Analytic Tableaux for all of <Emphasis Type="Italic">SIXTEEN</Emphasis><Subscript>3</Subscript>

In this paper we give an analytic tableau calculus P L _{1 6} for a functionally complete extension of Shramko and Wansing’s logic. The calculus is based on signed formulas and a single set of tableau rules is involved in axiomatising each of the four entailment relations ? _t , ? _f , ? _i , and ? under consideration—the differences only residing in initial assignments of signs to formulas. Proving that two sets of formulas are in one of the first three entailment relations will in general require developing four tableaux, while proving that they are in the ? relation may require six.     

Complexity Results for Modal Dependence Logic

Modal dependence logic was introduced recently by Väänänen. It enhances the basic modal language by an operator = (). For propositional variables p ₁, . . . , p _n , = (p ₁, . . . , p _n-1, p _n ) intuitively states that the value of p _n is determined by those of p ₁, . . . , p _n-1. Sevenster (J. Logic and Computation, 2009) showed that satisfiability for modal dependence logic is complete for nondeterministic exponential time. In this paper we consider fragments of modal dependence logic obtained by restricting the set of allowed propositional connectives. We show that satisfiability for poor man’s dependence logic, the language consisting of formulas built from literals and dependence atoms using ${\wedge, \square, \lozenge}$ (i. e., disallowing disjunction), remains NEXPTIME-complete. If we only allow monotone formulas (without negation, but with disjunction), the complexity drops to PSPACE-completeness. We also extend Väänänen’s language by allowing classical disjunction besides dependence disjunction and show that the satisfiability problem remains NEXPTIME-complete. If we then disallow both negation and dependence disjunction, satisfiability is complete for the second level of the polynomial hierarchy. Additionally we consider the restriction of modal dependence logic where the length of each single dependence atom is bounded by a number that is fixed for the whole logic. We show that the satisfiability problem for this bounded arity dependence logic is PSPACE-complete and that the complexity drops to the third level of the polynomial hierarchy if we then disallow disjunction. In this way we completely classify the computational complexity of the satisfiability problem for all restrictions of propositional and dependence operators considered by Väänänen and Sevenster.     

Systemic Family Therapy Competences in Child and Adolescent Mental Health Care

This article is based on a doctoral research project aiming to identify a comprehensive and detailed outline of the systemic therapist competences in child and adolescent mental health care in Norway. Because of the growing demands to offer specialized services within child and adolescent mental health care, I intended the identified competences to target the psychosocial difficulties that are categorized as associated abnormal psychosocial situations (axis 5) in the multiaxial diagnostic system (WHO, Multiaxial classification of child and adolescent psychiatric disorders. The ICD-10 classification of mental and behavioural disorders in children and adolescents. Cambridge University Press, Cambridge, 1996). The project is based on twelve qualitative in-depth interviews with six experienced systemic family therapists, and fieldwork observations of the therapists (participants) in practice. The qualitative methodology is based on Grounded Theory and five overarching categories were identified through the analysis: (1): the importance of ethical and contextual awareness in systemic therapy; (2) the systemic therapist’s stance; (3) therapeutic processes; (4) therapeutic practices; and (5) session-specific features. Challenges, such as limiting the systemic approach to five overarching competences, are discussed alongside this strengths and limitations of the study. The detailed outline of systemic therapist competences is intended to offer a framework for delivering flexible, yet specialized systemic therapy in the context of child and adolescent mental health care. This research may therefore facilitate a “bridge-building process” between mental health’s biomedical focus and postmodern systemic ideas.     

Extending Łukasiewicz Logics with a Modality: Algebraic Approach to Relational Semantics

This paper presents an algebraic approach of some many-valued generalizations of modal logic. The starting point is the definition of the [0, 1]-valued Kripke models, where [0, 1] denotes the well known MV-algebra. Two types of structures are used to define validity of formulas: the class of frames and the class of ? _n -valued frames. The latter structures are frames in which we specify in each world u the set (a subalgebra of ? _n ) of the allowed truth values of the formulas in u. We apply and develop algebraic tools (namely, canonical and strong canonical extensions) to generate complete modal n + 1-valued logics and we obtain many-valued counterparts of Shalqvist canonicity result.     

