Bilattice logic of epistemic actions and knowledge

International audienceBaltag, Moss, and Solecki proposed an expansion of classical modal logic, called logic of epistemic actions and knowledge (EAK), in which one can reason about knowledge and change of knowledge. Kurz and Palmigiano showed how duality theory provides a flexible framework for modeling such epistemic changes, allowing one to develop dynamic epistemic logics on a weaker propositional basis than classical logic (for example an intuitionistic basis). In this paper we show how the techniques of Kurz and Palmigiano can be further extended to define and axiomatize a bilattice logic of epistemic actions and knowledge (BEAK). Our propositional basis is a modal expansion of the well-known four-valued logic of Belnap and Dunn, which is a system designed for handling inconsistent as well as potentially conflicting information. These features, we believe, make our framework particularly promising from a computer science perspective

Assertion, Rejection, and Semantic Universals

Natural language contains simple lexical items for some but not all Boolean operators. English, for example, contains conjunction and, disjunction or, negated disjunction nor, but no word to express negated conjunction *nand nor any other Boolean connective. Natural language grammar can be described by a logic that expresses what the lexicon can express by its primitives, and the rest compositionally. Such logic for propositional connectives is described here as a bilateral extension of update semantics. The basic intuition is that a context can be updated by assertion or by rejection, and by one or multiple propositions at once. These distinctions suffice to characterize the logic of the lexicon

A family of graded epistemic logics

Multi-Agent Epistemic Logic has been investigated in Computer Science [Fagin, R., J. Halpern, Y. Moses and M. Vardi, “Reasoning about Knowledge,” MIT Press, USA, 1995] to represent and reason about agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge and probabilities [Fagin, R. and J. Halpern, Reasoning about knowledge and probability, Journal of the ACM 41 (1994), pp. 340–367] and also with a fuzzy semantics have been proposed [Fitting, M., Many-valued modal logics, Fundam. Inform. 15 (1991), pp. 235–254; Maruyama, Y., Reasoning about fuzzy belief and common belief: With emphasis on incomparable beliefs, in: IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16–22, 2011, 2011, pp. 1008–1013]. This paper introduces a parametric method to build graded epistemic logics inspired in the systematic method to build Multi-valued Dynamic Logics introduced in [Madeira, A., R. Neves and M. A. Martins, An exercise on the generation of many-valued dynamic logics, J. Log. Algebr. Meth. Program. 85 (2016), pp. 1011–1037. URL http://dx.doi.org/10.1016/j.jlamp.2016.03.004; Madeira, A., R. Neves, M. A. Martins and L. S. Barbosa, A dynamic logic for every season, in: C. Braga and N. Martí-Oliet, editors, Formal Methods: Foundations and Applications – 17th Brazilian Symposium, SBMF 2014, Maceió, AL, Brazil, September 29-October 1, 2014. Proceedings, Lecture Notes in Computer Science 8941 (2014), pp. 130–145. URL http://dx.doi.org/10.1007/978-3-319-15075-8_9]. The parameter in both methods is the same: an action lattice [Kozen, D., On action algebras, Logic and Information Flow (1994), pp. 78–88]. This algebraic structure supports a generic space of agent knowledge operators, as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non bivalent interpretation of the assertions (as a residuated lattice).publishe

Probabilistic epistemic updates on algebras

The present article contributes to the development of the mathematical theory of epistemic updates using the tools of duality theory. Here, we focus on Probabilistic Dynamic Epistemic Logic (PDEL). We dually characterize the product update construction of PDEL-models as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. Thanks to this construction, an interpretation of the language of PDEL can be defined on algebraic models based on Heyting algebras. This justifies our proposal for the axiomatization of the intuitionistic counterpart of PDEL

NEW PERSPECTIVES ON INQUISITIVE SEMANTICS

Inquisitive semantics offers a unified analysis of declarative and interrogative sentences by construing information exchange as a process of raising and resolving issues. In this dissertation, I apply and extend inquisitive semantics in various new ways. On the one hand, I build upon the theoretical insight of inquisitive semantics and explore the prospect of incorporating other types of content into our conception of information exchange. On the other hand, the logical framework underlying inquisitive semantics is also of great interest in itself as it enjoys certain unique properties and is thus worth further investigation. In the first paper, I provide an account of live possibilities and model the dynamics of bringing a possibility to salience using inquisitive semantics. This account gives rise to a new dynamic analysis of conditionals, which is capable of capturing what I call the Extended Sobel Inference. In the second paper, drawing on the fact that disjunction in inquisitive semantics is understood as introducing a set of alternative answers to a question, I propose a Questions-Under-Discussion-based account of informational redundancy to tackle various Hurford sentences. In the third paper, I explore the prospect of cashing out the theoretical intuition behind inquisitive semantics using a non-bivalent framework. I develop a new logic which invalidates the Law of Excluded Middle just like inquisitive logic, but unlike inquisitive logic, it employs a negation that vindicates Double Negation Elimination

