ExpTime Tableau Decision Procedures for Regular Grammar Logics with Converse

Grammar logics were introduced by Fariñas del Cerro and Penttonen in 1988 and have been widely studied. In this paper we consider regular grammar logics with converse (REG ^c logics) and present sound and complete tableau calculi for the general satisfiability problem of REG ^c logics and the problem of checking consistency of an ABox w.r.t. a TBox in a REG ^c logic. Using our calculi we develop ExpTime (optimal) tableau decision procedures for the mentioned problems, to which various optimization techniques can be applied. We also prove a new result that the data complexity of the instance checking problem in REG ^c logics is coNP-complete.     

Short-Term Kinesthetic Training for Sensorimotor Rhythms: Effects in Experts and Amateurs

The authors’ aim was to examine whether short-term kinesthetic training affects the level of sensorimotor rhythm (SMR) in different frequency band: alpha (8–12 Hz), lower beta (12.5–16 Hz) and beta (16.5–20 Hz) during the execution of a motor imagery task of closing and opening the right and the left hand by experts (jugglers, practicing similar exercises on an everyday basis) and amateurs (individuals not practicing any sports). It was found that the performance of short kinesthetic training increases the power of alpha rhythm when executing imagery tasks only in the group of amateurs. Therefore, kinesthetic training may be successfully used as a method increasing the vividness of motor imagery, for example, in tasks involving the control of brain–computer interfaces based on SMR.     

Socratic Trees

The method of Socratic proofs (SP-method) simulates the solving of logical problem by pure questioning. An outcome of an application of the SP-method is a sequence of questions, called a Socratic transformation. Our aim is to give a method of translation of Socratic transformations into trees. We address this issue both conceptually and by providing certain algorithms. We show that the trees which correspond to successful Socratic transformations—that is, to Socratic proofs—may be regarded, after a slight modification, as Gentzen-style proofs. Thus proof-search for some Gentzen-style calculi can be performed by means of the SP-method. At the same time the method seems promising as a foundation for automated deduction.     

Recognition of notated melodies by possessors and nonpossessors of absolute pitch

Musically trained listeners compared a notated melody presented visually and a comparison melody presented auditorily, and judged whether they were exactly the same or not, with respect to relative pitch. Listeners who had absolute pitch showed the poorest performance for melodies transposed to different pitch levels from the notated melodies, whereas they exhibited the highest performance for untransposed melodies. By comparison, the performance of melody recognition by listeners who did not have absolute pitch was not influenced by the actual pitch level at which melodies were played. These results suggest that absolute-pitch listeners tend to rely on absolute pitch even in recognizing transposed melodies, for which the absolute-pitch strategy is not useful.     

Erotetic Search Scenarios

The concept of search scenario is explicated in terms of erotetic logic, i.e., the logic of questions. Different kinds of erotetic search scenarios are characterized. The basic logical properties of erotetic search scenarios are analyzed.     

A Very Strong Set Theory?

Studia Logica - Using two distinct membership symbols makes possible to base set theory on one general axiom schema of comprehension. Is the resulting system consistent? Can set theory and...     

Annotation Theories over Finite Graphs

In the current paper we consider theories with vocabulary containing a number of binary and unary relation symbols. Binary relation symbols represent labeled edges of a graph and unary relations represent unique annotations of the graph’s nodes. Such theories, which we call annotation theories, can be used in many applications, including the formalization of argumentation, approximate reasoning, semantics of logic programs, graph coloring, etc. We address a number of problems related to annotation theories over finite models, including satisfiability, querying problem, specification of preferred models and model checking problem. We show that most of considered problems are NPTime- or co-NPTime-complete. In order to reduce the complexity for particular theories, we use second-order quantifier elimination. To our best knowledge none of existing methods works in the case of annotation theories. We then provide a new second-order quantifier elimination method for stratified theories, which is successful in the considered cases. The new result subsumes many other results, including those of [2, 28, 21].     

Towards a Rough Mereology-Based Logic for Approximate Solution Synthesis. Part 1

We are concerned with formal models of reasoning under uncertainty. Many approaches to this problem are known in the literature e.g. Dempster-Shafer theory [29], [42], bayesian-based reasoning [21], [29], belief networks [29], many-valued logics and fuzzy logics [6], non-monotonic logics [29], neural network logics [14]. We propose rough mereology developed by the last two authors [22-25] as a foundation for approximate reasoning about complex objects. Our notion of a complex object includes, among others, proofs understood as schemes constructed in order to support within our knowledge assertions/hypotheses about reality described by our knowledge incompletely.