Computational logic

About: Computational logic is a research topic. Over the lifetime, 4185 publications have been published within this topic receiving 135716 citations.

Introduction to Mathematical Logic

Abstract: Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, "The Calculi of Lambda-Conversion" (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, "Introduction to Mathematical Logic," defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the "Journal of Symbolic Logic" in 1936 and remained an editor until 1979 At his death in 1995, Church was still regarded as the greatest mathematical logician in the world.

Logic Programming with Focusing Proofs in Linear Logic

Abstract: The deep symmetry of linear logic [18] makes it suitable for providing abstract models of computation, free from implementation details which are, by nature, oriented and nonsymmetrical. I propose here one such model, in the area of logic programming, where the basic computational principle is Computation = Proof search Proofs considered here are those of the Gentzen style sequent calculus for linear logic. However, proofs in this system may be redundant, in that two proofs can be syntactically different although identical up to some irrelevant reordering or simplification of the applications of the inference rules. This leads to an untractable proof search where the search procedure is forced to make costly choices which turn out to be irrelevant. To overcome this problem, a subclass of proofs, called the 'focusing' proofs, which is both complete (any derivable formula in linear logic has a focusing proof) and tractable (many irrelevant choices in the search are eliminated when aimed at focusing proofs) is identified. The main constraint underlying the specification of focusing proofs has been to preserve the symmetry of linear logic, which is its most salient feature. In particular, dual connectives have dual properties with respect to focusing proofs. Then, a programming language, called LinLog, consisting of a fragment of linear logic, in which focusing proofs have a more compact form, is presented. Linlog deals with formulae which have a syntax similar to that of the definite clauses and goals of Horn logic, but the crucial difference here is that it allows clauses with multiple atoms in the head, connected by the 'par' (multiplicative disjunction). It is then shown that the syntactic restriction induced by LinLog is not performed at the cost of any expressive power: a mapping from full linear logic to LinLog, preserving focusing proofs, and analogous to the normalization to clausal form for classical logic, is presented.

A Computational Logic Handbook

Abstract: Contains a precise and complete description of the computational logic develo by the authors; will serve also as a reference guide to the associated mechanical theorem proving system. Annotation copyright Book News, Inc. Portland, Or.

Logic in Computer Science: Modelling and Reasoning About Systems

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