Logika otázek

Logic of Questions Michal Peliš PhD Thesis Abstract The thesis deals with logic of questions (erotetic logic), which is one of the branches of non- classical logic. In the introductory part we speak generally about formalization of questions and the newest approaches to questions in logic are summed up. We introduce a formalization based on sets of direct answers and point out the role of inferences with questions. The rest of the thesis consists of two parts that can be read independently. The first part focuses on relationships among consequence relations in inferential erotetic logic (IEL). We keep the framework of original IEL, introduced by Andrzej Wiśniewski, together with the representation of questions by sets of direct answers. Answers are strictly formulas of the declarative language. The mix of interrogatives and declaratives occours just on the level of consequences. Consequence relations with questions are defined by means of multiple-conclusion entailment among sets of declarative formulas. This way, one can work with classes of models and to make transparent some properties and relationships. We provide a general study of erotetic inferences based on IEL that is open for non-classical applications. The second part contains epistemic erotetic logic. A question is understood as a set of direct...Logika otázek Michal Peliš Disertační práce Abstrakt Práce se zabývá jedním z odvětví neklasických logik - logikou otázek (erotetickou logikou). V úvodní části se hovoří obecně o formalizovaném přístupu k otázkám v logice a současně je stručně shrnuta zejména nejnovější historie tohoto odvětví. Zde je též zdůvodňována smysluplnost zachycení úsudků, v nichž se otázky objevují, a je představena formalizace otázky založená na explicitním stanovení množiny přímých odpovědí. Zbytek práce je rozdělen na dvě části, které lze číst nezávisle. První část se zabývá důsledkovými relacemi v inferenční erotetické logice (inferential erotetic logic). Plně zde využíváme rámec původní inferenční erotetické logiky zavedené Andrzejem Wiśniewskim. Používáme výhradně formalizaci otázek pomocí množiny přímých odpovědí, kdy přímé odpovědi jsou formule deklarativního jazyka. Protože jsou důsledkové relace s otázkami definovány pomocí klasického vícezávěrového sémantického důsledku, využíváme při důkazech přístup založený na třídách modelů. V této části nám jde o obecný přístup ovšem s omezením, kdy je deklarativní jazyk rozšířen o otázky, ale k propojení deklarativního a interogativního jazyka dojde až na úrovni důsledkových relací. Primárním zájmem je studovat vztahy mezi jednotlivými erotetickými důsledkovými relacemi. Druhá...Department of LogicKatedra logikyFaculty of ArtsFilozofická fakult

Bilattice based Logical Reasoning for Automated Visual Surveillance and other Applications

The primary objective of an automated visual surveillance system is to observe and understand human behavior and report unusual or potentially dangerous activities/events in a timely manner. Automatically understanding human behavior from visual input, however, is a challenging task. The research presented in this thesis focuses on designing a reasoning framework that can combine, in a principled manner, high level contextual information with low level image processing primitives to interpret visual information. The primary motivation for this work has been to design a reasoning framework that draws heavily upon human like reasoning and reasons explicitly about visual as well as non-visual information to solve classification problems. Humans are adept at performing inference under uncertainty by combining evidence from multiple, noisy and often contradictory sources. This thesis describes a logical reasoning approach in which logical rules encode high level knowledge about the world and logical facts serve as input to the system from real world observations. The reasoning framework supports encoding of multiple rules for the same proposition, representing multiple lines of reasoning and also supports encoding of rules that infer explicit negation and thereby potentially contradictory information. Uncertainties are associated with both the logical rules that guide reasoning as well as with the input facts. This framework has been applied to visual surveillance problems such as human activity recognition, identity maintenance, and human detection. Finally, we have also applied it to the problem of collaborative filtering to predict movie ratings by explicitly reasoning about users preferences