Decidability and Complexity of Some Finitely-valued Dynamic Logics

Propositional Dynamic Logic, PDL, is a well known modal logic formalizing reasoning about complex actions. We study many-valued generalizations of PDL based on relational models where satisfaction of formulas in states and accessibility between states via action execution are both seen as graded notions, evaluated in a finite Łukasiewicz chain. For each n>1, the logic PDŁn is obtained using the n-element Łukasiewicz chain, PDL being equivalent to PDŁ2. These finitely-valued dynamic logics can be applied in formalizing reasoning about actions specified by graded predicates, reasoning about costs of actions, and as a framework for certain graded description logics with transitive closure of roles. Generalizing techniques used in the case of PDL we obtain completeness and decidability results for all PDŁn. A generalization of Pratt's exponential-time algorithm for checking validity of formulas is given and EXPTIME-hardness of each PDŁn validity problem is established by embedding PDL into PDŁn.

Reasoning about Petri Nets: A Calculus Based on Resolution and Dynamic Logic

Petri Nets are a widely used formalism to deal with concurrent systems. Dynamic Logics (DLs) are a family of modal logics where each modality corresponds to a program. Petri-PDL is a logical language that combines these two approaches: it is a dynamic logic where programs are replaced by Petri Nets. In this work we present a clausal resolution-based calculus for Petri-PDL. Given a Petri-PDL formula, we show how to obtain its translation into a normal form to which a set of resolution-based inference rules are applied. We show that the resulting calculus is sound, complete, and terminating. Some examples of the application of the method are also given.

A Simple Logic of Functional Dependence

This paper presents a simple decidable logic of functional dependence LFD, based on an extension of classical propositional logic with dependence atoms plus dependence quantifiers treated as modalities, within the setting of generalized assignment semantics for first order logic. The expressive strength, complete proof calculus and meta-properties of LFD are explored. Various language extensions are presented as well, up to undecidable modal-style logics for independence and dynamic logics of changing dependence models. Finally, more concrete settings for dependence are discussed: continuous dependence in topological models, linear dependence in vector spaces, and temporal dependence in dynamical systems and games.

Complexity of finite-variable fragments of products with K

We show that products and expanding relativized products of propositional modal logics where one component is the minimal monomodal logic K are polynomial-time reducible to their single-variable fragments. Therefore, the known lower-bound complexity and undecidability results for such logics are extended to their single-variable fragments. Similar results are obtained for products where one component is a polymodal logic with a K-style modality; these include products with propositional dynamic logics.

Emotions and Dispositional Predicates

Affective computing and affective calculus are currently one of the rapidly developing areas of interdisciplinary research. The aim of the article is to examine the approach to building a formalized theory of emotions developed by the Dutch logicians B. Steunebrink, M. Dastani and J.-J. Ch. Meyer, as well as the analysis of this theory for the use of dispositional predicates in it. Reduction definitions for observation predicates and dispositional predicates in the analyzed theory of emotions are constructed in terms of emotion triggers and emotion experience predicates, which are then reduced to expressions of the language of epistemic and dynamic logics.

Configurarea Paradigmei Terţului Inclus – Blaga, Bachelard, Lupaşcu1

This paper aims to present the connection and continuity between the implicit principles that configure the transgressive visions of Lucian Blaga, Gaston Bachelard and Ștefan Lupașcu, which inaugurate a paradigmatic change in consensus with the revolutionary ideas circulating in science, philosophy, poetry and art across the 20th century. The subtle paradigmatic axis which crosses implicitly or explicitly the work of Lucian Blaga proves to be the transgressive attempt of integration and overcoming of the antinomies under the sign of the included middle which underlies the transfiguring core of the dogmatic paradox. Thus, the nucleus of Blaga’s epistemological vision, the dogmatic paradox – a synthesis of the antinomies solved not in concrete level, but in transcendent one, creating a paradoxical logics – proves to be close to Gaston Bachelard’s transgressive theoretical constructions – the surrationalism and the philosophy of no –, as well as to Ştefan Lupaşcu’s integrative perspective of the dynamic logics of the contradictory. The subtly related nexus of theoretical ideas developed by Blaga, Bachelard and Lupașcu appear to be essential milestones in the avant-garde of the paradigmatic chain of the included middle, opening it towards the present European episteme.