Narrow Results

We consider propositional logic programs with negations. We define notions of constructive transformation and constructive completion of a program. We use these notions to characterize SLDNF-resolution in classical, intuitionistic and intermediate logics, and also to derive a characterization in modal logics of knowledge. We show that the three-valued and four-valued fix-point or declarative semantics for program P are equivalent to the two-valued semantics for the constructive version of P.

We argue that it would be beneficial to replace Negation as Failure by constructive transformation, and it would be beneficial to use the semantics for the constructive version of the program instead of multivalued semantics for the original program.

We apply a non-classical four-valued logic in the process of reasoning regarding strategies for cops in a modified game of “Cops and Robber” played on a graph. We extend the game by introducing uncertainty in a form of random failures of detecting devices. This is realized by allowing that a robber can be detected in a node only with the given probability P_A. Additionally, with the probability P_F, cops can be given a false-positive, i.e., they are informed that the robber is located at some node, whereas it is located somewhere else. Consequently, non-zero P_F introduces a measurement noise into the system. All the cops have access to information provided by the detectors and can communicate with each other, so they can coordinate the search. By adjusting the number of detectors, P_A, and P_F we can achieve a smooth transition between the two well-known variants of the game: “with fully visible robber” and “with invisible robber”. We compare a simple probabilistic strategy for cops with the non-parametric strategy based on reasoning with a four-valued paraconsistent logic. It is shown that this novel approach leads to a good performance, as measured by the required mean catch-time. We conclude that this type of reasoning can be applied in real-world applications where there is no knowledge about the underlying source of errors which is particularly useful in robotics.

Bosbach and Riečan states on residuated lattices both are analogues of probability measures on Boolean algebras. In this paper it is proved that Riečan states on a residuated lattice is uniquely determined by its restriction on the subset of all regular elements and consequently the same holds for Bosbach states on Glivenko residuated lattices. These results indicate that for studies of Riečan and Bosbach states one can concentrate only on involutive residuated lattices.

The theory of filters and fuzzy filters in logical algebras play a vital role in reasoning mechanism in information sciences, computer sciences, theory of control, artificial intelligence and many other important fields. We introduce the concept of fuzzy sub positive implicative filters of residuated lattice and investigate the properties of it, and further characterize the fuzzy sub positive implicative filters by proposing the equivalent conditions that a fuzzy filters to be a fuzzy sub positive implicative filters.