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Domains and Lambda-Calculi
Graduate text on mathematical foundations of programming languages, and operational and denotational semantics.
Gentzen Calculi for Modal Propositional Logic
The book is about Gentzen calculi for (the main systems of) modal logic. It is divided into three parts. In the first part we introduce and discuss the main philosophical ideas related to proof theory, and we try to identify criteria for distinguishing good sequent calculi. In the second part we present the several attempts made from the 50’s until today to provide modal logic with Gentzen calculi. In the third and and final part we analyse new calculi for modal logics, called tree-hypersequent calculi, which were recently introduced by the author. We show in a precise and clear way the main results that can be proved with and about them.
Relevancy Based Use of Lemmas in Connection Tableau Calculi
Automated deduction is a fundamental research area in the field of artificial intelligence. The aim of an automated deduction system is to find a formal proof for a given goal based on given axioms. Essentially automated deduction can be viewed as a search problem which spans huge search spaces. One main thrust of research in automated deduction is the development of techniques for achieving a reduction of the search space. A particularly promising approach for search space reduction relies on the integration of top-down and bottom-up reasoning. A possible approach employs bottom-up generated lemmas in top-down systems. Lemma use offers the possibility to shorten proofs and to overcome weakn...
Observational Calculi and Association Rules
Observational calculi were introduced in the 1960’s as a tool of logic of discovery. Formulas of observational calculi correspond to assertions on analysed data. Truthfulness of suitable assertions can lead to acceptance of new scientific hypotheses. The general goal was to automate the process of discovery of scientific knowledge using mathematical logic and statistics. The GUHA method for producing true formulas of observational calculi relevant to the given problem of scientific discovery was developed. Theoretically interesting and practically important results on observational calculi were achieved. Special attention was paid to formulas - couples of Boolean attributes derived from co...
