Decidability and Complexity of Fuzzy Description Logics

Some Complexity Results on Fuzzy Description Logics

We present and discuss some novel and somewhat surprising complexity results for a basic but significant fuzzy description logic (DL) which extends the classical ALC language. In particular we show that checking the consistency of a concept or a KB in fuzzy DLs has a complexity which jumps from linear-time to EXPTIME-complete, while the subsumption problem is always (at least) as hard as in cri...

Decidability of Circumscribed Description Logics Revisited

We revisit non-monotonic description logics based on circumscription (with preferences) and prove several decidability results for their satisfiability problem. In particular, we consider circumscribed description logics without the finite model property (DL-LiteF andALCFI) and with fixed roles (DL-LiteF and a fragment of DL-LiteR), improving upon previous decidability results that are limited ...

Logics for Real Time: Decidability and Complexity

Over the last fifteen years formalisms for reasoning about metric properties of computations were suggested and discussed. First as extensions of temporal logic, ignoring the framework of classical predicate logic, and then, with the authors’ work, within the framework of monadic logic of order. Here we survey our work on metric logic comparing it to the previous work in the field. We define a ...

Elementary Modal Logics – Decidability and Complexity

Modal logic was first introduced by philosophers to study the deductive behaviour of the expressions it is necessary that and it is possible that. Nowadays, it is widely used in several areas of computer science, including formal verification and artificial intelligence. Syntactically, modal logic extends propositional logic by two unary operators: ♦ and . The formal semantics is usually given ...

Fuzzy Description Logics