Belief Change in Branching Time: AGM-consistency and Iterated Revision

We study belief change in the branching-time structures introduced in Bonanno (Artif Intell 171:144–160, 2007). First, we identify a property of branching-time frames that is equivalent (when the set of states is finite) to AGM-consistency, which is defined as follows. A frame is AGM-consistent if the partial belief revision function associated with an arbitrary state-instant pair and an arbitrary model based on that frame can be extended to a full belief revision function that satisfies the AGM postulates. Second, we provide a set of modal axioms that characterize the class of AGM-consistent frames within the modal logic introduced in Bonanno (Artif Intell 171:144–160, 2007). Third, we introduce a generalization of AGM belief revision functions that allows a clear statement of principles of iterated belief revision and discuss iterated revision both semantically and syntactically.     

Coarsening a Knowledge Structure

This paper describes an assessment procedure which does not deal explicitly with the whole knowledge structure, but rather operates on a faithful summary of the structure. The summary is achieved through the notion of coarsening of a structure, where the knowledge states are grouped into equivalence classes. We first define a stochastic assessment procedure running on the coarsening. Then we specify a set of possible properties for the equivalence relation. In particular, we define a notion of convexity for a knowledge structure. The results are justified by a simulation study.     

Basic Infobase Change

Generalisations of theory change involving arbitrary sets of wffs instead of belief sets have become known as base change. In one view, a base should be thought of as providing more structure to its generated belief set, and can be used to determine the theory change operation associated with a base change operation. In this paper we extend a proposal along these lines by Meyer et al. We take an infobase as a finite sequence of wffs, with each element in the sequence being seen as an independently obtained bit of information, and define appropriate infobase change operations. The associated theory change operations satisfy the AGM postulates for theory change. Since an infobase change operation produces a new infobase, it allows for iterated infobase change. We measure iterated infobase change against the postulates proposed by Darwiche et al. and Lehmann.     

The relation between stimulus function and equivalence class formation

Fifty participants were exposed to a simple discrimination-training procedure during which six S+ functions were established for six arbitrary stimuli, and S- functions were established for a further six stimuli. Following this training, each participant was exposed to one of five conditions. In the S+ condition, participants were exposed to a stimulus equivalence training and testing procedure using only the six S+ stimuli as samples and comparisons. In the S+/S- condition, participants were exposed to the same training and testing sequence as in the S+ condition, the difference being that three S+ and three S- stimuli were used as sample and comparison stimuli, with each set of three corresponding to the trained equivalence relations. In the S+/S- mixed condition, the S+ and S- stimuli were assigned to their roles as samples and comparisons in a quasi-random order. In the S- condition, all six S- stimuli were used. The no-function condition served as a control condition and employed stimuli for which no stimulus-control functions had been established. The results showed that, on average, participants required more testing trials to form equivalence relations when the stimuli involved were functionally similar rather than functionally different. Moreover, participants required more test trials to form equivalence relations when novel arbitrary stimuli, rather than functionally distinct stimuli, were used as samples and comparisons. The speed of acquisition of stimulus equivalence was also related to the number of functionally similar stimuli established before training. These findings indicate a variety of ways in which the emergence of equivalence relations is affected by the functional classes in which the relevant stimuli participate.     

A characterization of the concept of independence in knowledge structures

In knowledge space theory a knowledge structure provides a deterministic representation of the implications among the items in a given set Q. Concrete procedures for the efficient assessment of knowledge by means of a knowledge structure have been proposed by Doignon and Falmagne [Falmagne, J.-C., & Doignon, J.-P. (1988a). A class of stochastic procedures for the assessment of knowledge. British Journal of Mathematical and Statistical Psychology, 41, 1-23; Falmagne, J.-C., & Doignon, J.-P. (1988b). A markovian procedure for assessing the state of a system. Journal of Mathematical Psychology, 32, 232-258]. The primitive idea at the core of such procedures is that the (correct or wrong) answers of a student to a subset A⊆Q of items could be inferred from the answers to a subset B⊆Q of items that were previously presented to that student. Since B provides information about A, from the viewpoint of the teacher these two subsets are not independent. This idea of dependence vs. independence is formalized in this paper in terms of an independence relation on the power set of Q. A nice characterization of this relation allows to express an arbitrary knowledge structure as the combination of a number of substructures each of which is independent of each other. An algorithm is then proposed which checks for independence in a knowledge structure and decomposes this last into a collection of independent substructures.     

