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Logic, Symbolic and mathematical.

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Rippling is a radically new technique for the automation of mathematical reasoning. It is widely applicable whenever a goal is to be proved from one or more syntactically similar givens. It was originally developed for inductive proofs, where the goal was the induction conclusion and the givens were the induction hypotheses. It has proved to be applicable to a much wider class of tasks, from summing series via analysis to general equational reasoning. The application to induction has especially important practical implications in the building of dependable IT systems, and provides solutions to issues such as the problem of combinatorial explosion. Rippling is the first of many new search control techniques based on formula annotation; some additional annotated reasoning techniques are also described here. This systematic and comprehensive introduction to rippling, and to the wider subject of automated inductive theorem proving, will be welcomed by researchers and graduate students alike.

Automatic theorem proving. --- Logic, Symbolic and mathematical.

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Infinite --- Logic, Symbolic and mathematical --- Set theory

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Logic, Symbolic and mathematical --- Mathematics --- Semantics (Philosophy) --- Philosophy

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This book gives an overview of paraconsistent logics – that is logics which allow for inconsistency. Although allowing for inconsistency, paraconsistent logics are worth considering : Logical systems are worth considering in their own right since we can learn about very abstract structural properties of logics and the concepts employed within them such as negation, necessity and consistency. Some non-classical logics are especially of interest from a philosophical perspective since they alone offer the possibility of solving or even stating some philosophical problems. These introductory lectures argue from a philosophical perspective that some paraconsistent logics are of interest or even the best candidates for dealing with specific philosophical problems. Although logic is seen from the point of view of its philosophical use, various formal systems are described, compared and employed.

Inconsistency (Logic) --- Logic, Symbolic and mathematical --- Inconsistance (Logique) --- Logique symbolique et mathématique --- Logic, symbolic and mathematical