The tableau methodology, invented in the 1950's by Beth and
Hintikka and later perfected by Smullyan and Fitting, is today one
of the most popular proof theoretical methodologies. Firstly
because it is a very intuitive tool, and secondly because it
appears to bring together the proof-theoretical and the semantical
approaches to the presentation of a logical system. The increasing
demand for improved tableau methods for various logics is mainly
prompted by extensive applications of logic in computer science,
artificial intelligence and logic programming, as well as its use
as a means of conceptual analysis in mathematics, philosophy,
linguistics and in the social sciences. In the last few years the
renewed interest in the method of analytic tableaux has generated a
plethora of new results, in classical as well as non-classical
logics. On the one hand, recent advances in tableau-based theorem
proving have drawn attention to tableaux as a powerful deduction
method for classical first-order logic, in particular for
non-clausal formulas accommodating equality. On the other hand,
there is a growing need for a diversity of non-classical logics
which can serve various applications, and for algorithmic
presentations of these logicas in a unifying framework which can
support (or suggest) a meaningful semantic interpretation. From
this point of view, the methodology of analytic tableaux seems to
be most suitable. Therefore, renewed research activity is being
devoted to investigating tableau systems for intuitionistic, modal,
temporal and many-valued logics, as well as for new families of
logics, such as non-monotonic and substructural logics. The results
require systematisation. This Handbook isthe first to provide such
a systematisation of this expanding field. It contains several
chapters on the use of tableaux methods in classical logic, but
also contains extensive discussions on: the uses of the methodology
in intuitionistic logics modal and temporal logics substructural
logics, nonmonotonic and many-valued logics the implementation of
semantic tableaux a bibliography on analytic tableaux theorem
proving. The result is a solid reference work to be used by
students and researchers in Computer Science, Artificial
Intelligence, Mathematics, Philosophy, Cognitive Sciences, Legal
Studies, Linguistics, Engineering and all the areas, whether
theoretical or applied, in which the algorithmic aspects of logical
deduction play a role.
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