Dynamic Topological Completeness for

Dynamic topological logic (DTL) combines topological and temporalmodalities to express asymptotic properties of dynamic systemson topological spaces. A dynamic topological model is a tripleX ,f , V , where X is a topological space, f : X X a continuousfunction and V a truth valuation assigning subsets of X to propositionalvariables. Valid formulas are those that are true in every model,independently of X or f. A natural problem that arises is toidentify the logics obtained on familiar spaces, such as . It [9] it was shown that any satisfiable formulacould be satisfied in some for n large enough, but the question of how the logic varieswith n remained open. In this paper we prove that any fragment of DTL that is completefor locally finite Kripke frames is complete for . This includes DTL; it also includes some largerfragments, such as DTL₁, where "henceforth" may not appear inthe scope of a topological operator. We show that satisfiabilityof any formula of our language in a locally finite Kripke frameimplies satisfiability in by constructing continuous, open maps from the plane intoarbitrary locally finite Kripke frames, which give us a typeof bisimulation. We also show that the results cannot be extendedto arbitrary formulas of DTL by exhibiting a formula which isvalid in but not in arbitrarytopological spaces.     

Information–movement coupling in developing cricketers under changing ecological practice constraints

Changing informational constraints of practice, such as when using ball projection machines, has been shown to significantly affect movement coordination of skilled cricketers. To date, there has been no similar research on movement responses of developing batters, an important issue since ball projection machines are used heavily in cricket development programmes. Timing and coordination of young cricketers (n = 12, age = 15.6 ± 0.7 years) were analyzed during the forward defensive and forward drive strokes when facing a bowling machine and bowler (both with a delivery velocity of 28.14 ± 0.56 m s⁻¹). Significant group performance differences were observed between the practice task constraints, with earlier initiation of the backswing, front foot movement, downswing, and front foot placement when facing the bowler compared to the bowling machine. Peak height of the backswing was higher when facing the bowler, along with a significantly larger step length. Altering the informational constraints of practice caused major changes to the information–movement couplings of developing cricketers. Data from this study were interpreted to emanate from differences in available specifying variables under the distinct practice task constraints. Considered with previous findings, results confirmed the need to ensure representative batting task constraints in practice, cautioning against an over-reliance on ball projection machines in cricket development programmes.     

Object correspondence across brief occlusion is established on the basis of both spatiotemporal and surface feature cues

The correspondence problem is a classic issue in vision and cognition. Frequent perceptual disruptions, such as saccades and brief occlusion, create gaps in perceptual input. How does the visual system establish correspondence between objects visible before and after the disruption? Current theories hold that object correspondence is established solely on the basis of an object’s spatiotemporal properties and that an object’s surface feature properties (such as color or shape) are not consulted in correspondence operations. In five experiments, we tested the relative contributions of spatiotemporal and surface feature properties to establishing object correspondence across brief occlusion. Correspondence operations were strongly influenced both by the consistency of an object’s spatiotemporal properties across occlusion and by the consistency of an object’s surface feature properties across occlusion. These data argue against the claim that spatiotemporal cues dominate the computation of object correspondence. Instead, the visual system consults multiple sources of relevant information to establish continuity across perceptual disruption.     

Why don’t well-educated adults understand accumulation? A challenge to researchers,educators, and citizens

Accumulation is a fundamental process in dynamic systems: inventory accumulates production less shipments; the national debt accumulates the federal deficit. Effective decision making in such systems requires an understanding of the relationship between stocks and the flows that alter them. However, highly educated people are often unable to infer the behavior of simple stock–flow systems. In a series of experiments we demonstrate that poor understanding of accumulation, termed stock–flow failure, is a fundamental reasoning error. Persistent poor performance is not attributable to an inability to interpret graphs, lack of contextual knowledge, motivation, or cognitive capacity. Rather, stock–flow failure is a robust phenomenon that appears to be rooted in failure to appreciate the most basic principles of accumulation, leading to the use of inappropriate heuristics. We show that many people, including highly educated individuals with strong technical training, use what we term the “correlation heuristic”, erroneously assuming that the behavior of a stock matches the pattern of its flows. We discuss the origins of stock–flow failure and implications for management and education.     

Keep ‘hoping’ for rationality: a solution to the backward induction paradox

We formalise a notion of dynamic rationality in terms of a logic of conditional beliefs on (doxastic) plausibility models. Similarly to other epistemic statements (e.g. negations of Moore sentences and of Muddy Children announcements), dynamic rationality changes its meaning after every act of learning, and it may become true after players learn it is false. Applying this to extensive games, we “simulate” the play of a game as a succession of dynamic updates of the original plausibility model: the epistemic situation when a given node is reached can be thought of as the result of a joint act of learning (via public announcements) that the node is reached. We then use the notion of “stable belief”, i.e. belief that is preserved during the play of the game, in order to give an epistemic condition for backward induction: rationality and common knowledge of stable belief in rationality. This condition is weaker than Aumann’s and compatible with the implicit assumptions (the “epistemic openness of the future”) underlying Stalnaker’s criticism of Aumann’s proof. The “dynamic” nature of our concept of rationality explains why our condition avoids the apparent circularity of the “backward induction paradox”: it is consistent to (continue to) believe in a player’s rationality after updating with his irrationality.     

