Hybrid logics with Sahlqvist axioms

Non-dual modal operators as a basis for 4-valued accessibility relations in Hybrid logic

14 Hybrid logics

Hybrid logics are an extension of modal logics where it is possible to refer to a specific state, thus allowing the description of what happens at specific states, equalities and transitions between them. This makes hybrid logics very desirable to work with relational structures.

Axiomatizing hybrid products: How can we reason many-dimensionally in hybrid logic?

Hybrid logic with the difference modality for generalisations of graphs

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.

I build a canonical model for constant domain basic first-order logic (BQLCD), the constant domain first-order extension of Visser's basic propositional logic, and use the canonical model to verify that BQLCD satisfies the disjunction and existence properties.

Summary This is a preliminary article to prove the completeness theorem of an extension of basic propositional temporal logic. We base it on the proof of completeness for basic propositional temporal logic given in [12]. We introduce n-ary connectives and prove their properties. We derive temporal logic formulas.

Boolean connexive logic is an extension of Boolean logic that is closed under Modus Ponens and contains Aristotle's and Boethius' theses. According to these theses (i) a sentence cannot imply its negation and the negation of a sentence cannot imply the sentence; and (ii) if the antecedent implies the consequent, then the antecedent cannot imply the negation of the consequent and if the antecedent implies the negation of the consequent, then the antecedent cannot imply the consequent. Such a logic was first introduced by Jarmużek and Malinowski, by means of so-called relating semantics and tableau systems. Subsequently its modal extension was determined by means of the combination of possible-worlds semantics and relating semantics. In the following article we present axiomatic systems of some basic and modal Boolean connexive logics. Proofs of completeness will be carried out using canonical models defined with respect to maximal consistent sets.

Argument evaluation , one of the central problems in argumentation theory, consists in studying what makes an argument a good one. This paper proposes a formal approach to argument evaluation from the perspective of justification logic. We adopt a multi-agent setting, accepting the intuitive idea that arguments are always evaluated by someone. Two general restrictions are imposed on our analysis: non-deductive arguments are left out and the goal of argument evaluation is fixed: supporting a given proposition. Methodologically, our approach uses several existing tools borrowed from justification logic, awareness logic, doxastic logic and logics for belief dependence. We start by introducing a basic logic for argument evaluation, where a list of argumentative and doxastic notions can be expressed. Later on, we discuss how to capture the mentioned form of argument evaluation by defining a preference operator in the object language. The intuitive picture behind this definition is that, when assessing a couple of arguments, the agent puts them to a test consisting of several criteria (filters). As a result of this process, a preference relation among the evaluated arguments is established by the agent. After showing that this operator suffers a special form of logical omniscience, called preferential omniscience, we discuss how to define an explicit version of it, more suitable to deal with non-ideal agents. The present work exploits the formal notion of awareness in order to model several informal phenomena: awareness of sentences, availability of arguments and communication between agents and external sources (advisers). We discuss several extensions of the basic logic and offer completeness and decidability results for all of them.

In the process of information semantic integration for product design and manufacturing, it is very important to express the product information semantic. Description logics (DLs) are a family of state-of-the-art knowledge representation languages, and a decidable subset of first-order logic. Firstly, by analyzing the characteristics of product information, proposed a semantic information description framework based on description logics for product information integration, which is divided into three levels: basic description logic, classic extended logic and unusual extended logic. Then, in the framework, reducer was taken for example to illustrate the application of their description logic in product design and manufacturing formal semantic information. Finally, based on description logic, discussed reasoning problems of product design and manufacturing information.

We consider an extension of modal logic with an operator for constructing inflationary fixed points, just as the modal µ-calculus extends basic modal logic with an operator for least fixed points. Least and inflationary fixed point operators have been studied and compared in other contexts, particularly in finite model theory, where it is known that the logics IFP and LFP that result from adding such fixed point operators to first order logic have equal expressive power. As we show, the situation in modal logic is quite different, as the modal iteration calculus (MIC) we introduce has much greater expressive power than the µ-calculus. Greater expressive power comes at a cost: the calculus is algorithmically much less manageable.

Two cut‐free sequent calculi which are conservative extensions of Visser's Formal Propositional Logic (FPL) are introduced. These satisfy a kind of subformula property and by this property the interpolation theorem for FPL are proved. These are analogies to Aghaei‐Ardeshir's calculi for Visser's Basic Propositional Logic.

Conflicting rules and rules with exceptions are very common in natural language specification to describe the behaviour of devices operating in a real-world context. This is common exactly because those specifications are processed by humans, and humans apply common sense and strategic reasoning about those rules. In this paper, we deal with the challenge of providing, step by step, a model of energy saving rule specification and processing methods that are used to reduce the consumptions of a system of devices. We argue that a very promising non-monotonic approach to such a problem can lie upon Defeasible Logic. Starting with rules specified at an abstract level, but compatibly with the natural aspects of such a specification (including temporal and power absorption constraints), we provide a formalism that generates the extension of a basic defeasible logic, which corresponds to turned on or off devices. We define a procedure to achieve automatic synthesis of best practices, to be used as rules to obtain savings in electric consumptions.

Conflicting rules and rules with exceptions are very common in natural language specification to describe the behaviour of devices operating in a real-world context. This is common exactly because those specifications are processed by humans, and humans apply common sense and strategic reasoning about those rules. In this paper, we deal with the challenge of providing, step by step, a model of energy saving rule specification and processing methods that are used to reduce the consumptions of a system of devices. We argue that a very promising non-monotonic approach to such a problem can lie upon Defeasible Logic. Starting with rules specified at an abstract level, but compatibly with the natural aspects of such a specification (including temporal and power absorption constraints), we provide a formalism that generates the extension of a basic defeasible logic, which corresponds to turned on or off devices.