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arXiv · 1808.10320

Logic of Approximate Entailment in quasimetric spaces

Thomas Vetterlein
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Abstract

The logic LAE discussed in this paper is based on an approximate entailment relation. LAE generalises classical propositional logic to the effect that conclusions can be drawn with a quantified imprecision. To this end, properties are modelled by subsets of a distance space and statements are of the form that one property implies another property within a certain limit of tolerance. We adopt the conceptual framework defined by E. Ruspini; our work is towards a contribution to the investigation of suitable logical calculi. LAE is based on the assumption that the distance function is a quasimetric. We provide a proof calculus for LAE and we show its soundness and completeness for finite theories. As our main tool for showing completeness, we use a representation of proofs by means of weighted directed graphs.

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Thomas Vetterlein. 2018-08-30. Logic of Approximate Entailment in quasimetric spaces. https://arxiv.org/abs/1808.10320

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