Theoretical Computer Science
Nonclausal deduction in first-order temporal logic
Journal of the ACM (JACM)
On the interpretability of arithmetic in temporal logic
Theoretical Computer Science
The power of the “always“ operator in first-order temporal logic
Theoretical Computer Science
Temporal versus first-order logic to query temporal databases
PODS '96 Proceedings of the fifteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A first step towards implementing dynamic algebraic dependences
Theoretical Computer Science - Special issue: database theory
Improving Temporal Logic Tableaux Using Integer Constraints
ICTL '94 Proceedings of the First International Conference on Temporal Logic
Temporal Query Languages: A Survey
ICTL '94 Proceedings of the First International Conference on Temporal Logic
A Tableau System for Linear-TIME Temporal Logic
TACAS '97 Proceedings of the Third International Workshop on Tools and Algorithms for Construction and Analysis of Systems
Bounded Model Search in Linear Temporal Logic and Its Application to Planning
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
METATEM: A Framework for Programming in Temporal Logic
Stepwise Refinement of Distributed Systems, Models, Formalisms, Correctness, REX Workshop
First Order Linear Temporal Logic over Finite Time Structures
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
The Declarative Past and Imperative Future: Executable Temporal Logic for Interactive Systems
Temporal Logic in Specification
First Order Linear Temporal Logic over Finite Time Structures
LPAR '99 Proceedings of the 6th International Conference on Logic Programming and Automated Reasoning
An order-sorted quantified modal logic for meta-ontology
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
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In this work, the notion of provability for first order linear temporal logic over finite time structures, FO-LTLfin, is studied. We show that the validity problem for such a logic is not recursively enumerable, hence FO-LTLfin is not recursively axiomatizable. This negative result however does not hold in the case of bounded validity, that is truth in all temporal models where the object domain is possibly infinite, but the underlying sequence of time points does not exceed a given size. A formula is defined to be k-valid if it is true in all temporal models whose underlying time frame is not greater them k, where k is any fixed positive integer. In this work a tableau calculus is defined, that is sound and complete with respect to k-validity, when given as input the initial formula and the bound k on the size of the temporal models. The main feature of the system, extending the prepositional calculus defined in [7], is that of explicitly denoting time points and having tableau nodes labelled by either expressions intuitively stating that a formula holds in a given temporal interval, or "temporal constrsiints", i.e. linear inequalities on time points. Branch closure is reduced to unsatisfiability over the integers of the set of temporal constreiints in the branch.