A COMPLETE AXIOM SYSTEM FOR PROPOSITIONAL INTERVAL TEMPORAL LOGIC WITH INFINITE TIME
Interval Temporal Logic (ITL) is an established temporal formalism for reasoning about time periods. For over 25 years, it has been applied in a number of ways and several ITL variants, axiom systems and tools have been investigated. We solve the longstanding open problem of finding a complete axiom system for basic quantifier-free propositional ITL (PITL) with infinite time for analysing nonterminating computational systems. Our completeness proof uses a reduction to completeness for Pill with finite time and conventional propositional linear-time temporal logic. Unlike completeness proofs or equally expressive logics with nonelementary computational complexity, OM semantic approach does not use tableaux, subformula closures or explicit deductions involving encodings of omega automata and nontrivial techniques for complementing them. We believe that our result also provides evidence of the naturalness of interval-based reasoning.
axiom system interval temporal logic axiomatic completeness omega-regular languages omega-regular logics compositionality