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Induction and decision procedures.

Deepak Kapur, Jürgen Giesl, Mahadevan Subramaniam (2004)

RACSAM

Mechanization of inductive reasoning is an exciting research area in artificial intelligence and automated reasoning with many challenges. An overview of our work on mechanizing inductive reasoning based on the cover set method for generating induction schemes from terminating recursive function definitions and using decision procedures is presented. This paper particularly focuses on the recent work on integrating induction into decision procedures without compromising their automation.

Inf-datalog, modal logic and complexities

Eugénie Foustoucos, Irène Guessarian (2009)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Inf-Datalog extends the usual least fixpoint semantics of Datalog with greatest fixpoint semantics: we defined inf-Datalog and characterized the expressive power of various fragments of inf-Datalog in [16]. In the present paper, we study the complexity of query evaluation on finite models for (various fragments of) inf-Datalog. We deduce a unified and elementary proof that global model-checking (i.e. computing all nodes satisfying a formula in a given structure) has 1. quadratic data complexity...

Inf-datalog, Modal Logic and Complexities

Eugénie Foustoucos, Irène Guessarian (2007)

RAIRO - Theoretical Informatics and Applications

Inf-Datalog extends the usual least fixpoint semantics of Datalog with greatest fixpoint semantics: we defined inf-Datalog and characterized the expressive power of various fragments of inf-Datalog in [CITE]. In the present paper, we study the complexity of query evaluation on finite models for (various fragments of) inf-Datalog. We deduce a unified and elementary proof that global model-checking (i.e. computing all nodes satisfying a formula in a given structure) has 1. quadratic data complexity...

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