Deciding regular grammar logics with converse through first-order logic

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. A consequence of the translation is that the general satisfiability problem for regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Using the same method, we show how some other modal logics can be naturally translated into GF2, including nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed point-operators.Comment: 34 page

Semantic transfer and contradictory evidence in intuitionistic fuzzy sets

The relationship between object level intuitionistic fuzzy sets and predicate based intuitionistic fuzzy sets is explored. Mass assignment uses a process called semantic unification to evaluate the degree to which one set supports another, the inverse function is semantic separation. Intuitionistic fuzzy sets are mapped onto a mass assignment framework and the semantic unification operator is generalised to support both mass assignment and intuitionistic fuzzy sets, as is semantic separation. Transfer of inconsistent and contradictory evidence are also dealt with

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

On Deriving Nested Calculi for Intuitionistic Logics from Semantic Systems

This paper shows how to derive nested calculi from labelled calculi for propositional intuitionistic logic and first-order intuitionistic logic with constant domains, thus connecting the general results for labelled calculi with the more refined formalism of nested sequents. The extraction of nested calculi from labelled calculi obtains via considerations pertaining to the elimination of structural rules in labelled derivations. Each aspect of the extraction process is motivated and detailed, showing that each nested calculus inherits favorable proof-theoretic properties from its associated labelled calculus

The Logic of Partitions: Introduction to the Dual of the Logic of Subsets

Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms--which is reflected in the duality between quotient objects and subobjects throughout algebra. Modern categorical logic as well as the Kripke models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic might be the logic of subsets of a given universe set. If "propositional" logic is thus seen as the logic of subsets of a universe set, then the question naturally arises of a dual logic of partitions on a universe set. This paper is an introduction to that logic of partitions dual to classical subset logic. The paper goes from basic concepts up through the correctness and completeness theorems for a tableau system of partition logic