Propositional Logic Syntax Acquisition Using Induction and Self-Organisation

In this paper we present a framework for fusing approximate knowledge obtained from various distributed, heterogenous knowledge sources. This issue is substantial in modeling multi-agent systems, where a group of loosely coupled heterogeneous agents cooperate in achieving a common goal. In paper [5] we have focused on defining general mechanism for knowledge fusion. Next, the techniques ensuring tractability of fusing knowledge expressed as a Horn subset of propositional dynamic logic were developed in [13,16]. Propositional logics may seem too weak to be useful in real-world applications. On the other hand, propositional languages may be viewed as sublanguages of first-order logics which serve as a natural tool to define concepts in the spirit of description logics [2]. These notions may be further used to define various ontologies, like e.g. those applicable in the Semantic Web. Taking this step, we propose a framework, in which our Horn subset of dynamic logic is combined with deductive database technology. This synthesis is formally implemented in the framework of HSPDL architecture. The resulting knowledge fusion rules are naturally applicable to real-world data.

State-dependent alpha peak frequency shifts: Experimental evidence, potential mechanisms and functional implications

Evidences support that thrombolysis is associated to a better functional outcome but not to intact cognition after subacute stroke. The purpose of this study is to compare cognition and functional capacity, 6−10 months after stroke, in patients treated with thrombolysis with rt-PA (tissular plasminogen activator) and those who were not. From October 2008 to March 2010, 15 patients treated with thrombolysis with rt-PA and 30 patients who did not receive this treatment, underwent an extensive neuropsychological assessment and answered questionnaire about functionality. General cognitive performance, measured through the mean score of each cognitive domain, showed impairment with z score ≥ -1.50. Functional capacity was verified using PFAQ (Pfeffer Functional Activities Questionnaire) relative to instrumental activities of daily living. Five or more points in PFAQ demonstrated functional impairment. Continuous variables were analyzed by students’ t-test and categorical ones by Chi-square. Cognitive deficits were present in 20% of all subjects. In the group who received treatment with thrombolysis with rt-PA, 46.7% had language impairment, 33.3% had visuospatial impairment, and 26.7% had visual memory impairment. This group presented 20% of patients with functional impairment. General cognitive performance (p = 0.624) and functional capacity (p = 0.664) showed no difference between groups. There was a statistically significant difference between groups concerning neglect (p = 0.004) and sustained visual attention (p = 0.028). Findings suggest that patients who received thrombolysis presented less neglect and less visual attention deficits but did not show better general cognitive functioning or functional capacity.

We have seen in chapters 2 and 3 that a specification SPEC defines the class Alg(SPEC) of algebras for that specification. We have been able to single out a specific isomorphism class of algebras, the initial algebras, which due to their properties of being generated and typical can serve as favorite candidates for semantics of specification. That we could do so, is intrinsically a property of equations which we used as axioms in specifications. One could think of axioms other than equations, and allow Horn-clauses or even arbitrary first order formulas. It is indeed not obvious that initial algebras exist as models of a specification, and it is even possible to show that with arbitrary first order formulas as axioms aninitial algebra in the defined class of models not always exists.

Schizotypy, a putative schizophrenia endophenotype, has been associated with brain-structural variations partly overlapping with those in psychotic disorders. Variations in precuneus structure have been repeatedly reported, whereas the involvement of fronto-striatal networks - as in schizophrenia - is less clear. While shared genetic architecture is thought to increase vulnerability to environmental insults, beneficial factors like general intelligence might buffer their effect. To further investigate the role of fronto-striatal networks in schizotypy, we examined the relationship of voxel- and surface-based brain morphometry and a measure of schizotypal traits (Schizotypal Personality Questionnaire, with subscores Cognitive-Perceptual, Interpersonal, Disorganised) in 115 healthy participants [54 female, mean age (s.d.) = 27.57(8.02)]. We tested intelligence (MWT-B) as a potential moderator. We found a positive association of SPQ Cognitive-Perceptual with putamen volume (p = 0.040, FWE peak level-corrected), moderated by intelligence: with increasing IQ, the correlation of SPQ Cognitive-Perceptual and striatal volume decreased (p = 0.022). SPQ Disorganised was positively correlated with precentral volume (p = 0.013, FWE peak level-corrected). In an exploratory analysis (p < 0.001, uncorrected), SPQ total score was positively associated with gyrification in the precuneus and postcentral gyrus, and SPQ Disorganised was negatively associated with gyrification in the inferior frontal gyrus. Our findings support the role of fronto-striatal networks for schizotypal features in healthy individuals, and suggest that these are influenced by buffering factors like intelligence. We conclude that protective factors, like general cognitive capacity, might attenuate the psychosis risk associated with schizotypy. These results endorse the idea of a continuous nature of schizotypy, mirroring similar findings in schizophrenia.

Understanding sex differences in cognitive insight across first-and-multiple episode psychosis

First-order logic augments the expressive power of propositional logic as it links the logical assertions to properties of objects of some non-empty universe: the domain of discourse. This is achieved by allowing the propositional symbols to take arguments that range over elements of the domain of discourse. These are now called predicate symbols and are interpreted as relations on the domain. Elements of the domain of discourse are denoted by terms built up from variables, constants, and functions applied to other terms. First-order logic also expands the lexicon of propositional logic with the quantifiers “for all” and “there exists” that are interpreted consistently with their natural language meaning.This chapter is devoted to classical first-order logic. Our presentation is similar to the one conducted for propositional logic. We first define the syntax of first-order logic, followed by its semantics. Next we define a proof system for it and present the fundamental theoretical results of soundness and completeness. We also discuss the decision problems related to this logic. The remaining sections of the chapter cover variations and extensions of first-order logic, as well as first-order theories.

