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Temporal Many-valued Conditional Logics: a Preliminary Report

Mario Alviano, Laura Giordano, Daniele Theseider Dupré

TL;DR

This paper starts from a many-valued logic with typicality, and extends it with the temporal operators of the Linear Time Temporal Logic (LTL), thus providing a formalism which is able to capture the dynamics of a system, trough strict and defeasible temporal properties.

Abstract

In this paper we propose a many-valued temporal conditional logic. We start from a many-valued logic with typicality, and extend it with the temporal operators of the Linear Time Temporal Logic (LTL), thus providing a formalism which is able to capture the dynamics of a system, trough strict and defeasible temporal properties. We also consider an instantiation of the formalism for gradual argumentation.

Temporal Many-valued Conditional Logics: a Preliminary Report

TL;DR

This paper starts from a many-valued logic with typicality, and extends it with the temporal operators of the Linear Time Temporal Logic (LTL), thus providing a formalism which is able to capture the dynamics of a system, trough strict and defeasible temporal properties.

Abstract

In this paper we propose a many-valued temporal conditional logic. We start from a many-valued logic with typicality, and extend it with the temporal operators of the Linear Time Temporal Logic (LTL), thus providing a formalism which is able to capture the dynamics of a system, trough strict and defeasible temporal properties. We also consider an instantiation of the formalism for gradual argumentation.
Paper Structure (8 sections, 2 theorems, 4 equations)

This paper contains 8 sections, 2 theorems, 4 equations.

Table of Contents

  1. Introduction
  2. A Many-valued Preferential Logics with Typicality
  3. KLM properties of conditionals
  4. A Temporal Preferential Logic with Typicality
  5. Temporal graded Formulas
  6. Weighted temporal knowledge bases
  7. Towards a temporal conditional logic for gradual argumentation
  8. Conclusions

Key Result

Proposition 1

Under the choice of combination functions as in Gödel logic, 1-entailment satisfies the KLM postulates of a preferential consequence relation given above.

Theorems & Definitions (9)

  • Definition 1
  • Definition 2
  • Definition 3
  • Proposition 1
  • Definition 4
  • Proposition 2
  • Definition 5
  • Definition 6: Satisfiability and entailment
  • Definition 7