Representing decision-makers using styles of behavior: An approach designed for group decision support systems

Supporting decision-making processes when the elements of a group are geographically dispersed and on a tight schedule is a complex task. Aiming to support decision-makers anytime and anywhere, Web-based group decision support systems have been studied. However, the limitations in the decision-makers’ interactions associated to this scenario bring new challenges. In this work, we propose a set of behavioral styles from which decision-makers’ intentions can be modelled into agents. The goal is that, besides having agents represent typical preferences of the decision-makers (towards alternatives and criteria), they can also represent their intentions. To do so, we conducted a survey with 64 participants in order to find homogeneous operating values so as to numerically define the proposed behavioral styles in four dimensions. In addition, we also propose a communication model that simulates the dialogues made by decision-makers in face-to-face meetings. We developed a prototype to simulate decision scenarios and found that agents are capable of acting according to the decision-makers’ intentions and fundamentally benefit from different possible behavioral styles, just as a face-to-face meeting benefits from the heterogeneity of its participants.     

Entailment with Near Surety of Scaled Assertions of High Conditional Probability

An assertion of high conditional probability or, more briefly, an HCP assertion is a statement of the type: The conditional probability of B given A is close to one. The goal of this paper is to construct logics of HCP assertions whose conclusions are highly likely to be correct rather than certain to be correct. Such logics would allow useful conclusions to be drawn when the premises are not strong enough to allow conclusions to be reached with certainty. This goal is achieved by taking Adams" (1966) logic, changing its intended application from conditionals to HCP assertions, and then weakening its criterion for entailment. According to the weakened entailment criterion, called the Criterion of Near Surety and which may be loosely interpreted as a Bayesian criterion, a conclusion is entailed if and only if nearly every model of the premises is a model of the conclusion. The resulting logic, called NSL, is nonmonotonic. Entailment in this logic, although not as strict as entailment in Adams" logic, is more strict than entailment in the propositional logic of material conditionals. Next, NSL was modified by requiring that each HCP assertion be scaled; this means that to each HCP assertion was associated a bound on the deviation from 1 of the conditional probability that is the subject of the assertion. Scaling of HCP assertions is useful for breaking entailment deadlocks. For example, it it is known that the conditional probabilities of C given A and of ¬ C given B are both close to one but the bound on the former"s deviation from 1 is much smaller than the latter"s, then it may be concluded that in all likelihood the conditional probability of C given A B is close to one. The resulting logic, called NSL-S, is also nonmonotonic. Despite great differences in their definitions of entailment, entailment in NSL is equivalent to Lehmann and Magidor"s rational closure and, disregarding minor differences concerning which premise sets are considered consistent, entailment in NSL-S is equivalent to entailment in Goldszmidt and Pearl"s System-Z ⁺. Bacchus, Grove, Halpern, and Koller proposed two methods of developing a predicate calculus based on the Criterion of Near Surety. In their random-structures method, which assumed a prior distribution similar to that of NSL, it appears possible to define an entailment relation equivalent to that of NSL. In their random-worlds method, which assumed a prior distribution dramatically different from that of NSL, it is known that the entailment relation is different from that of NSL.     

Admissibility of Cut in <Emphasis Type="Italic">LC</Emphasis> with Fixed Point Combinator

The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the similar proof for LC with proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof. Presented by Robert Goldblatt     

What are symbols symbols of? Situated action,mythological bootstrapping and the emergence of the Self

This paper addresses the question of how symbols should be understood in analytical psychology and psychoanalysis. The point of view examined focuses on the recent turn to more cognitive and developmental models in both disciplines and briefly reviews and critiques the evolutionary and cognitive arguments. The paper then presents an argument based on dynamic systems theory in which no pre-existing template or structure for either mind or behaviour is assumed. Within the dynamic systems model the Self is viewed as an emergent phenomenon deriving from the dynamic patterns existing in a complex system that includes the physiological characteristics of the infant, the intentional attributions of the caregiver and the cultural or symbolic resources that constitute the environment. The symbol can then be seen as a discrete, and in important ways an autonomous, element in the dynamic system. Conclusions are drawn for further research into the nature of the symbol with implications for both theory and practice in analytical psychology and psychoanalysis.     

Experience and inference: how far will science carry us?

This paper begins with a view of the remarkable understanding of infant and child development that has evolved from research and observation. The limitations of this contribution from science to the multi-dimensional context-based individuality of each human in his or her intersubjective realm are then considered. For a contemporary view we must recognize the influence of the variability of experiences and the inferences drawn from them. Inferences involve symbolization and culturally derived archetypes as illustrated in a clinical example.     

Algebras of Intervals and a Logic of Conditional Assertions

Intervals in boolean algebras enter into the study of conditional assertions (or events) in two ways: directly, either from intuitive arguments or from Goodman, Nguyen and Walker's representation theorem, as suitable mathematical entities to bear conditional probabilities, or indirectly, via a representation theorem for the family of algebras associated with de Finetti's three-valued logic of conditional assertions/events. Further representation theorems forge a connection with rough sets. The representation theorems and an equivalent of the boolean prime ideal theorem yield an algebraic completeness theorem for the three-valued logic. This in turn leads to a Henkin-style completeness theorem. Adequacy with respect to a family of Kripke models for de Finetti's logic, ukasiewicz's three-valued logic and Priest's Logic of Paradox is demonstrated. The extension to first-order yields a short proof of adequacy for Körner's logic of inexact predicates.     

On Modal μ-Calculus and Non-Well-Founded Set Theory

A finitary characterization for non-well-founded sets with finite transitive closure is established in terms of a greatest fixpoint formula of the modal -calculus. This generalizes the standard result in the literature where a finitary modal characterization is provided only for wellfounded sets with finite transitive closure. The proof relies on the concept of automaton, leading then to new interlinks between automata theory and non-well-founded sets.     

Categorical Abstract Algebraic Logic Metalogical Properties

Metalogical properties that have traditionally been studied in the deductive system context (see, e.g., [21]) and transferred later to the institution context [33], are here formulated in the -institution context. Preservation under deductive equivalence of -institutions is investigated. If a property is known to hold in all algebraic -institutions and is preserved under deductive equivalence, then it follows that it holds in all algebraizable -institutions in the sense of [36].