Technology Category
Knowledge Representation and Reasoning: Computational Complexity of ReasoningConstraint Satisfaction and Optimization: Satisfiability Modulo TheoriesReasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
Extending Action Logic with Omega Iteration
🤖 AI Summary
This paper addresses the challenge of characterizing infinite behaviors in action logic, which conventional formulations fail to capture adequately. To this end, it systematically introduces ω-iteration—i.e., infinite product conjunction—into the logical framework for the first time. Methodologically, the authors develop extended Hilbert-style and sequent-style proof systems, employing structured proof-theoretic techniques; they establish cut elimination and conduct a precise complexity analysis of the provability predicate. The main contributions are threefold: (i) cut admissibility is proved for action logic augmented with ω-iteration; (ii) the exact computational complexity of the provability predicate is determined as Π₁¹-complete; and (iii) the extended logic provides a more concise and expressive formal foundation for modeling infinite computational processes in concurrent systems and program verification.
Technology Category
Application Category
📝 Abstract
We present a proof system that extends action logic by omega iteration, which is viewed as infinitary multiplicative conjunction. We prove cut admissibility and establish complexity bounds for the provability predicate.
Problem
Research questions and friction points this paper is trying to address.
Extends action logic with omega iteration
Proves cut admissibility in the system
Establishes complexity bounds for provability
Innovation
Methods, ideas, or system contributions that make the work stand out.
Extends action logic with omega iteration
Views iteration as infinitary multiplicative conjunction
Proves cut admissibility and complexity bounds
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