Publication details

Algebraic Approach to Tense Operators

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Year of publication 2015
Type Monograph
MU Faculty or unit

Faculty of Science

Description Propositional logics usually do not incorporate the dimension of time. However, even Aristotle already mentioned that time plays an important role in the evaluation of truth values of propositions. After Aristotle's time, a lot was created by men and, nowadays, logic is not an exceptional area for human reasoning. From the 1940's on, computers were built and the era of the Artificial Intelligence gently started. Nowadays, practically any more advanced product contains some kind of processor which decides situations in a way similar to that of a human being. However, for such technical devices the forecast for truth values of propositions in the future is not only a speculation. Due to the constructions and the technical possibilities, we can often compute these values, and propositions concerning the near future are of great importance. This has motivated many authors to investigate the so-called temporal logic, i.e., the logic where time is considered as a variable of the propositional formula. The logical language of tense logic contains, in addition to the ususal truth-functional operators, four the so-called tense operators. The aim of the monograph is to present an algebraic approach to an axiomatization of tense operators which are the most powerful tools in every tense logic.The authors hope that their monograph will be an incentive for further research.
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