A Way to Interpret Łukasiewicz Logic and Basic Logic

Fuzzy logics are in most cases based on an ad-hoc decision about the interpretation of the conjunction. If they are useful or not can typically be found out only by testing them with example data. Why we should use a specific fuzzy logic can in general not be made plausible. Since the difficulties arise from the use of additional, unmotivated structure with which the set of truth values is endowed, the only way to base fuzzy logics on firm ground is the development of alternative semantics to all of whose components we can associate a meaning. In this paper, we present one possible approach to justify ex post Łukasiewicz Logic as well as Basic Logic. The notion of ambiguity is central. Our framework consists of a Boolean or a Heyting algebra, respectively, endowed with an equivalence relation expressing ambiguity. The quotient set bears naturally the structure of an MV- or a BL-algebra, respectively, and thus can be used to interpret propositions of the mentioned logics.     

Racism as a transference state: episodes of racial hostility in the psychoanalytic context

Episodes of racial prejudice emerging in the context of a psychoanalytic therapy suggest that racism can be thought of as a regressed state of transference, characterized by polarized representations of self and other, categorical thinking, and the predominance of splitting and projection as defenses. The author suggests that activation of racial hostility in the clinical situation occurs as a result of events and processes not atypical in an analytic process. Though such states occurring outside of the analytic context are more likely made conscious in certain situations and in certain persons, the author suggests that racism can be more generally described as an ever-potential state of mind for most people living in racialized contexts.     

Ecobiopsychology

The latest scientific discoveries acknowledge that the universe, from the atom to the galaxies, is a system behaving as a whole where each single set composing it seems informed by the global state of the system. In-formation can be exemplified as a “software” governing the “hardware” that is composed of the objects of the universe. This in formation comes from an Akashic Field or archetypal field that can breed each single form as well as the relevant states of consciousness. Ecobiopsychology, through the study of vital analogies and symbols, supports reflective consciousness to have access to the archetypal field studying the relation between the aspects of matter (infrared) and those referred to the psyche (ultraviolet). With this perspective the human's reflective consciousness field can gradually expand until becoming accessible to the reality of the Unus Mundus, represented by the coherence of the single structures of the universe and their own embedded state of implicit consciousness.     

Transitional knowledge in the acquisition of concepts

These studies explore children's conceptual knowledge as it is expressed through their verbal and gestural explanations of concepts. We build on previous work that has shown that children who produce a large proportion of gestures that do not match their verbal explanations are in transition with respect to the concept they are explaining. This gesture/speech mismatch has been called “discordance.” Previous work discovered this phenomenon with respect to 5- to 7-year-old children's explanations of conservation problems. Study 1 shows: (1) that older children (10 to 11 years old) exhibit gesture/speech discordance with respect to another concept, understanding the equivalence relationship in mathematical equations, and; (2) that children who produce many discordant responses in their explanations of mathematical equivalence are more likely to benefit from instruction in the concept than are children who produce few such responses. Studies 2 and 3 explore the properties and usefulness of discordance as an index of transitional knowledge in a child's acquisition of mathematical equivalence. Under any circumstance in which new concepts are acquired, there exists a mental bridge connecting the old knowledge state to the new. The studies reported here suggest that the combination of gesture and speech may be an easily observable and significantly interpretable reflection of knowledge states, both static and in flux.     

Decoding the Large-Scale Structure of Brain Function by Classifying Mental States Across Individuals

ABSTRACT— Brain-imaging research has largely focused on localizing patterns of activity related to specific mental processes, but recent work has shown that mental states can be identified from neuroimaging data using statistical classifiers. We investigated whether this approach could be extended to predict the mental state of an individual using a statistical classifier trained on other individuals, and whether the information gained in doing so could provide new insights into how mental processes are organized in the brain. Using a variety of classifier techniques, we achieved cross-validated classification accuracy of 80% across individuals (chance = 13%). Using a neural network classifier, we recovered a low-dimensional representation common to all the cognitive-perceptual tasks in our data set, and we used an ontology of cognitive processes to determine the cognitive concepts most related to each dimension. These results revealed a small organized set of large-scale networks that map cognitive processes across a highly diverse set of mental tasks, suggesting a novel way to characterize the neural basis of cognition.     

