal of Philosophical Logic, 2018

The standard account of modal expressions in natural language analyzes them as quantifiers over a set of possible worlds determined by the evaluation world and an accessibility relation. A number of authors – most notably Yalcin (2007) – have recently argued for an alternative account according to which modals are analyzed as quantifying over a domain of possible worlds that is specified directly in the points of evaluation. But the new approach only handles the data motivating it if it is supplemented with a non-standard account of attitude verbs and conditionals. It can be shown the the relational account handles the same data equally well if it too is supplemented with a non-standard account of such expressions.

Mind, 2007

Epistemic modal operators give rise to something very like, but also very unlike, Moore's paradox. I set out the puzzling phenomena, explain why a standard relational semantics for these operators cannot handle them, and recommend an alternative semantics. A pragmatics appropriate to the semantics is developed and interactions between the semantics, the pragmatics, and the definition of consequence are investigated. The semantics is then extended to probability operators. Some problems and prospects for probabilistic representations of content and context are explored.

2008

Epistemic modals are interesting in part because their semantics is bound up both with our information about the world and with how that information changes as we share what we know. Given that epistemic modals are dependent in some way on the information available in the contexts in which they are used, it's not surprising that there is a minor but growing industry of work in semantics and the philosophy of language concerned with the precise nature of the context-dependency of epistemically modalized sentences.

Epistemic modals are a prominent topic in the literature on natural language semantics, with wide-ranging implications for issues in philosophy of language and philosophical logic. Considerations about the role that epistemic "might" and "must" play in discourse and reasoning have led to the development of several important alternatives to classical possible worlds semantics for natural language modal expressions. This is an opinionated overview of what I take to be some of the most exciting issues and developments in the field.

Lecture Notes in Computer Science, 2006

Modal logic programming is one of appropriate approaches to deal with reasoning about epistemic states of agents. We specify here the least model semantics, the fixpoint semantics, and an SLD-resolution calculus for modal logic programs in the multimodal logic KD4Ig5a, which is intended for reasoning about belief and common belief of agents. We prove that the presented SLD-resolution calculus is sound and complete. We also present a formalization of the wise men puzzle using a modal logic program in KD4Ig5a. This shows that it is worth to study modal logic programming for multi-agent systems.

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

Theory and Decision Library, 1997

In the field of Artificial Intelligence and Computer Science, the modal system S5 is a familiar logic to model knowledge. Although the system on the one hand models an idealized notion of knowledge (the epistemic agent is assumed to be fully introspective, for example, and S5 knowledge also suffers from the problem of logical omniscience-the agent knows all logical validities, and his knowledge is closed under logical consequence-see Wansing, 1990 for a discussion and relaxations of these properties), its nice mathematical properties, on the other hand, often motivate researchers to adopt this system in their first exploration of the field. Then, for specific purposes, such as decisionand game-theoretic applications, some or many of these idealizations concerning introspective properties or logical omniscience are given up or, sometimes, replaced by weaker assumptions about knowledge. It is a well-known fact that the idealized modal system S5 exactly describes the valid formulas of Kripke models in which the accessibility relation is an equivalence relation. In the case of one agent, one may use a result about preservation of truth under taking so-called generated sub-models (the formulas 35

2003

Page 1. Epistemic Modals and Conditionals Revisited Kai von Fintel Massachusetts Institute of Technology UMass Linguistics Colloquium, December 12, 2003 Epistemic Modals and Conditionals Outline Outline of this Talk What I Learned in Grad School Complaints An Expressive Analysis of Epistemic Modals and Conditionals?