Are Logical Languages Compositional?

In this paper I argue that in contrast to natural languages, logical languages typically are not compositional. This does not mean that the meaning of expressions cannot be determined at all using some well-defined set of rules. It only means that the meaning of an expression cannot be determined without looking at its form. If one is serious about the compositionality of a logic, the only possibility I see is to define it via abstraction from a variable free language.     

Undecidability of the Problem of Recognizing Axiomatizations of Superintuitionistic Propositional Calculi

We give a new proof of the following result (originally due to Linial and Post): it is undecidable whether a given calculus, that is a finite set of propositional formulas together with the rules of modus ponens and substitution, axiomatizes the classical logic. Moreover, we prove the same for every superintuitionistic calculus. As a corollary, it is undecidable whether a given calculus is consistent, whether it is superintuitionistic, whether two given calculi have the same theorems, whether a given formula is derivable in a given calculus. The proof is by reduction from the undecidable halting problem for the so-called tag systems introduced by Post. We also give a historical survey of related results.     

Classification in well-defined and ill-defined categories: evidence for common processing strategies

Early work in perceptual and conceptual categorization assumed that categories had criterial features and that category membership could be determined by logical rules for the combination of features. More recent theories have assumed that categories have an ill-defined structure and have prosposed probabilistic or global similarity models for the verification of category membership. In the experiments reported here, several models of categorization were compared, using one set of categories having criterial features and another set having an ill-defined structure. Schematic faces were used as exemplars in both cases. Because many models depend on distance in a multidimensional space for their predictions, in Experiment 1 a multidimensional scaling study was performed using the faces of both sets as stimuli, In Experiment 2, subjects learned the category membership of faces for the categories having criterial features. After learning, reaction times for category verification and typicality judgments were obtained. Subjects also judged the similarity of pairs of faces. Since these categories had characteristic as well as defining features, it was possible to test the predictions of the feature comparison model (Smith et al.), which asserts that reaction times and typicalities are affected by characteristic features. Only weak support for this model was obtained. Instead, it appeared that subjects developed logical rules for the classification of faces. A characteristic feature affected reaction times only when it was part of the rule system devised by the subject. The procedure for Experiment 3 was like that for Experiment 2, but with ill-defined rather than well-defined categories. The obtained reaction times had high correlations with some of the models for ill-defined categories. However, subjects' performance could best be described as one of feature testing based on a logical rule system for classification. These experiments indicate that whether or not categories have criterial features, subjects attempt to develop a set of feature tests that allow for exemplar classification. Previous evidence supporting probabilistic or similarity models may be interpreted as resulting from subjects' use of the most efficient rules for classification and the averaging of responses for subjects using different sets of rules.     

Facial expression analysis with AFFDEX and FACET: A validation study

The goal of this study was to validate AFFDEX and FACET, two algorithms classifying emotions from facial expressions, in iMotions’s software suite. In Study 1, pictures of standardized emotional facial expressions from three databases, the Warsaw Set of Emotional Facial Expression Pictures (WSEFEP), the Amsterdam Dynamic Facial Expression Set (ADFES), and the Radboud Faces Database (RaFD), were classified with both modules. Accuracy (Matching Scores) was computed to assess and compare the classification quality. Results show a large variance in accuracy across emotions and databases, with a performance advantage for FACET over AFFDEX. In Study 2, 110 participants’ facial expressions were measured while being exposed to emotionally evocative pictures from the International Affective Picture System (IAPS), the Geneva Affective Picture Database (GAPED) and the Radboud Faces Database (RaFD). Accuracy again differed for distinct emotions, and FACET performed better. Overall, iMotions can achieve acceptable accuracy for standardized pictures of prototypical (vs. natural) facial expressions, but performs worse for more natural facial expressions. We discuss potential sources for limited validity and suggest research directions in the broader context of emotion research.     