Nodal structure and the partitioning of equivalence classes

By definition, all of the stimuli in an equivalence class have to be functionally interchangeable with each other. The present experiment, however, demonstrated that this was not the case when using post-class-formation dual-option response transfer tests. With college students, two 4-node 6-member equivalence classes with nodal structures of A-->B-->C-->D-->E-->F were produced by training AB, BC, CD, DE, and EF. Then, unique responses were trained to the C and D stimuli in each class. The responses trained to C generalized to B and A, while the responses trained to D generalized to E and F. Thus, each 4-node 6-member equivalence class was bifurcated into two 3-member functional classes: A-->B-->C and D-->E-->F, with class membership precisely predicted by nodal structure. A final emergent relations test documented the intactness of the underlying 4-node 6-member equivalence classes. The coexistence of the interchangeability of stimuli in an equivalence class and the bifurcation of such a class in terms of nodal structure was explained in the following manner. The conditional discriminations that are used to establish a class also imposes a nodal structure on the stimuli in the class. Thus, the stimuli in the class acquire two sets of relational properties. If the format of a test trial allows only one response option per class, responding on those trials will be in accordance with class membership and will not express the effects of nodal distance. If the format of a test trial allows more than one response option per class, responding on those trials will be determined by the nodal structure of the class. Thus, the relational properties expressed by the stimuli in an equivalence class are determined by the discriminative function served by the format of a test trial.     

HRTEM study of the {252}γ austenite–martensite interface in an Fe—8Cr–1C alloy

Abstract

High-resolution transmission electron microscopy has been used to image the atomic structure of the (2S2)_γ austenite-martensite interface. By imaging along [101]_γ ∥[111]_α, the interface was viewed edge-on and seen to consist of facets on the close-packed (111)_γ, planes. From the correspondence of atoms in the close-packed planes across the austenite-martensite interface, the magnitude of the shear can be analysed as (a/24)<112> on every close-packed plane in the plane of projection. Comparison with theory indicates that this is an (a/12)<112> Burgers vector out of the plane of projection. Hence, each atomic facet can be viewed as a structural ledge containing an (a/12)<112> transformation dislocation.     

A search for the physical content of Luders' rule

An interpretation of quantum mechanics that rejects hidden variables has to say something about the way measurement can be understood as a transformation on states of individual systems, and that leads to the core of the interpretive problems posed by Luders' projection rule: What, if any, is its physical content? In this paper I explore one suggestion which is implicit in usual interpretations of the rule and show that this view does not stand on solid ground. In the process, important aspects of the role played by the projection postulate in the conceptual structure of quantum mechanics will be clarified. It will be shown in particular that serious objections can be raised against the (often implicit) view that identifies the physical relation of compatibility preserved by Luders' rule with the relation of simultaneous measurability.     

Some tests of response membership in acquired equivalence classes

Pigeons were trained on many-to-one matching in which pairs of samples, each consisting of a visual stimulus and a distinctive pattern of center-key responding, occasioned the same reinforced comparison choice. Acquired equivalence between the visual and response samples then was evaluated by reinforcing new comparison choices to one set of samples, and examining generalization of these choices to the other samples. Three separate experiments found no evidence of such generalization, as indexed by performance on class-consistent versus class-inconsistent tests. Other tests showed that the pigeons' center-key response patterns during training had indeed served as a conditional cue for choice. These results do not support the hypothesis that different defined responses can become members of acquired equivalence classes.     

