Quantitative Logic Reasoning
This work provides a unifying framework for logic systems with quantitative aspects, which could benefit researchers in logic and AI, though it appears incremental as it synthesizes existing systems.
The paper identifies similarities among logic systems that combine deductive and quantitative inference, proposing the term 'Quantitative Logic Reasoning' and demonstrating that linear algebraic techniques can be applied to satisfiability decision problems across these systems.
In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous properties hold throughout that class, for whose members there exists a set of linear algebraic techniques applicable in the study of satisfiability decision problems. In this presentation, we consider as Quantitative Logic Reasoning the tasks performed by propositional Probabilistic Logic; first-order logic with counting quantifiers over a fragment containing unary and limited binary predicates; and propositional Lukasiewicz Infinitely-valued Probabilistic Logic