# Quantitative Logic Reasoning

## TL;DR

This paper explores the commonalities among various logic systems that combine deductive and quantitative reasoning, proposing a unified framework called Quantitative Logic Reasoning with applicable linear algebraic techniques.

## Contribution

It introduces the concept of Quantitative Logic Reasoning, unifying different logic systems and demonstrating their shared properties and solvability via linear algebraic methods.

## Key findings

- Identifies similarities among probabilistic, counting, and many-valued logic systems.
- Shows applicability of linear algebraic techniques to satisfiability problems.
- Proposes a unified framework for quantitative logic reasoning.

## Abstract

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