Dynamic epistemic logic with branching temporal structures

van Bentham et al. (Merging frameworks for interaction: DEL and ETL, 2007) provides a framework for generating the models of Epistemic Temporal Logic (ETL: Fagin et al., Reasoning about knowledge, 1995; Parikh and Ramanujam, Journal of Logic, Language, and Information, 2003) from the models of Dynamic Epistemic Logic (DEL: Baltag et al., in: Gilboa (ed.) Tark 1998, 1998; Gerbrandy, Bisimulations on Planet Kripke, 1999). We consider the logic TDEL on the merged semantic framework, and its extension with the labeled past-operator “P _ϵ” (“The event ϵ has happened before which. . .”). To axiomatize the extension, we introduce a method for transforming a given model into a normal form in a suitable sense. These logics suggest further applications of DEL in the theory of agency, the theory of learning, etc.     

Dynamic traffic management on a familiar road: Failing to detect changes in variable speed limits

Variable speed limits (VSL) are used more commonly around the globe lately. Although on a macroscopic level positive effects of VSLs have been reported, the caveat is that the impact of VSLs is very sensitive to the level of driver compliance. Thus far it is unknown whether all individual drivers are actually able to notice when a speed limit changes into another speed limit; a prerequisite for purposeful speed limit compliance in the first place. To simulate regular driving conditions, twenty-four participants were familiarised with a particular route by driving the same route in a driving simulator nineteen times on five separate days. Part of the route consisted of a motorway where VSL signs were regularly displayed above every driving lane. At drive nineteen, speed limits changed from 80 km/h to 100 km/h on four out of eight consecutive signs. After passing all signs, one expects 6.25% of the participants still to be unaware that the speed limit had increased (based on chance), while the results showed most participants had failed to notice the speed limit change (58.3%). Instead, they saw what they expected to see: a speed limit of 80 km/h. If the speed change had been vice versa, in other words from 100 km/h to 80 km/h, this would immediately result in speed offences, though not deliberately at all.     

The Undecidability of Propositional Adaptive Logic

We investigate and classify the notion of final derivability of two basic inconsistency-adaptive logics. Specifically, the maximal complexity of the set of final consequences of decidable sets of premises formulated in the language of propositional logic is described. Our results show that taking the consequences of a decidable propositional theory is a complicated operation. The set of final consequences according to either the Reliability Calculus or the Minimal Abnormality Calculus of a decidable propositional premise set is in general undecidable, and can be -complete. These classifications are exact. For first order theories even finite sets of premises can generate such consequence sets in either calculus.     

My beliefs about your beliefs: a case study in theory of mind and epistemic logic

We model three examples of beliefs that agents may have about other agents’ beliefs, and provide motivation for this conceptualization from the theory of mind literature. We assume a modal logical framework for modelling degrees of belief by partially ordered preference relations. In this setting, we describe that agents believe that other agents do not distinguish among their beliefs (‘no preferences’), that agents believe that the beliefs of other agents are in part as their own (‘my preferences’), and the special case that agents believe that the beliefs of other agents are exactly as their own (‘preference refinement’). This multi-agent belief interaction is frame characterizable. We provide examples for introspective agents. We investigate which of these forms of belief interaction are preserved under three common forms of belief revision.     

Working with countertransference

The transference-countertransference relationship is only one of five modalities of relationship that research has identified as potentially present in the therapeutic encounter. This paper gives the background and definition to one aspect of this - the countertransference - and traces the development of the concept from Freud's first use of the term in 1910 to the contemporary view that it is a useful tool of psychotherapy. The first part explains its connection with the Kleinian concept of projective identification and discusses its elaboration by the object relations school. There is general acceptance nowadays that the countertransference contains a great deal of information about the client's psychological world. It is therefore important to understand this process and the authors have identified three main dimensions to countertransference. These are its vector (or direction and force), its variance (the quality it represents), and its valence (its effect on the client). The second part of the article illustrates, through the use of example and metaphor, how these three dimensions are defined and can be recognized. Common themes and paradigms of countertransference are identified and discussed along with some ways in which experience has shown how these might be contained and worked with constructively. Finally, a clinical vignette is presented in which some of the dimensions of countertransference are identified and used to understand the client's psychic world and foster therapeutic change.