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On Binary Computation Structures
Author(s) -
Heinemann Bernhard
Publication year - 1997
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19970430205
Subject(s) - decidability , mathematics , modal logic , modal operator , completeness (order theory) , generalization , fragment (logic) , class (philosophy) , discrete mathematics , binary relation , computation , normal modal logic , dynamic logic (digital electronics) , modal , algebra over a field , binary number , pure mathematics , computer science , algorithm , arithmetic , artificial intelligence , mathematical analysis , chemistry , physics , transistor , voltage , quantum mechanics , polymer chemistry
Based on a modification of Moss' and Parikh's topological modal language [8], we study a generalization of a weakly expressive fragment of a certain propositional modal logic of time. We define a bimodal logic comprising operators for knowledge and nexttime. These operators are interpreted in binary computation structures. We present an axiomatization of the set T of theorems valid for this class of semantical domains and prove – as the main result of this paper – its completeness. Moreover, the question of decidability of T is treated.