Universal Logic

Quantitative logic

Institute of Mathematics , Shaanxi Normal University , Xi’an , China

Research Center for Science, Xi’an Jiaotong University , Xi’an , China

This talk will deal with the elementary theory of quantitative logic, which is divided into the following parts and sub-parts.

§1. Introduction

In this section we will give a brief introduction to the origin of quantitative logic, and will discuss some relationships between quantitative logic, possibility logic, and computational logic.

§2. Propositional logic and its completeness

§3. Several standard complete propositional logics:

Classical propositional logic, Lukasiewicz prepositional fuzzy logic and its n-valued extension, and R_0 propositional fuzzy logic and its n-valued extension.

§4. Elementary theory of quantitative logic

§4.1. Satisfiability degree of a logic formula

§ 4.1.1 . Satisfiability degree of a formula in n-valued propositional logic

§ 4.1.2 . Satisfiability degree of a formula in continuous-valued propositional logic

§4.2. Similarity degree of formulae

§4.3. Logic metric space (F(S), ρ)

§4.4. Approximate reasoning in (F(S), ρ)

§ 4.4.1 . Deduction theorem in the above-mentioned logics

§ 4.4.2 . Divergence degree of a formal theory

§ 4.4.3 . Approximate reasoning in (F(S), ρ)

§4.5.Consistency degree of a formal theory

§ 4.5.1 . Basic ideas

§ 4.5.2 . Consistency degree of a finite theory

§ 4.5.3 . Consistency degree of a general theory

§ 4.5.4 . The concept of consistency degree is a reasonable candidate for measuring

§5. Results in quantitative predicate logic


	Quantitative logic Guojun Wang Institute of Mathematics , Shaanxi Normal University , Xi’an , China Research Center for Science, Xi’an Jiaotong University , Xi’an , China

	This talk will deal with the elementary theory of quantitative logic, which is divided into the following parts and sub-parts. §1. Introduction In this section we will give a brief introduction to the origin of quantitative logic, and will discuss some relationships between quantitative logic, possibility logic, and computational logic. §2. Propositional logic and its completeness §3. Several standard complete propositional logics: Classical propositional logic, Lukasiewicz prepositional fuzzy logic and its n-valued extension, and R_0 propositional fuzzy logic and its n-valued extension. §4. Elementary theory of quantitative logic §4.1. Satisfiability degree of a logic formula § 4.1.1 . Satisfiability degree of a formula in n-valued propositional logic § 4.1.2 . Satisfiability degree of a formula in continuous-valued propositional logic			§4.2. Similarity degree of formulae §4.3. Logic metric space (F(S), ρ) §4.4. Approximate reasoning in (F(S), ρ) § 4.4.1 . Deduction theorem in the above-mentioned logics § 4.4.2 . Divergence degree of a formal theory § 4.4.3 . Approximate reasoning in (F(S), ρ) §4.5.Consistency degree of a formal theory § 4.5.1 . Basic ideas § 4.5.2 . Consistency degree of a finite theory § 4.5.3 . Consistency degree of a general theory § 4.5.4 . The concept of consistency degree is a reasonable candidate for measuring §5. Results in quantitative predicate logic