Interval Temporal Logic (ITL) is an established formalism for reasoning about time periods. We elucidate here the relationship between various kinds of compositional propositional ITL formulas. Several are closed under conjunction and the standard temporal operator known as “box” and “always”.

We introduce a methodology whereby an arbitrary logic system L can be en riched with temporal features to create a new system T L The new system is constructed by combining L with a pure propositional temporal logic T such as linear temporal logic with Since and Until in a special way We refer to this method as adding a temporal dimension to L or just temporalising L We show that the logic syst...

This paper presents a comprehensive framework for run-time self-checking of logical agents, by means of temporal axioms to be dynamically checked. These axioms are specified via an agent-oriented interval temporal logic defined to this purpose, with fully defined syntax, semantics and pragmatics.

A fragment of linear time temporal logic (LTL) is presented. It is proved that the satisfiability problem for this fragment is NPcomplete. The fragment is larger than previously known NP-complete fragments. It is obtained by prohibiting the use of until operator and requiring to use only next operators indexed by a letter.

It is shown that a stutter-invariant property is expressible in Temporal Logic of Actions if and only if it is expressible in Second-order Temporal Logic. In particular, validity questions can be translated from one logic to the other. The proof is based on equivalence transformations between the formulas of Temporal Logic of Actions and Second-order Temporal Logic. The translation from Second-...