In recent years, internal coordinates have become the preferred means of expressing potential energy surfaces. The ability to transform quantities from chemically significant internal coordinates to primitive Cartesian coordinates and spectroscopically relevant normal coordinates is thus critical to the further development of computational chemistry. In the present work, general nth order formulas are presented for the Cartesian derivatives of the five most commonly used internal coordinates--bond stretching, bond angle, torsion, out-of-plane angle, and linear bending. To compose such formulas in a reasonably understandable fashion, a new notation is developed that is a generalization of that which has been used previously for similar purposes. The notation developed leads to easily programmable and reasonably understandable arbitrary order formulas, yet it is powerful enough to express the arbitrary order B tensor of a general, N-point internal coordinate, as is done herein. The techniques employed in the derivation of such formulas are relatively straightforward, and could presumably be applied to a number of other internal coordinates as needed.

The article deals with the problem of using communicative methods in foreign language teaching (real language practice; breaking down the language barriers; speech spontaneity; fluent English speaking and comprehension, etc.). The basic principles of its using are defined (active participation of each communicant in the educational process; a teacher motivates students’ speech, directs, corrects intelligently; communicants learn to explain and express their thoughts through verbal and non-verbal means of communication; using concentrated learning technology; engaging students into the cultural content of English speaking countries, etc.). The advantages (the communicative approach encourages students to make a guess about the meaning of a new word in a context that promotes better memorization; a relaxed atmosphere in lessons helps to overcome the language barrier: students are not afraid to speak and make mistakes, etc.) and the disadvantages of the communicative method (the communicative method may not suit particularly shy and uncertain students, indirect grammar, a lack of emphasis on mastering writing skills, etc.) are identified. The most effective communication tasks for the development and improvement of foreign language communicative competence are offered. The method of communicative task-based teaching helps students perform a specific speech task by immersing them into a real life situation, when oral communication is of fundamental importance. Much attention is given to the task itself, but not to grammatical or lexical constructions. The goal is to complete the speech task. The language here becomes a communication tool that aims to help students to cope with the task successfully. Such methods of research as comparison, generalization, analysis are used in the article. It helps get into the essence of the outlined problem and make reasonable conclusions on the successful students’ foreign language communication, speech spontaneity in educational situations close to real life situations.

Tractable reasoning via approximation

The dynamics of adaptation are difficult to predict because it is highly stochastic even in large populations. The uncertainty emerges from random genetic drift arising in a vanguard of particularly fit individuals of the population. Several approaches have been developed to analyze the crucial role of genetic drift on the expected dynamics of adaptation, including the mean fitness of the entire population, or the fate of newly arising beneficial deleterious mutations. However, little is known about how genetic drift causes fluctuations to emerge on the population level, where it becomes palpable as variations in the adaptation speed and the fitness distribution. Yet these phenomena control the decay of genetic diversity and variability in evolution experiments and are key to a truly predictive understanding of evolutionary processes. Here, we show that correlations induced by these emergent fluctuations can be computed at any arbitrary order by a suitable choice of a dynamical constraint. The resulting linear equations exhibit fluctuation-induced terms that amplify short-distance correlations and suppress long-distance ones. These terms, which are in general not small, control the decay of genetic diversity and, for wave-tip dominated ("pulled") waves, lead to anticorrelations between the tip of the wave and the lagging bulk of the population. While it is natural to consider the process of adaptation as a branching random walk in fitness space subject to a constraint (due to finite resources), we show that other traveling wave phenomena in ecology and evolution likewise fall into this class of constrained branching random walks. Our methods, therefore, provide a systematic approach toward analyzing fluctuations in a wide range of population biological processes, such as adaptation, genetic meltdown, species invasions, or epidemics.

We show that Kleene algebra with tests (KAT) subsumes propositional Hoare logic (PHL). Thus the specialized syntax and deductive apparatus of Hoare logic are inessential and can be replaced by simple equational reasoning. In addition, we show that all relationally valid inference rules are derivable in KAT and that deciding the relational validity of such rules is PSPACE -complete.

In classical deterministic planning, solutions to planning tasks are simply sequences of actions, but that is not sufficient for contingent plans in non-deterministic environments. Contingent plans are often expressed through policies that map states to actions. An alternative is to specify contingent plans as programs, e.g. in the syntax of Propositional Dynamic Logic (PDL). PDL is a logic for reasoning about programs with sequential composition, test and non-deterministic choice. However, as we show in the paper, none of the existing PDL modalities directly captures the notion of a solution to a planning task under non-determinism. We add a new modality to star-free PDL correctly capturing this notion. We prove the appropriateness of the new modality by showing how to translate back and forth between policies and PDL programs under the new modality. More precisely, we show how a policy solution to a planning task gives rise to a program solution expressed via the new modality, and vice versa. We also provide an axiomatisation of our PDL extension through reduction axioms into standard star-free PDL.

"This book describes the aspects of mathematical logic related to computer sciences. The materials adopted in this book are intended to attend to both the peculiarities of logical systems and the requirements of computer science."

We derive new formulas for the high dimensional biharmonic potential acting on Gaussians or Gaussians times special polynomials. These formulas can be used to construct accurate cubature formulas of an arbitrary high order which are fast and effective also in very high dimensions. Numerical tests show that the formulas are accurate and provide the predicted approximation rate $$O(h^8)$$ up to the dimension $$10^7$$ .