Assessing Parameter Invariance in the BLIM: Bipartition Models

In knowledge space theory, the knowledge state of a student is the set of all problems he is capable of solving in a specific knowledge domain and a knowledge structure is the collection of knowledge states. The basic local independence model (BLIM) is a probabilistic model for knowledge structures. The BLIM assumes a probability distribution on the knowledge states and a lucky guess and a careless error probability for each problem. A key assumption of the BLIM is that the lucky guess and careless error probabilities do not depend on knowledge states (invariance assumption). This article proposes a method for testing the violations of this specific assumption. The proposed method was assessed in a simulation study and in an empirical application. The results show that (1) the invariance assumption might be violated by the empirical data even when the model’s fit is very good, and (2) the proposed method may prove to be a promising tool to detect invariance violations of the BLIM.     

Pattern uncertainty and the discrimination of visual patterns

Sixty Ss individually sorted eight decks of 50 cards each. A deck contained 25 cards each of two stimulus patterns. The patterns were drawn from different sets of five-dot patterns judged to be equivalent. The eight decks represented pairs of patterns drawn (a) from the same equivalence set, (b) from different equivalence sets of the same size, and (c) from different equivalence sets of different sizes. Sorting times were shown to increase with increasing size of equivalence set, and were shown to be greater for patterns drawn from within the same equivalence set than for patterns drawn from different equivalence sets. Ratings of pattern goodness were found to be useful predictors of sorting time only in their capacity to discriminate between equivalence sets of different sizes. The results were interpreted as supporting the importance of equivalence set membership in a discrimination task where the S logically does not have to consider stimuli other than the given criterion stimuli.     

Two notions of compactness in Gödel logics

Compactness is an important property of classical propositional logic. It can be defined in two equivalent ways. The first one states that simultaneous satisfiability of an infinite set of formulae is equivalent to the satisfiability of all its finite subsets. The second one states that if a set of formulae entails a formula, then there is a finite subset entailing this formula as well.In propositional many-valued logic, we have different degrees of satisfiability and different possible definitions of entailment, hence the questions of compactness is more complex. In this paper we will deal with compactness of Gödel, Gödel_Δ, and Gödel_～ logics.There are several results (all for the countable set of propositional variables) concerning the compactness (based on satisfiability) of these logic by Cintula and Navara, and the question of compactness (based on entailment) for Gödel logic was fully answered by Baaz and Zach (see papers [3] and [2]).In this paper we give a nearly complete answer to the problem of compactness based on both concepts for all three logics and for an arbitrary cardinality of the set of propositional variables. Finally, we show a tight correspondence between these two concepts     

Sitting on the word “chair”: Behavioral support, contextual cues, and the literal use of symbols

Recent work from an embodied-cognition perspective suggests that symbolic understanding involves bodily actions. Indeed, laboratory evidence and cultural phenomena such as magic rituals and symbolic aggression show that the behaviors evoked by a word and its referent can be quite similar to each other. In other circumstances, however, words and objects fail to display the expected degree of functional equivalence: Although we regularly sit on chairs, for example, we normally do not sit on the word “chair.” In two experiments we evaluated whether functional equivalence between word and object depended on behavioral support and contextual stimuli, as suggested by some Pavlovian views of symbolic performance. Children spent more or less time seated on a token of the word “chair,” depending on supports for sitting and background stimuli. This study may help to understand the determinants of response frequency in symbolic understanding.     

Secondary generalization and categorization in pigeons

In Experiment 1, one group of pigeons learned to classify a set of stimuli into the human language classes cat, flower, car, and chair (categorization); another group learned to classify the same set into arbitrary classes (pseudocategorization). Then, both groups were trained on a new categorization task and their performance compared to that of a control group that had no initial classification training. Hull's (1943) notion of secondary generalization (generalization that is not based on physical similarity but on mediating associations) predicts that categorization experience will facilitate the learning of a new categorization task, whereas pseudocategorization experience will impair it. However, in Experiment 1, performance on the new categorization task was not differently affected by prior experience. In Experiment 2, pigeons initially trained to classify a set of 48 stimuli (original training) were later trained to classify a subset of four of these stimuli using new responses (reassignment training). Then, they were tested on the 44 remaining stimuli. Performance better accorded with original than with reassignment training, indicating that categorization training did not lead to the formation of equivalence classes of stimuli, in which the equivalence relationship is mediated by secondary generalization. The lack of evidence of secondary generalization implies that our pigeons failed to meet Lea's (1984) criterion for conceptual behavior.