Analytic Tableaux and Database Repairs: Foundations

Database Repairs and Analyti Tableaux

Free Variable Tableaux for Propositional Modal Logics

Free-variable semantic tableaux are a well-established technique for first-order theorem proving where free variables act as a meta-linguistic device for tracking the eigenvariables used during proof search. We present the theoretical foundations to extend this technique to propositional modal logics, including non-trivial rigorous proofs of soundness and completeness, and also present various ...

Semantic foundations for the view update problem

We present a declarative framework for updating views over indefinite databases, that is, databases with null values. The framework follows the standard database approach, which allows for a unique null constant. As the main contributions of the paper, we introduce the concept of an indefinite deductive database as a formal representation of a view over an indefinite database, propose a semanti...

Bivalent semantics, generalized compositionality and analytic classic-like tableaux for finite-valued logics

The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a mechanism for producing a classic-like description of them in terms of an effective variety of bivalent semantics; (ii) a mechanism for extracting, from the bival...

Tableau Cycling and Catalan Numbers

We develop two combinatorial proofs of the fact that certain Young tableaux are counted by the Catalan numbers. The setting is a larger class of tableaux where labels increase along rows without attention to whether labels increase down columns. We define a new operation called tableau cycling. It is used to duplicate the reflection argument attributed to André in the tableaux setting, and also...