An algebraic study of well-foundedness

A foundational algebra ( , f, ) consists of a hemimorphism f on a Boolean algebra with a greatest solution to the condition f(x). The quasi-variety of foundational algebras has a decidable equational theory, and generates the same variety as the complex algebras of structures (X, R), where f is given by R-images and is the non-wellfounded part of binary relation R.The corresponding results hold for algebras satisfying =0, with respect to complex algebras of wellfounded binary relations. These algebras, however, generate the variety of all ( ,f) with f a hemimorphism on ).Admitting a second hemimorphism corresponding to the transitive closure of R allows foundational algebras to be equationally defined, in a way that gives a refined analysis of the notion of diagonalisable algebra.The research reported in this paper was carried out while the author was at the Department of Mathematics and Statistics, University of Auckland, under a teaching exchange with the Victoria University of Wellington.     

The semantics of Hoare's Iteration Rule

Hoare's Iteration Rule is a principle of reasoning that is used to derive correctness assertions about the effects of implementing a while-command. We show that the propositional modal logic of this type of command is axiomatised by Hoare's rule in conjunction with two additional axioms. The proof also establishes decidability of the logic. The paper concludes with a discussion of the relationship between the logic of while and Segerberg's axiomatisation of propositional dynamic logic.     

An abstract setting for Henkin proofs

A general result is proved about the existence of maximally consistent theories satisfying prescribed closure conditions. The principle is then used to give streamlined proofs of completeness and omitting-types theorems, in which inductive Henkin-style constructions are replaced by a demonstration that a certain theory respects a certain class of inference rules.     

The Finite Model Property for Logics with the Tangle Modality

The tangle modality is a propositional connective that extends basic modal logic to a language that is expressively equivalent over certain classes of finite frames to the bisimulation-invariant fragments of both first-order and monadic second-order logic. This paper axiomatises several logics with tangle, including some that have the universal modality, and shows that they have the finite model property for Kripke frame semantics. The logics are specified by a variety of conditions on their validating frames, including local and global connectedness properties. Some of the results have been used to obtain completeness theorems for interpretations of tangled modal logics in topological spaces.     

Parallel action: Concurrent dynamic logic with independent modalities

Regular dynamic logic is extended by the program construct, meaning and executed in parallel. In a semantics due to Peleg, each command is interpreted as a set of pairs (s,T), withT being the set of states reachable froms by a single execution of, possibly involving several processes acting in parallel. The modalities << and [] are given the interpretations<>A is true ats iff there existsT withsRT andA true throughoutT, and[]A is true ats iff for allT, ifsRT thenA is true throughoutT, which make <> and [] no longer interdefinable via negation, as they are in the regular case.We prove that the logic defined by this modelling is finitely axiomatisable and has the finite model property, hence is decidable. This requires the development a new theory of canonical models and filtrations for reachability relations.     

A simple system for the remote detection and analysis of sniffing in explosives detection dogs

In this article, we describe a device that we have developed, for both research and operational purposes, to assist handlers of sniffer dogs and improve efficiency of search. The device transmits sounds from the dog’s muzzle area to a listener, enabling determination of whether the dog is actually sniffing during a search. Both the aural and the computerized sound analyses enable study of the dog’s sniffing behavior under a variety of situations. Correlation of these data with the visually monitored behavior of the working dog contributes additional and important information and leads to a greater under-standing of detector dogs’ behavior and abilities.     

The role of context specificity in learning: the effects of training context on explosives detection in dogs

Various experiments revealed that if an animal learns a stimulus–response–reinforcer relationship in one context and is then tested in another context there is usually a lessening of stimulus control, and the same discriminative stimuli that reliably controlled the behavior in the first context will have less effect in the new context. This reduction in performance is known as the context shift effect. The effect of changing context on the probability of detecting explosives was investigated in seven highly trained explosives detection dogs (EDDs). In experiment 1 the dogs were trained alternately on path A, which always had five hidden explosives, and on a very similar path B, which never had any explosives. Within a few sessions the dogs showed a significant decrease in search behavior on path B, but not on path A. In experiment 2 the same dogs were trained only on path B with a target density of one explosive hidden every 4th day. The probability of the dogs now detecting the explosive was found to be significantly lower than in experiment 1. In experiment 3 the effect of the low target density as used in experiment 2 was investigated on a new but very similar path C. Both the detection probability for the one explosive every 4th day on the new path and the motivation to search were significantly higher than found in experiment 2. Finally, in experiment 4, an attempt was made to recondition the dogs to search on path B. Although trained for 12 daily sessions with one explosive hidden every session, the dogs failed to regain the normal levels of motivation they had shown on both new paths and on the paths that they knew usually contained explosives. The findings reveal that even a very intensively trained EDD will rapidly learn that a specific stretch of path does not contain explosives. The dog will then be less motivated to search and will miss newly placed targets. This learning is specific to the formerly always-clean path and is to some extent irreversible. However, the dog will search and detect normally on new paths even if they are very similar to the always-clean path. The data are discussed in terms of variables affecting renewal. The results suggest that following training designed to make a behavior context independent, any extinction training will not generalize beyond that specific context used during the extinction training. In addition, if the behavior is extinguished in a specific context, it will be very difficult to restore that behavior in that context. These conclusions should be considered by anyone attempting to extinguish well-established trans-context behaviors.This research reports portions of a doctoral dissertation submitted by Irit Gazit to Tel Aviv University.     

Grishin Algebras and Cover Systems for Classical Bilinear Logic

Grishin algebras are a generalisation of Boolean algebras that provide algebraic models for classical bilinear logic with two mutually cancelling negation connectives. We show how to build complete Grishin algebras as algebras of certain subsets (??propositions??) of cover systems that use an orthogonality relation to interpret the negations. The variety of Grishin algebras is shown to be closed under MacNeille completion, and this is applied to embed an arbitrary Grishin algebra into the algebra of all propositions of some cover system, by a map that preserves all existing joins and meets. This representation is then used to give a cover system semantics for a version of classical bilinear logic that has first-order quantifiers and infinitary conjunctions and disjunctions.     

Attentional bias for threat: Evidence for delayed disengagement from emotional faces

This study examined cognitive aspects of coping with stress, how these related to religiosity, and how they related to outcomes (positive mood and distress). Participants (n=126) were of Protestant or Jewish background, and had all experienced recent major stress. They were assessed on measures of religiosity, religious coping, perception of the consequences of the stressful event, attributions for its occurrence, and distress, intrusive unpleasant thoughts, and positive affect. Religiosity affected ways of thinking about the stressful situation, namely: Belief that G-d is enabling the individual to bear their troubles (religious/spiritual support), belief that it was all for the best, and (more weakly) belief that all is ultimately controlled by G-d. Religiosity affected neither the proportion of positive consequences perceived as outcomes of the event, nor the causal attributions examined. Religious background (Protestant vs. Jewish) had negligible effects on the cognitions measures. Causal pathway analysis suggested that religion-related cognitions might directly affect positive affect, but not distress. Problems of design and interpretation are discussed. The study suggests some cognitively mediated means by which religion may have comforting effects.