Erotetic Epistemic Logic

What do epistemic logic and cognitive science have to do with each other?

Epistemic Logic and Information Update

This handbook provides a systematic survey of the central areas of philosophical logic. It is divided into four volumes, each devoted to a major sub-field within the disciplines. The articles should be of value to general philosophers, linguists, logicians, mathematicians and computer scientists. Volume 1, Elements of Classical Logic, deals with the background to what has come to be considered the standard formulation of predicate logic - both as far as its semantics and proof theory are concerned. The central chapter on predicate logic is followed by chapters outlining various alternative, but essentially equivalent ways of constructing the semantics for first-order logic as well as its proof theory. In addition, this volume contains a discussion of higher-order extensions of first-order logic and a compendium of the algorithmic and decision-theoretic prerequisites in the study of logical systems. Volume 2, Extensions of Classical Logic, surveys the most significant extensions of predicate logic and their applications to various philosophical fields of inquiry. The 12 chapters in this volume together provide a succinct introduction to a variety of intensional frameworks, a discussion of the most well-known logical systems, as well as an overview of major applications and of the open problems in the respective fields. Volume 3, Alternatives to Classical Logic, consists of a series of surveys of some of the alternatives to the basic assumptions of classical logic. These include many-valued logic, partial logic, free logic, relevance and entailment logics, dialogue logic, quantum logic and intuitionism. Volume 4, Topics in the Philosophy of Language, presents a panorama of the applications of logical tools and methods in the formal analysis of natural language. Since a number of developments in philosophical logic were originally stimulated by concern arising in the semantic analysis of natural language discourse, the chapters in this volume provide some criteria of evaluation of the applications of work in philosophical logic. In revealing both the adequacies and inadequacies of logical investigations in the semantic structures of natural discourse, these chapters also point the way to future developments in philosophical logic in general and thus close again the circle of inquiry relating logic and language.

In this paper, we exploit epistemic logic (or the modal logic of knowledge) for multiagent systems to discuss the compositionality of several privacy-related information-hiding/disclosure properties. The properties considered here are anonymity, privacy, onymity, and identity. Our initial observation reveals that anonymity/privacy properties are not necessarily sequentially compositional. This means that even though a system comprising several sequential phases satisfies a certain unlinkability property in each phase, the entire system does not always enjoy a desired unlinkability property. We show that the compositionality can be guaranteed provided that the phases of the system satisfy what we call independence assumptions. More specifically, we develop a series of theoretical case studies of what assumptions are sufficient to guarantee the sequential compositionality of various degrees of anonymity, privacy, onymity, and/or identity properties. Similar results for parallel composition are also discussed. Further, we use the probabilistic extension of epistemic logic to consider the compositionality of probabilistic anonymity/privacy. We show that the compositionality can also be guaranteed in the probabilistic setting, provided that the phases of the system satisfy a probabilistic independence assumption.

In this paper I examine a cluster of concepts relevant to the methodology of truth theories: 'informative definition', 'recursive method', 'semantic structure', 'logical form', 'compositionality', etc. The interrelations between these concepts, I will try to show, are more intricate and multi-dimensional than commonly assumed.

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundness, completeness, and finite model property of our multi-agent justification logic with respect to this Kripke-style semantics. We demonstrate that our logic is a conservative extension of Yavorskaya's minimal bimodal explicit evidence logic, which is a two-agent version of LP. We discuss the relationship of our logic to the multi-agent modal logic S4 with common knowledge. Finally, we give a brief analysis of the coordinated attack problem in the newly developed language of our logic.

The Logic of Proofs LP captures the invariant propositional properties of proof predicates t is a proof of F with a set of operations on proofs sufficient for realizing the whole modal logic S4 and hence the intuitionistic logic IPC. Some intuitive properties of proofs, however, are not invariant and hence not present in LP. For example, the choice function '+' in LP, which is specified by the condition s:F∨t:F → (s+t):F, is not necessarily symmetric. In this paper, we introduce an extension of the Logic of Proofs, SLP, which incorporates natural properties of the standard proof predicate in Peano Arithmetic: t is a code of a derivation containing F, including the symmetry of Choice. We show that SLP produces Brouwer-Heyting-Kolmogorov proofs with a rich structure, which can be useful for applications in epistemic logic and other areas.

We show that dynamic epistemic logic (DEL) is a substructural logic and that it is an extension of the update logic introduced in the companion article [12]. We identify axioms and inference rules that completely characterize the DEL product update, and we provide a sequent calculus for DEL. Finally, we show that DEL with a finite number of atomic events is as expressive as epistemic logic. In parallel, we provide a sequent calculus for update logic which turns out to be a generalization of the non-associative Lambek calculus.

