We are not able to resolve this OAI Identifier to the repository landing page. If you are the repository manager for this record, please head to the Dashboard and adjust the settings.
Interval temporal logics (ITLs) are logics for reasoning about temporal statements expressed over intervals,
i.e., periods of time. The most famous ITL studied so far is Halpern and Shoham’s HS, which
is the logic of the thirteen Allen’s interval relations. Unfortunately, HS and most of its fragments have
an undecidable satisfiability problem. This discouraged the research in this area until recently, when
a number non-trivial decidable ITLs have been discovered. This paper is a contribution towards the
complete classification of all different fragments of HS. We consider different combinations of the
interval relations begins (B), after (A), later (L) and their inverses A, B and L. We know from previous
works that the combination ABBA is decidable only when finite domains are considered (and
undecidable elsewhere), and that ABB is decidable over the natural numbers. We extend these results
by showing that decidability of ABB can be further extended to capture the language ABBL, which
lies in between ABB and ABBA, and that turns out to be maximal w.r.t decidability over strongly
discrete linear orders (e.g. finite orders, the naturals, the integers). We also prove that the proposed
decision procedure is optimal with respect to the EXPSPACE complexity class
Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.