Reusing Topological Nexttime Logic

Studia Logica 108 (6):1207-1234 (2020)
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Abstract

In this paper, a particular extension of the constitutive bi-modal logic for single-agent subset spaces will be provided. That system, which originally was designed for revealing the intrinsic relationship between knowledge and topology, has been developed in several directions in recent years, not least towards a comprehensive knowledge-theoretic formalism. This line is followed here to the extent that subset spaces are supplied with a finite number of functions which shall represent certain knowledge-enabling actions. Due to the corresponding functional modalities, another basic system for subset spaces, topological nexttime logic, comes into play. The resulting merge of logics can, for example, be applied to comparing the different effects of those actions in respect of knowledge. Subsequently, the completeness and the decidabilty of the basic combined system and of a certain extension thereof will be proved.

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References found in this work

Logics of Time and Computation.Robert Goldblatt - 1990 - Studia Logica 49 (2):284-286.
Topological reasoning and the logic of knowledge.Andrew Dabrowski, Lawrence S. Moss & Rohit Parikh - 1996 - Annals of Pure and Applied Logic 78 (1-3):73-110.
Logics for multi-subset spaces.Bernhard Heinemann - 2010 - Journal of Applied Non-Classical Logics 20 (3):219-240.

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