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

Refutation Systems : An Overview and Some Applications to Philosophical Logics

Refutation systems are systems of formal, syntactic derivations, designed to derive the non-valid formulas or logical consequences of a given logic. Here we provide an overview with comprehensive references on the historical development of the theory of refutation systems and discuss some of their applications to philosophical logics

Semantic Games for Algorithmic Players

We describe a class of semantic extensive entailment game (eeg) with algorithmic players, related to game-theoretic semantics (gts), and generalized to classical first-order semantic entailment. Players have preferences for parsimonious spending of computational resources, and compute partial strategies, under qualitative uncertainty about future histories. We prove the existence of local preferences for moves, and strategic fixpoints, that allow to map eeg game-tree to the building rules and closure rules of Smullyan's semantic tableaux (st). We also exhibit a strategy profile that solves the fixpoint selection problem, and can be mapped to systematic constructions of semantic trees, yielding a completeness result by translation. We conclude on possible generalizations of our games

Asking and Answering

Questions are everywhere and the ubiquitous activities of asking and answering, as most human activities, are susceptible to failure - at least from time to time. This volume offers several current approaches to the systematic study of questions and the surrounding activities and works toward supporting and improving these activities. The contributors formulate general problems for a formal treatment of questions, investigate specific kinds of questions, compare different frameworks with regard to how they regulate the activities of asking and answering of questions, and situate these activities in a wider framework of cognitive/epistemic discourse. From the perspectives of logic, linguistics, epistemology, and philosophy of language emerges a report on the state of the art of the theory of questions

Meeting Hintikka's Challenge to Paraconsistentism

http://dx.doi.org/10.5007/1808-1711.2009v13n3p283Em uma série de seminários e conferências no Brasil em 2008, Jaakko Hintikka, em uma série de palestras no Brasil em 2008, defendeu que a “IF-lógica” (“independence friendly logic”) e a lógica paraconsistente são, em certo sentido, bastante similares. A partir do esboço de um novo sistema paraconsistente, ele afirma que várias potencialidades da IF-lógica podem ser reproduzidas na lógica paraconsistente. Uma das grandes dificuldades, deixada como um desafio, seria a formulação de condições de verdade para esta nova linguagem paraconsistente de primeira ordem, com vistas a garantir uma maior inter-relação entre esta e a IF-lógica. Argumento que tais condições de verdade não somente sugerem uma abordagem inovadora em semântica de jogos para a paraconsistência, mas também que a partir deste ponto de vista as “Lógicas da Inconsistência Formal” podem modelar a lógica interna dos elencos socráticos. Pretendo discutir estes e outros pontos levantados por Hintikka, tomando-os como desafios e oportunidades para o paraconsistentismo e para a IF-lógica, bem como levantar algumas críticas sobre a visão de Hintikka sobre a paraconsistência

Hilbert's Metamathematical Problems and Their Solutions

This dissertation examines several of the problems that Hilbert discovered in the foundations of mathematics, from a metalogical perspective. The problems manifest themselves in four different aspects of Hilbert’s views: (i) Hilbert’s axiomatic approach to the foundations of mathematics; (ii) His response to criticisms of set theory; (iii) His response to intuitionist criticisms of classical mathematics; (iv) Hilbert’s contribution to the specification of the role of logical inference in mathematical reasoning. This dissertation argues that Hilbert’s axiomatic approach was guided primarily by model theoretical concerns. Accordingly, the ultimate aim of his consistency program was to prove the model-theoretical consistency of mathematical theories. It turns out that for the purpose of carrying out such consistency proofs, a suitable modification of the ordinary first-order logic is needed. To effect this modification, independence-friendly logic is needed as the appropriate conceptual framework. It is then shown how the model theoretical consistency of arithmetic can be proved by using IF logic as its basic logic. Hilbert’s other problems, manifesting themselves as aspects (ii), (iii), and (iv)—most notably the problem of the status of the axiom of choice, the problem of the role of the law of excluded middle, and the problem of giving an elementary account of quantification—can likewise be approached by using the resources of IF logic. It is shown that by means of IF logic one can carry out Hilbertian solutions to all these problems. The two major results concerning aspects (ii), (iii) and (iv) are the following: (a) The axiom of choice is a logical principle; (b) The law of excluded middle divides metamathematical methods into elementary and non-elementary ones. It is argued that these results show that IF logic helps to vindicate Hilbert’s nominalist philosophy of mathematics. On the basis of an elementary approach to logic, which enriches the expressive resources of ordinary first-order logic, this dissertation shows how the different problems that Hilbert discovered in the foundations of mathematics can be solved

Beyond Logic. Proceedings of the Conference held in Cerisy-la-Salle, 22-27 May 2017

The project "Beyond Logic" is devoted to what hypothetical reasoning is all about when we go beyond the realm of "pure" logic into the world where logic is applied. As such extralogical areas we have chosen philosophy of science as an application within philosophy, informatics as an application within the formal sciences, and law as an application within the field of social interaction. The aim of the conference was to allow philosophers, logicians and computer scientists to present their work in connection with these three areas. The conference took place 22-27 May, 2017 in Cerisy-la-Salle at the Centre Culturel International de Cerisy. The proceedings collect abstracts, slides and papers of the presentations given, as well as a contribution from a speaker who was unable to attend