We prove the canonical models introduced in [D] do not exist for some graded normal logics with symmetric models, namelyKB°, KBD°, KBT°, so that we define a new kind of canonical models, the general ones, and show they exist and work well in every case.

We study a modal system $\overline{T}$, that extends the classical modal system T and whose language is provided with modal operators $M_{n}$ to be interpreted, in the usual kripkean semantics, as "there are more than n accessible worlds such that...". We find reasonable axioms for $\overline{T}$ and we prove for it completeness, compactness and decidability theorems.

We consider some modal languages with a modal operator $D$ whose semantics is based on the relation of inequality. Basic logical properties such as definability, expressive power and completeness are studied. Also, some connections with a number of other recent proposals to extend the standard modal language are pointed at.

We consider some modal languages with a modal operator D whose semantics is based on the relation of inequality. Basic logical properties such as definability, expressive power and completeness are studied. Also, some connections with a number of other recent proposals to extend the standard modal language are pointed at.

We study a modal system ¯T, that extends the classical (prepositional) modal system T and whose language is provided with modal operators M inn (nN) to be interpreted, in the usual kripkean semantics, as there are more than n accessible worlds such that.... We find reasonable axioms for ¯T and we prove for it completeness, compactness and decidability theorems.

Description Logics are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can be computationally problematical.We present an algorithm that decides satisfiability of the DL ALC extended with transitive and inverse roles and functional restrictions with respect to general concept inclusion axioms and role hierarchies; early experiments indicate that this algorithm is well-suited for implementation. Additionally, we show that ALC extended with (...) just transitive and inverse roles is still in PSPACE. We investigate the limits of decidability for this family of DLs, showing that relaxing the constraints placed on the kinds of roles used in number restrictions leads to the undecidability of all inference problems. Finally, we describe a number of optimisation techniques that are crucial in obtaining implementations of the decision procedures, which, despite the high worst-case complexity of the problem, exhibit good performance with real-life problems. (shrink)