On the Predicate Logic of Linear Kripke Frames and some of its Extensions

We propose a new, rather simple and short proof of Kripke-completeness for the predicate variant of Dummett's logic. Also a family of Kripke-incomplete extensions of this logic that are complete w.r.t. Kripke frames with equality (or equivalently, w.r.t. Kripke sheaves [8]), is described.     

A Cut-Free Sequent System for the Smallest Interpretability Logic

The idea of interpretability logics arose in Visser [Vis90]. He introduced the logics as extensions of the provability logic GLwith a binary modality . The arithmetic realization of A B in a theory T will be that T plus the realization of B is interpretable in T plus the realization of A (T + A interprets T + B). More precisely, there exists a function f (the relative interpretation) on the formulas of the language of T such that T + B C implies T + A f(C).The interpretability logics were considered in several papers. An arithmetic completeness of the interpretability logic ILM, obtained by adding Montagna's axiom to the smallest interpretability logic IL, was proved in Berarducci [Ber90] and Shavrukov [Sha88] (see also Hájek and Montagna [HM90] and Hájek and Montagna [HM92]). [Vis90] proved that the interpretability logic ILP, an extension of IL, is also complete for another arithmetic interpretation. The completeness with respect to Kripke semantics due to Veltman was, for IL, ILMand ILP, proved in de Jongh and Veltman [JV90]. The fixed point theorem of GLcan be extended to ILand hence ILMand ILP(cf. de Jongh and Visser [JV91]). The unary pendant "T interprets T + A" is much less expressive and was studied in de Rijke [Rij92]. For an overview of interpretability logic, see Visser [Vis97], and Japaridze and de Jongh [JJ98].In this paper, we give a cut-free sequent system for IL. To begin with, we give a cut-free system for the sublogic IL4of IL, whose -free fragment is the modal logic K4. A cut-elimination theorem for ILis proved using the system for IK4and a property of Löb's axiom.     

Coherence in Substructural Categories

It is proved that MacLane's coherence results for monoidal and symmetric monoidal categories can be extended to some other categories with multiplication; namely, to relevant, affine and cartesian categories. All results are formulated in terms of natural transformations equipped with graphs (g-natural transformations) and corresponding morphism theorems are given as consequences. Using these results, some basic relations between the free categories of these classes are obtained.     

The role of honour concerns in emotional reactions to offences

We investigated the role of honour concerns in mediating the effect of nationality and gender on the reported intensity of anger and shame in reaction to insult vignettes. Spain, an honour culture, and The Netherlands, where honour is of less central significance, were selected for comparison. A total of 260 (125 Dutch, 135 Spanish) persons participated in the research. Participants completed a measure of honour concerns and answered questions about emotional reactions of anger and shame to vignettes depicting insults in which type of threat was manipulated. It was found that Spanish participants responded especially intensely to insults that threaten family honour, and that this effect of nationality on emotional reactions to threats to family honour was mediated by individual differences in concern for family honour.     

Interpolation and Amalgamation; Pushing the Limits. Part II

This is the second part of the paper [Part I] which appeared in the previous issue of this journal.     

Special issue: Combining probability and logic

This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers.     

How do people learn from negative evidence? Non-monotonic generalizations and sampling assumptions in inductive reasoning

A robust finding in category-based induction tasks is for positive observations to raise the willingness to generalize to other categories while negative observations lower the willingness to generalize. This pattern is referred to as monotonic generalization. Across three experiments we find systematic non-monotonicity effects, in which negative observations raise the willingness to generalize. Experiments 1 and 2 show that this effect emerges in hierarchically structured domains when a negative observation from a different category is added to a positive observation. They also demonstrate that this is related to a specific kind of shift in the reasoner’s hypothesis space. Experiment 3 shows that the effect depends on the assumptions that the reasoner makes about how inductive arguments are constructed. Non-monotonic reasoning occurs when people believe the facts were put together by a helpful communicator, but monotonicity is restored when they believe the observations were sampled randomly from the environment.     

The Role of Reasoning and Pragmatics in the Modifier Effect

The modifier effect refers to the fact that the perceived likelihood of a property in a noun category is diminished if the noun is modified. For example, “Pigs live on farms” is rated as more likely than “Dirty pigs live on farms.” The modifier effect has been demonstrated in many studies, but the underlying cognitive mechanisms are still unclear. This paper reports two series of experiments that jointly point to the conclusion that the modifier effect is the result of a superposition of three cognitive mechanisms: (a) probabilistically softened default inheritance, (b) pragmatic implicatures due to Gricean relevance assumptions, and (c) inference based on world knowledge. We present evidence that the pragmatic effects operate largely on an unconscious level and that their influence can be reduced by changing the presentation format of the cognitive task.     

The temporal-relevance temporal-uncertainty model of prospective duration judgment

A model aimed at explaining prospective duration judgments in real life settings (as well as in the laboratory) is presented. The model is based on the assumption that situational meaning is continuously being extracted by humans’ perceptual and cognitive information processing systems. Time is one of the important dimensions of situational meaning. Based on the situational meaning, a value for Temporal Relevance is set. Temporal Relevance reflects the importance of temporal aspects for enabling adaptive behavior in a specific moment in time. When Temporal Relevance is above a certain threshold a prospective duration judgment process is evoked automatically. In addition, a search for relevant temporal information is taking place and its outcomes determine the level of Temporal Uncertainty which reflects the degree of knowledge one has regarding temporal aspects of the task to be performed. The levels of Temporal Relevance and Temporal Uncertainty determine the amount of attentional resources allocated for timing by the executive system. The merit of the model is in connecting timing processes with the ongoing general information processing stream. The model rests on findings in various domains which indicate that cognitive-relevance and self-relevance are powerful determinants of resource allocation policy. The feasibility of the model is demonstrated by analyzing various temporal phenomena. Suggestions for further empirical validation of the model are presented.