Welcome to the site about the Interval Temporal Logics (ITL)

This site aims to gather together informations about the research activity in the area of Interval temporal Logics.

What are Interval Temporal Logics?

Interval Temporal Logics (ITL) are modal logics particularly suitable for expressing properties changing along the time line. They are characterized by the choice of the time period as the primitive temporal entity, instead of the time instant, used in the classical temporal logics. This causes a blow up in complexity, so in the interval temporal logics setting undecidability is the rule. The quest for decidable fragments and systems of temporal logics with interval-based semantics is one of the main research problems in the area of interval logics.

Why Interval Temporal Logics?

Interval-based temporal logics provide a natural framework for temporal representation and reasoning. They stem from four major scientific areas:
  • Philosophy. The philosophical roots of interval temporal logics can be traced back to Zeno and Aristotle. The nature of Time has always been a favourite subject in philosophy, and in particular, the discussion whether time instants or time periods should be regarded as the primary objects of temporal ontology has a distinct philosophical flavour.
  • Linguistics. Interval-based logical formalisms have featured in the study of natural languages since the seminal work of Reichenbach, 1947. They arise as suitable frameworks for modeling progressive tenses and expressing various language constructions involving time periods and event duration which cannot be adequately grasped by point-based temporal languages.
  • Artificial Intelligence. Interval temporal languages and logics have sprung up from expert systems, planning systems, theories of actions and change, natural language analysis and processing, etc. as formal tools for temporal representation and reasoning in artificial intelligence.
  • Computer science. Some applications of interval temporal logics to computer science concern temporal databases, specification and design of hardware components, cuncurrent real-time processes, bioinformatics, model checking tools and techniques. In particular, suitable interval logics for specification and verification of real-time processes in computer science are the duration calculi, introduced as extensions of interval logics, allowing representation and reasoning about time durations for which a system is in a given state.