With the amount of information available to us today, making sense of potentially conflicting information is a problem that we are bound to run into. We aim to study this problem from the perspective of epistemic logic. So far, we have studied logics for reasoning about information distributed across groups of agents in the epistemic logic framework, focusing on the notion of distributed belief. We have introduced the notions of cautious and bold distributed belief. These are intended as alternatives to the standard distributed belief, behaving better when agents have conflicting beliefs. With standard distributed belief, such situations lead to explosion: everything becomes distributedly believed. The idea behind the new notions is that we look at maximal consistent subgroups, allowing us to meaningfully express that a group collectively possesses information supporting a belief, also in cases where some group members disagree. Going forward, we are interested in continuing to explore the aggregation of potentially conflicting information in the setting of epistemic logic, e.g. by looking at distributed belief in richer extensions of epistemic logic and in relation to other areas that deal with similar problems.

The aim of this paper is to explore the advantages deriving from the application of relating semantics in epistemic logic. As a first step, I will discuss two versions of relating semantics and how they can be differently exploited for studying modal and epistemic operators. Next, I consider several standard frameworks which are suitable for modelling knowledge and related notions, in both their implicit and their explicit form and present a simple strategy by virtue of which they can be associated with intuitive systems of relating logic. As a final step, I will focus on the logic of knowledge based on justification logic and show how relating semantics helps us to provide an elegant solution to some problems related to the standard interpretation of the explicit epistemic operators.

The idealizations resulting from the use of Kripke semantics in Epistemic Logic are inherited by formalizations of group epistemic notions. For example, distributed knowledge is often taken to reflect the potential knowledge of a group: what agents would know if they had unbounded means of communication and deductive ability. However, this does not specify whether/how this potential can be actualized, especially since real people are not unbounded reasoners. Inspired by experiments on group reasoning, we identify two dimensions of actualizing distributed knowledge: communication and inference. We build a dynamic framework with effortful actions accounting for both, combining impossible-worlds semantics and action models, and we provide a method for extracting a sound and complete axiomatization.

We study imagination as reality-oriented mental simulation (ROMS): the activity of simulating nonactual scenarios in one’s mind, to investigate what would happen if they were realized. Three connected questions concerning ROMS are: What is the logic, if there is one, of such an activity? How can we gain new knowledge via it? What is voluntary in it and what is not? We address them by building a list of core features of imagination as ROMS, drawing on research in cognitive psychology and the philosophy of mind. We then provide a logic of imagination as ROMS which models such features, combining techniques from epistemic logic, action logic, and subject matter semantics. Our logic comprises a modal propositional language with non-monotonic imagination operators, a formal semantics, and an axiomatization.

The enormous influence of Kazimierz Twardowski on the shape of 20th-century Polish culture is unquestionable. The volume Reason and Will specifies which spheres did this influence concern. Firstly, the volume reconstructs the image of Twardowski’s personality and work in the eyes of his contemporaries Poles, and also pictures how they assessed this work (Jacek Jadacki, Ryszard Kleszcz). Both the image and the assessment were confronted with the facts, and this confrontation showed that they correspond to reality (Kleszcz). There were also recollected the attempts by communist ideologists to disavow the “legend” of Twardowski and his school (Jadacki) after the Second World War. Secondly, it was shown that Twardowski fulfills the criteria of being an analytical philosopher, and the analytic methods applied by him were reconstructed (Anna Brożek). Thirdly, the results achieved by Twardowski, which were of the greatest importance for the history of philosophy, were compared and thoroughly described. Some of them influenced the views not only of Polish but also foreign thinkers; e.g. the approach to intentionality on Höfler and Husserl, the object theory on Meinong, the concept of absolute truth, via Łukasiewicz and Tarski, on formal logic and logical semantics (Jan Woleński). Other Twardowski’s results have so far played an inspiring role only «locally». These include: the postulate of separating philosophy and worldview (Dariusz Łukasiewicz), the reconstruction of the concepts of understanding and reasoning, including induction (Jadacki), the exposition the practical dimension of medical “cognition” (Aleksandra Horecka), formulating the principles of rational philosophical historiography (Jadacki), explication of the notions of homeland and patriotism as the key notions of the philosophy of politics (Ryszard Mordarski, Jadacki) and systematizing the rules of general didactics and the theory of education (Wojciech Rechlewicz). Fourthly and finally, some essential ideas of Twardowski and his students were subjected to a critical analysis, including: the idea of metaphysical neutrality of logic and the idea of clarity of the scientific language (Jadacki).

This paper proposes a concise overview of the role of possibility theory in logical approaches to reasoning under uncertainty. It shows that three traditions of reasoning under or about uncertainty (set-functions, epistemic logic and three-valued logics) can be reconciled in the setting of possibility theory. We offer a brief presentation of basic possibilistic logic, and of its generalisation that comes close to a modal logic albeit with simpler more natural epistemic semantics. Past applications to various reasoning tasks are surveyed, and future lines of research are also outlined.

This chapter gives a general characterization of the notion of logical form in the light of the truth-theoretic, and then generalized fulfillment-theoretic, approach to natural language semantics. The chapter takes logical form to be semantic form. It explicates the notion of sameness of logical form by making use of the idea of corresponding canonical proofs of appropriate theorems for the sentences in interpretive truth or fulfillment theories for their languages. The chapter discusses also briefly the issue of the identification of logical constants in the language in the light of the semantic framework it employs, and some issues having to do with the extension of the notion of logical validity and logical consequence to natural languages.