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This paper explores the relationship between dynamic and truth conditional semantics for epistemic modals. It provides a generalization of a standard dynamic update semantics for modals. This new semantics derives a Kripke semantics for modals and a standard dynamic semantics for modals as special cases. The semantics allows for new characterizations of a variety of principles in modal logic, including the inconsistency of 'p and might not p'. Finally, the semantics provides a construction procedure for transforming any truth conditional semantics for modals into a dynamic semantics for modals with similar properties. [ABSTRACT FROM AUTHOR]

Modal 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. [ABSTRACT FROM AUTHOR]

Since the advent of BAN logic, many logics have been proposed for verifying authentication protocols. In one line of research, scholars have presented logics that can be utilized in verifying timed requirements of the protocols. Although many temporal epistemic logics have been developed to this end, there is no complete logic of this kind to prevent logical omniscience. Thus, they may lead to misleading judgments about the properties of the protocol being analyzed. In this paper, we propose a complete and omniscience-free temporal epistemic logic for analyzing authentication protocols. The main challenging issue in devising this logic is formulating intuitive models that on one hand reflect what is naturally meant by a protocol execution and on the other hand make it possible to achieve properties such as completeness. We show that such models can build on interpreted systems and that the resulting logic is useful in analyzing authentication protocols. [ABSTRACT FROM AUTHOR]

The fragment of the language of modal logic that consists of all implications A → B, where A and B are built from variables, the constant ⊤ (truth), and the connectives ∧ and ◊1,◊2,...,◊m. For the polymodal logic S5m (the logic of m equivalence relations) and the logic K4.3 (the logic of irreflexive linear orders), an axiomatization of such fragments is found and their algorithmic decidability in polynomial time is proved. [ABSTRACT FROM AUTHOR]

In this work, we combine features from Justification Logics and Logics of Plausibility-Based Beliefs to build a logic for Multi-Agent Systems where each agent can explicitly state his justification for believing in a given sentence. Our logic is a normal modal logic based on the standard Kripke semantics, where we provide a semantic definition for the evidence terms and define the notion of plausible evidence for an agent, based on plausibility relations in the model. As we deal with beliefs, justifications can be faulty and unreliable. In our logic, agents can disagree not only over whether a sentence is true or false, but also on whether some evidence is a valid justification for a sentence or not. After defining our logic and its semantics, we provide a strongly complete axiomatic system for it, show that it has the finite model property, analyze the complexity of its Model-Checking Problem and show that its Satisfiability Problem has the same complexity as the one from basic modal logics. Thus, this logic seems to be a good first step for the development of a dynamic logic that can model the processes of argumentation and debate in Multi-Agent Systems. [ABSTRACT FROM AUTHOR]

In this paper we investigate Kripke models, used to model knowledge or belief in a static situation, and action models, used to model communicative actions that change this knowledge or belief. The appropriate notion for structural equivalence between modal structures such as Kripke models is bisimulation: Kripke models that are bisimilar are modally equivalent. We would like to find a structural relation that can play the same role for the action models that play a prominent role in information updating. Two action models are equivalent if they yield the same results when updating Kripke models. More precisely, two action models are equivalent if it holds for all Kripke models that the result of updating with one action model is bisimilar to the result of updating with the other action model. We propose a new notion of action emulation that characterizes the structural equivalence of the important class of canonical action models. Since every action model has an equivalent canonical action model, this gives a method to decide the equivalence of any pair of action models. We also give a partial result that holds for the class of all action models. Our results extend the work in van Eijck et al. (Synthese 185(1):131–151, 2012 ). [ABSTRACT FROM AUTHOR]

The present work is motivated by two questions. (1) What should an intuitionistic epistemic logic look like? (2) How should one interpret the knowledge operator in a Kripke-model for it? In what follows we outline an answer to (2) and give a model-theoretic definition of the operator K. This will shed some light also on (1), since it turns out that K, defined as we do, fulfills the properties of a necessity operator for a normal modal logic. The interest of our construction also lies in a better insight into the intuitionistic solution to Fitch's paradox, which is discussed in the third section. In particular we examine, in the light of our definition, DeVidi and Solomon's proposal of formulating the verification thesis as $\phi \rightarrow \neg \neg K\phi$. We show, as our main result, that this definition excapes the paradox, though it is validated only under restrictive conditions on the models. [ABSTRACT FROM AUTHOR]

Standard Kripke models are inadequate to model situations of inexact knowledge with introspection, since positive and negative introspection force the relation of epistemic indiscernibility to be transitive and euclidean. Correlatively, Williamson’s margin for error semantics for inexact knowledge invalidates axioms 4 and 5. We present a new semantics for modal logic which is shown to be complete for K45, without constraining the accessibility relation to be transitive or euclidean. The semantics corresponds to a system of modular knowledge, in which iterated modalities and simple modalities are not on a par. We show how the semantics helps to solve Williamson’s luminosity paradox, and argue that it corresponds to an integrated model of perceptual and introspective knowledge that is psychologically more plausible than the one defended by Williamson. We formulate a generalized version of the semantics, called token semantics, in which modalities are iteration-sensitive up to degree n and insensitive beyond n. The multi-agent version of the semantics yields a resource-sensitive logic with implications for the representation of common knowledge in situations of bounded rationality. [ABSTRACT FROM AUTHOR]