We investigate the computational complexity of some maze problems, namely the reachability problem for (undirected) grid graphs with diagonal edges, and the solvability of Xmas tree mazes. Simply speaking, in the latter game one has to move sticks of a certain length through a maze, ending in a particular game situation. It turns out that when the number of sticks is bounded by some constant, t...

We consider the fuzzy logic ALCI with semantics based on a finite residuated lattice. We show that the problems of satisfiability and subsumption of concepts in this logic are ExpTime-complete w.r.t. general TBoxes and PSpace-complete w.r.t. acyclic TBoxes. This matches the known complexity bounds for reasoning in crisp ALCI.

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

Commutative, integral and bounded GBL-algebras form a subvariety of residuated lattices which provides the algebraic semantics of an interesting common fragment of intuitionistic logic and of several fuzzy logics. It is known that both the equational theory and the quasiequational theory of commutative GBL-algebras are decidable (in contrast to the noncommutative case), but their complexity has...

The collection CL(T ) of nonempty convex sublattices of a lattice T ordered by bi-domination is a lattice. We say that T has the fixed point property for convex sublattices (CLFPP for short) if every order preserving map f ∶ T → CL(T ) has a fixed point, that is x ∈ f(x) for some x ∈ T . We examine which lattices may have CLFPP. We introduce the selection property for convex sublattices (CLSP);...

form a complete lattice, the D e d e k i n d M a c N e i l l e c o m p l e t i o n (or short comp l e t i o n ) of (P, <). It is the smallest complete lattice containing a subset orderisomorphic with (P, <). The size of the completion may be exponential in [PI. The completion can be computed in steps: first complete a small part of (P, <), then add another element, complete again, et cetera. Ea...