Connectionist and Memory-Array Models of Artificial Grammar Learning

Subjects exposed to strings of letters generated by a finite state grammar can later classify grammatical and nongrammatical test strings, even though they cannot adequately say what the rules of the grammar are (e.g., Reber, 1989). The MINERVA 2 (Hintzman, 1986) and Medin and Schaffer (1978) memory-array models and a number of connectionist outoassociator models are tested against experimental data by deriving mainly parameter-free predictions from the models of the rank order of classification difficulty of test strings. The importance of different assumptions regarding the coding of features (How should the absence of a feature be coded? Should single letters or digrams be coded?), the learning rule used (Hebb rule vs. delta rule), and the connectivity (Should features be predicted only by previous features in the string, or by all features simultaneously?) is investigated by determining the performance of the models with and without each assumption. Only one class of connectionist model (the simultaneous delta rule) passes all the tests. It is shown that this class of model can be regarded by abstracting a set of representative but incomplete rules of the grammar.     

On Structural Features of the Implication Fragment of Frege’s <Emphasis Type="Italic">Grundgesetze</Emphasis>

We set out the implication fragment of Frege’s Grundgesetze, clarifying the implication rules and showing that this system extends Absolute Implication, or the implication fragment of Intuitionist logic. We set out a sequent calculus which naturally captures Frege’s implication proofs, and draw particular attention to the Cut-like features of his Hypothetical Syllogism rule.     

Hard and Soft Preparation Sets in Boolean Games

A fundamental problem in game theory is the possibility of reaching equilibrium outcomes with undesirable properties, e.g., inefficiency. The economics literature abounds with models that attempt to modify games in order to avoid such undesirable properties, for example through the use of subsidies and taxation, or by allowing players to undergo a bargaining phase before their decision. In this paper, we consider the effect of such transformations in Boolean games with costs, where players control propositional variables that they can set to true or false, and are primarily motivated to seek the satisfaction of some goal formula, while secondarily motivated to minimise the costs of their actions. We adopt (pure) preparation sets (prep sets) as our basic solution concept. A preparation set is a set of outcomes that contains for every player at least one best response to every outcome in the set. Prep sets are well-suited to the analysis of Boolean games, because we can naturally represent prep sets as propositional formulas, which in turn allows us to refer to prep formulas. The preference structure of Boolean games with costs makes it possible to distinguish between hard and soft prep sets. The hard prep sets of a game are sets of valuations that would be prep sets in that game no matter what the cost function of the game was. The properties defined by hard prep sets typically relate to goal-seeking behaviour, and as such these properties cannot be eliminated from games by, for example, taxation or subsidies. In contrast, soft prep sets can be eliminated by an appropriate system of incentives. Besides considering what can happen in a game by unrestricted manipulation of players’ cost function, we also investigate several mechanisms that allow groups of players to form coalitions and eliminate undesirable outcomes from the game, even when taxes or subsidies are not a possibility.     

Reliability of testimonial norms in scientific communities

Several current debates in the epistemology of testimony are implicitly motivated by concerns about the reliability of rules for changing one’s beliefs in light of others’ claims. Call such rules testimonial norms (tns). To date, epistemologists have neither (i) characterized those features of communities that influence the reliability of tns, nor (ii) evaluated the reliability of tns as those features vary. These are the aims of this paper. I focus on scientific communities, where the transmission of highly specialized information is both ubiquitous and critically important. Employing a formal model of scientific inquiry, I argue that miscommunication and the “communicative structure” of science strongly influence the reliability of tns, where reliability is made precise in three ways.     

Embedding the elementary ontology of stanisław Leśniewski into the monadic second-order calculus of predicates

LetEO be the elementary ontology of Le?niewski formalized as in Iwanu? [1], and letLS be the monadic second-order calculus of predicates. In this paper we give an example of a recursive function ?, defined on the formulas of the language ofEO with values in the set of formulas of the language of LS, such that ? _EO A iff ? _LS ?(A) for each formulaA.     

