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Some notes on grounding singletons of modal conjunctions

Katarzyniak R. P.

Systems Science

2006

Vol. 32, no 1

45-55

In this paper, properties of grounding sets of modal conjunctions are overviewed and used to describe theoretical context in which the phenomenon of grounding singletons of modal conjunctions is analyzed. Conditions of proper grounding are defined by the so-called epistemic satisfaction relation. This epistemic satisfaction relation holds between internal states of cognition of communicative cognitive agents and modal conjunctions. The grounding is assumed to take place for a modal conjunction if the related epistemic satisfaction relation holds. The original theorem presented in this paper deals with the case of singleton of modal conjunction extended with possibility operator. To be grounded this singleton requires more constrained cases of systems of modality thresholds implemented in artificial communicative agents. Other results related to grounding of singletons are overviewed and adapted to additionally constrained systems of modality thresholds.