Logical Reasoning

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Decidable Reasoning About Time in Finite-Domain Situation Calculus Theories
Feb 5, 2024Till Hofmann, Stefan Schupp, Gerhard LakemeyerLogical Reasoning Reachability Analysis
Knowledge-Based Systems Group, RWTH Aachen University · Cyber-Physical Systems Group, TU Wien
Querying and Repairing Inconsistent Prioritized Knowledge Bases: Complexity Analysis and Links with Abstract Argumentation
Mar 12, 2020Meghyn Bienvenu, Camille BourgauxLogical Reasoning Computational Argumentation
CNRS & University of Bordeaux, France · DI ENS, ENS, CNRS, PSL University & Inria, Paris, France
GLaMoR: Consistency Checking of OWL Ontologies using Graph Language Models
Date pendingJustin Mücke, Ansgar ScherpLogical Reasoning Language Modeling
University of Ulm Ulm, Germany

Feb 5, 2024, cs.AIJ/K move · Enter open · S save

Decidable Reasoning About Time in Finite-Domain Situation Calculus Theories

Till Hofmann, Stefan Schupp, Gerhard Lakemeyer

Knowledge-Based Systems Group, RWTH Aachen University · Cyber-Physical Systems Group, TU Wien

Logical Reasoning Reachability Analysis Symbolic Planning Formal Verification

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Representing time is crucial for cyber-physical systems and has been studied extensively in the situation calculus. The most commonly used approach represents time by adding a real-valued function

\mathit{time}(a)

that attaches a time point to each action and consequently to each situation. We show that in this approach, checking whether there is a reachable situation that satisfies a given formula is undecidable, even when the domain contains only finitely many objects. We present an alternative approach based on well-established results from timed automata theory by introducing clocks as real-valued fluents with restricted successor state axioms and comparison operators. With this restriction, we can show that the reachability problem for finite-domain basic action theories is decidable. Finally, we apply our results to Golog program realization by presenting a decidable procedure for determining an action sequence that is a successful execution of a given program.

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Latest papers 123

Decidable Reasoning About Time in Finite-Domain Situation Calculus Theories

Querying and Repairing Inconsistent Prioritized Knowledge Bases: Complexity Analysis and Links with Abstract Argumentation

GLaMoR: Consistency Checking of OWL Ontologies using Graph Language Models