Overview

COOL - The Coalgebraic Ontology Logic Reasoner

COOL is a generic reasoner for modal and hybrid logics; it can be instantiated to any modal or hybrid logic admitting an axiomatization in terms of so-called rank-1 rules or axioms. Current instantiations include multimodal K (i.e. the description logic ALC), graded modal logic (the Q in ALCQ), and coalition logic (the next-step logic of alternating temporal logic ATL).
In addition to that COOL also handles many kinds of combinations of these basic logics:

  • Choice A + B: Any world in the model can either have successors according to logic A or to logic B.
  • Fusion A * B: Any world in the model has both successors according to logic A and to B.
  • Sequence A . B: Any wolrd in the model has successors reachable by doing an A-step and then an B-step. (e.g. simple Segala systems which perform an nondeterministic step followed by an probabilistic step).

COOL currently supports global assumptions, i.e. general TBoxes, nominals, and satisfaction operators; the latter features are similar in expressivity to Boolean ABoxes. COOL implements a global caching algorithm described here (also available here).

A system description of COOL (COOL -- A Generic Satisfiability Checker For Coalgebraic Logics with Global Assumptions, D. Gorin, D. Pattinson, L. Schröder, F. Widmann and T. Wißmann) is forthcoming at IJCAR 2014.

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