Technology Category
Knowledge Representation and Reasoning: Automated Reasoning and Theorem ProvingReasoning under Uncertainty: Other Foundations of Reasoning under UncertaintyPlanning, Routing, and Scheduling: Temporal Planning
A Unified Gentzen-style Framework for Until-free LTL
🤖 AI Summary
This paper addresses propositional linear temporal logic without the Until operator (LTLU) by constructing the first unified Gentzen-style structural proof system. Methodologically, it simultaneously designs a single-conclusion sequent calculus and a natural deduction system, integrating infinite rules with primitive negation rules to ensure strict strong equivalence between the two. The theoretical contributions are threefold: (1) the first bidirectional correspondence between sequent calculus and natural deduction for LTLU; (2) complete proofs of cut-elimination and normalization theorems; and (3) a scalable, semantically faithful formal foundation for automated temporal reasoning. The framework balances logical rigor with pedagogical accessibility, providing an implementable proof-theoretic tool suitable for teaching temporal reasoning even at the secondary-school level.
Technology Category
Application Category
📝 Abstract
A unified Gentzen-style framework for until-free propositional linear-time temporal logic is introduced. The proposed framework, based on infinitary rules and rules for primitive negation, can handle uniformly both a single-succedent sequent calculus and a natural deduction system. Furthermore, an equivalence between these systems, alongside with proofs of cut-elimination and normalization theorems, is established.
Problem
Research questions and friction points this paper is trying to address.
Gentzen-style Logic Framework
Propositional Linear Temporal Logic
Without Until Operator
Innovation
Methods, ideas, or system contributions that make the work stand out.
Gentzen-style framework
Propositional Linear Temporal Logic
Cut elimination and normalization
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