Squares in Fork Arrow Logic

In this paper we show that the class of fork squares has a complete orthodox axiomatization in fork arrow logic (FAL). This result may be seen as an orthodox counterpart of Venema's non-orthodox axiomatization for the class of squares in arrow logic. FAL is the modal logic of fork algebras (FAs) just as arrow logic is the modal logic of relation algebras (RAs). FAs extend RAs by a binary fork operator and are axiomatized by adding three equations to RAs equational axiomatization. A proper FA is an algebra of relations where the fork is induced by an injective operation coding pair formation. In contrast to RAs, FAs are representable by proper ones and their equational theory has the expressive power of full first-order logic. A square semantics (the set of arrows is U×U for some set U) for arrow logic was defined by Y. Venema. Due to the negative results about the finite axiomatizability of representable RAs, Venema provided a non-orthodox finite axiomatization for arrow logic by adding a new rule governing the applications of a difference operator. We address here the question of extending the type of relational structures to define orthodox axiomatizations for the class of squares. Given the connections between this problem and the finitization problem addressed by I. Németi, we suspect that this cannot be done by using only logical operations. The modal version of the FA equations provides an orthodox axiomatization for FAL which is complete in view of the representability of FAs. Here we review this result and carry it further to prove that this orthodox axiomatization for FAL also axiomatizes the class of fork squares.     

Mathematical modal logic: A view of its evolution

This is a survey of the origins of mathematical interpretations of modal logics, and their development over the last century or so. It focuses on the interconnections between algebraic semantics using Boolean algebras with operators and relational semantics using structures often called Kripke models. It reviews the ideas of a number of people who independently contributed to the emergence of relational semantics, and compares them with the work of Kripke. It concludes with an account of several applications of modal model theory to mathematics and theoretical computer science.     

Computing with Cylindric Modal Logics and Arrow Logics,Lower Bounds

The complexity of the satisfiability problems of various arrow logics and cylindric modal logics is determined. As is well known, relativising these logics makes them decidable. There are several parameters that can be set in such a relativisation. We focus on the following three: the number of variables involved, the similarity type and the kind of relativised models considered. The complexity analysis shows the importance and relevance of these parameters.     

PEAK关系训练系统：孤独症语言障碍康复的新方法

PEAK (Promoting the Emergence of Advanced Knowledge, 促进高阶知识涌现)关系训练系统是全球首个同时整合了斯金纳的《言语行为》和后斯金纳主义的“关系框架理论”, 促进孤独症谱系障碍(Autism spectrum disorders, ASD)患者的语言、学习、社交等核心技能发展的语言行为评估训练系统。截至2018年底, PEAK关系训练系统由以下4个模块组成：直接训练模块、泛化模块、等价关系模块、功能转化模块。每一模块依据难易程度分别设置了184个目标能力的评估方法及训练课程。已发表的多项实证研究表明, PEAK关系训练系统打破了《语言行为里程碑评估及安置程序》(Verbal Behavior Milestones and Placement Program, VB-MAPP) 对ASD患者进行里程碑评估时出现的“天花板效应”, 有望比VB-MAPP提供更全面、高阶的语言行为评估体系。此外, PEAK关系训练系统表现出的评估工具的信效度良好、多项效果研究显著、实践中易操作等特性, 使其不仅适用于专业人员教学, 未来在ASD患者家庭干预模式中也有潜在的应用价值。     

The wording of conclusions in relational reasoning

Literature on relational reasoning mainly focuses on the performance question. It is typically argued that problem difficulty relies on the number of "mental models" compatible with the problem. However, no study has ever investigated the wording of conclusions that participants formulate. In the present work, we analyze the relational terms that people use in drawing conclusions from spatial relation problems (A is to the left of B, B is to the left C, D is in front of A, E is in front C, What is the relation between D and E?). We observed a general preference for expressing conclusions with 'left' rather than conclusions with 'right'. We also found that three factors had an influence on the wording of the conclusions: the linguistic form of premises, the question type and the presentation format. On the other hand, the number of models and premise order did not affect the wording of conclusions. Our study shows that the type of conclusion produced provides a new key to identifying the mental processes involved in spatial reasoning. Implications for the two main approaches to reasoning processes (i.e. the analogical and the propositional approaches) are discussed.     

Representations of monadic <Emphasis Type="Italic">MV</Emphasis> -algebras

Representations of monadic MV -algebra, the characterization of locally finite monadic MV -algebras, with axiomatization of them, definability of non-trivial monadic operators on finitely generated free MV -algebras are given. Moreover, it is shown that finitely generated m-relatively complete subalgebra of finitely generated free MV -algebra is projective.     

Friendships of aggressive youth: considering the influences of being disliked and of being perceived as popular

Past research provides conflicting evidence regarding whether aggressive youth have problems in the domain of friendship. The current study tested whether being disliked by peers exacerbates the negative effects of aggression on friendship and whether being perceived as popular by peers mitigates these damaging effects. Participants were 607 third-, fifth-, seventh-, and ninth-grade students. Support for the hypothesis that being disliked or being perceived as popular would moderate relations between aggression and friendship adjustment was found for the association between relational aggression and friendship conflict. Specifically, relational aggression was associated with having conflictual friendships for youth who were disliked but not for youth who were perceived as popular. In addition, similarity between friends was found in terms of how aggressive youth were as well as in terms of how disliked they were and how popular they were perceived to be. Implications for the well-being and development of aggressive youth are discussed.     

Acceptance and commitment therapy: model, processes and outcomes

The present article presents and reviews the model of psychopathology and treatment underlying Acceptance and Commitment Therapy (ACT). ACT is unusual in that it is linked to a comprehensive active basic research program on the nature of human language and cognition (Relational Frame Theory), echoing back to an earlier era of behavior therapy in which clinical treatments were consciously based on basic behavioral principles. The evidence from correlational, component, process of change, and outcome comparisons relevant to the model are broadly supportive, but the literature is not mature and many questions have not yet been examined. What evidence is available suggests that ACT works through different processes than active treatment comparisons, including traditional Cognitive-Behavior Therapy (CBT). There are not enough well-controlled studies to conclude that ACT is generally more effective than other active treatments across the range of problems examined, but so far the data are promising.     

The effects of cumulative practice on mathematics problem solving

This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.     

Communication and Strong Compositionality

Ordinary semantic compositionality (meaning of whole determined from meanings of parts plus composition) can serve to explain how a hearer manages to assign an appropriate meaning to a new sentence. But it does not serve to explain how the speaker manages to find an appropriate sentence for expressing a new thought. For this we would need a principle of inverse compositionality, by which the expression of a complex content is determined by the expressions of it parts and the mode of composition. But this presupposes that contents have constituent structure, and this cannot be taken for granted. However, it can be proved that if a certain principle of substitutivity is valid for a particular language, then the meanings expressed by its sentences can justifiably be treated as structured. In its simplest form, this principle says that if in a complex expression a constituent is replaced by another constituent with a different meaning, the new complexhas a meaning different from the original. This principle is again inversely related to the normal compositional principle of substitutivity. The combination of ordinary and inverse compositionality is here called strong compositionality. The proof is carried out in the algebraic framework developed by Wilfrid Hodges and Dag Westerståhl.