Labelled Modal Tableaux

Labelled tableaux are extensions of semantic tableaux with annotations (labels, indices) whose main function is to enrich the modal object language with semantic elements. This paper consists of three parts. In the first part we consider some options for labels: simple constant labels vs labels with free variables, logic depended inference rules vs labels manipulation based on a label algebra. In the second and third part we concentrate on a particular labelled tableaux system called KEM using free variable and a specialised label algebra. Specifically in the second part we show how labelled tableaux (KEM) can account for different types of logics (e.g., non-normal modal logics and conditional logics). In the third and final part we investigate the relative complexity of labelled tableaux systems and we show that the uses of KEM's label algebra can lead to speed up on proofs

Labelled tableaux for nonmonotonic reasoning: Cumulative consequence relations

In this paper we present a labelled proof method for computing nonmonotonic consequence relations in a conditional logic setting. The method exploits the strong connection between these deductive relations and conditional logics, and it is based on the usual possible world semantics devised for the latter. The label formalism KEM, introduced to account for the semantics of normal modal logics, is easily adapted to the semantics of conditional logic by simply indexing labels with formulas. The basic inference rules are provided by the propositional system KE+ - a tableau-like analytic proof system devised to be used both as a refutation method and a direct method of proof - that is the classical core of KEM which is thus enlarged with suitable elimination rules for the conditional connective. The resulting algorithmic framework is able to compute cumulative consequence relations in so far as they can be expressed as conditional implications

Proceedings of the Joint Automated Reasoning Workshop and Deduktionstreffen: As part of the Vienna Summer of Logic – IJCAR 23-24 July 2014

Preface For many years the British and the German automated reasoning communities have successfully run independent series of workshops for anybody working in the area of automated reasoning. Although open to the general public they addressed in the past primarily the British and the German communities, respectively. At the occasion of the Vienna Summer of Logic the two series have a joint event in Vienna as an IJCAR workshop. In the spirit of the two series there will be only informal proceedings with abstracts of the works presented. These are collected in this document. We have tried to maintain the informal open atmosphere of the two series and have welcomed in particular research students to present their work. We have solicited for all work related to automated reasoning and its applications with a particular interest in work-in-progress and the presentation of half-baked ideas. As in the previous years, we have aimed to bring together researchers from all areas of automated reasoning in order to foster links among researchers from various disciplines; among theoreticians, implementers and users alike, and among international communities, this year not just the British and German communities

A Fibred Tableau Calculus for Modal Logics of Agents

In previous works we showed how to combine propositional multimodal logics using Gabbay's \emph{fibring} methodology. In this paper we extend the above mentioned works by providing a tableau-based proof technique for the combined/fibred logics. To achieve this end we first make a comparison between two types of tableau proof systems, (\emph{graph} $\&$ \emph{path}), with the help of a scenario (The Friend's Puzzle). Having done that we show how to uniformly construct a tableau calculus for the combined logic using Governatori's labelled tableau system \KEM. We conclude with a discussion on \KEM's features

Labelled Modal Sequents

In this paper we present a new labelled sequent calculus for modal logic. The proof method works with a more ``liberal'' modal language which allows inferential steps where different formulas refer to different labels without moving to a particular world and there computing if the consequence holds. World-paths can be composed, decomposed and manipulated through unification algorithms and formulas in different worlds can be compared even if they are sub-formulas which do not depend directly on the main connective. Accordingly, such a sequent system can provide a general definition of modal consequence relation. Finally, we briefly sketch a proof of the soundness and completeness results

An Algebraic Approach for Action Based Default Reasoning

Often, we assume that an action is permitted simply because it is not explicitly forbidden; or, similarly, that an action is forbidden simply because it is not explicitly permitted. This kind of assumptions appear, e.g., in autonomous computing systems where decisions must be taken in the presence of an incomplete set of norms regulating a particular scenario. Combining default and deontic reasoning over actions allows us to formally reason about such assumptions. With this in mind, we propose a logical formalism for default reasoning over a deontic action logic. The novelty of our approach is twofold. First, our formalism for default reasoning deals with actions and action operators, and it is based on the deontic action logic originally proposed by Segerberg. Second, inspired by Segerberg´s approach, we use tools coming from the theory of Boolean Algebra. These tools allow us to extend Segerberg´s algebraic completeness result to the setting of Default Logics.Fil: Castro, Pablo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Río Cuarto. Facultad de Ciencias Exactas Fisicoquímicas y Naturales; ArgentinaFil: Cassano, Valentin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaFil: Fervari, Raul Alberto. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Areces, Carlos Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; ArgentinaSeventeenth Conference on Theoretical Aspects of Rationality and KnowledgeToulouseFranciaUniversité Toulous

An algebraic approach for action based default reasoning

Often, we assume that an action is permitted simply because it is not explicitly forbidden; or, similarly, that an action is forbidden simply because it is not explicitly permitted. This kind of assumptions appear, e.g., in autonomous computing systems where decisions must be taken in the presence of an incomplete set of norms regulating a particular scenario. Combining default and deontic reasoning over actions allows us to formally reason about such assumptions. With this in mind, we propose a logical formalism for default reasoning over a deontic action logic. The novelty of our approach is twofold. First, our formalism for default reasoning deals with actions and action operators, and it is based on the deontic action logic originally proposed by Segerberg in [27]. Second, inspired by Segerberg?s approach, we use tools coming from the theory of Boolean Algebra. These tools allow us to extend Segerberg?s algebraic completeness result to the setting of Default Logics.Fil: Castro, Pablo Francisco. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Rio Cuarto. Facultad de Cs.exactas Fisicoquímicas y Naturales. Departamento de Computación. Grupo de Ingeniería de Software; ArgentinaFil: Cassano, Valentin. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Fervari, Raul Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; ArgentinaFil: Areces, Carlos Eduardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Deductive Systems in Traditional and Modern Logic

The book provides a contemporary view on different aspects of the deductive systems in various types of logics including term logics, propositional logics, logics of refutation, non-Fregean logics, higher order logics and arithmetic

Temporal Reasoning and MAS

In this paper we investigate if it is possible and useful to reason about time within social/normative multi-agent systems (MAS) by taking into account the general guidelines of tense logic. We focus on the combination of special-purpose logics: we provide a formal account in which a minimal temporalization helps in reasoning about time in an abstract way. We also explore a new variant of deontic tense logic by using a hybrid tense logic. The accounts provided allow to model temporal provisions within both particular norms and general legal principles, and also help in the detection of breaches of good faith and confidence.Facultad de Ciencias Jurídicas y SocialesFacultad de Informátic