There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

Investigates the application of logic to problem solving and computer programming. Requires no previous knowledge in this field, and therefore can be used as an introduction to logic, the theory of problem-solving and computer programming. Annotation copyrighted by Book News, Inc., Portland, OR.

Many proposals for logic-based formalisations of argumentation consider an argument as a pair (Φ,α), where the support Φ is understood as a minimal consistent subset of a given knowledge base which has to entail the claim α. In case the arguments are given in the full language of classical propositional logic reasoning in such frameworks becomes a computationally costly task. For instance, the problem of deciding whether there exists a support for a given claim has been shown to be -complete. (...) In order to better understand the sources of complexity (and to identify tractable fragments), we focus on arguments given over formulæ in which the allowed connectives are taken from certain sets of Boolean functions. We provide a complexity classification for four different decision problems (existence of a support, checking the validity of an argument, relevance and dispensability) with respect to all possible sets of Boolean functions. Moreover, we make use of a general schema to enumerate all arguments to show that certain restricted fragments permit polynomial delay. Finally, we give a classification also in terms of counting complexity. (shrink)