Translation of first order formulas into ground formulas via a completion theory

A translation technique is presented which transforms a class of First Order Logic formulas, called Restricted formulas, into ground formulas. For the formulas in this class the range of quantified variables is restricted by Domain formulas.If we have a complete knowledge of the predicates involved in the Domain formulas their extensions can be evaluated with the Relational Algebra and these extensions are used to transform universal (respectively existential) quantifiers into finite conjunctions (respectively disjunctions).It is assumed that the complete knowledge is represented by Completion Axioms and Unique Name Axioms à la Reiter. These axioms involve the equality predicate. However, the translation allows to remove the equality in the ground formulas and for a large class of formulas their consequences are the same as the initial First Order formulas. This result open the door for the design of efficient deduction techniques.     

Symmetry-based methodology for decision-rule identification in same-different experiments

The standard practice of reducing every same-different data set to two numbers (hits and false alarms) is wasteful, because the response pattern to all four stimulus pairs carries information about the decision rule adopted by the observer. We describe eight rules organized in three families: differencing, covert classification, and likelihood ratio. We prove that each family produces a characteristic pattern of (in)equalities among the response probabilities. We propose two simple qualitative tests. Is the performance on stimulus pairs AA and BB statistically indistinguishable? If not, differencing and likelihood-ratio strategies can be rejected. Is the performance on pairs AB and BA indistinguishable? If not, covert classification can be rejected. We present algorithms for fitting two covert-classification models and illustrate the new methodology in a perceptual learning experiment on visual motion-direction discrimination. The standard assumption of symmetric decision criteria was violated.     

A Protective Factors Model for Alcohol Abuse and Suicide Prevention Among Alaska Native Youth

This study provides an empirical test of a culturally grounded theoretical model for prevention of alcohol abuse and suicide risk with Alaska Native youth, using a promising set of culturally appropriate measures for the study of the process of change and outcome. This model is derived from qualitative work that generated an heuristic model of protective factors from alcohol (Allen et al. in J Prev Interv Commun 32:41–59, 2006; Mohatt et al. in Am J Commun Psychol 33:263–273, 2004a; Harm Reduct 1, 2004b). Participants included 413 rural Alaska Native youth ages 12–18 who assisted in testing a predictive model of Reasons for Life and Reflective Processes about alcohol abuse consequences as co-occurring outcomes. Specific individual, family, peer, and community level protective factor variables predicted these outcomes. Results suggest prominent roles for these predictor variables as intermediate prevention strategy target variables in a theoretical model for a multilevel intervention. The model guides understanding of underlying change processes in an intervention to increase the ultimate outcome variables of Reasons for Life and Reflective Processes regarding the consequences of alcohol abuse.     

Are event-related potentials to dynamic facial expressions of emotion related to individual differences in the accuracy of processing facial expressions and identity?

Despite a wealth of knowledge about the neural mechanisms behind emotional facial expression processing, little is known about how they relate to individual differences in social cognition abilities. We studied individual differences in the event-related potentials (ERPs) elicited by dynamic facial expressions. First, we assessed the latent structure of the ERPs, reflecting structural face processing in the N170, and the allocation of processing resources and reflexive attention to emotionally salient stimuli, in the early posterior negativity (EPN) and the late positive complex (LPC). Then we estimated brain–behavior relationships between the ERP factors and behavioral indicators of facial identity and emotion-processing abilities. Structural models revealed that the participants who formed faster structural representations of neutral faces (i.e., shorter N170 latencies) performed better at face perception (r = –.51) and memory (r = –.42). The N170 amplitude was not related to individual differences in face cognition or emotion processing. The latent EPN factor correlated with emotion perception (r = .47) and memory (r = .32), and also with face perception abilities (r = .41). Interestingly, the latent factor representing the difference in EPN amplitudes between the two neutral control conditions (chewing and blinking movements) also correlated with emotion perception (r = .51), highlighting the importance of tracking facial changes in the perception of emotional facial expressions. The LPC factor for negative expressions correlated with the memory for emotional facial expressions. The links revealed between the latency and strength of activations of brain systems and individual differences in processing socio-emotional information provide new insights into the brain mechanisms involved in social communication.     

Uncertainty and Persistence: a Bayesian Update Semantics for Probabilistic Expressions

This paper presents a general-purpose update semantics for expressions of subjective uncertainty in natural language. First, a set of desiderata are established for how expressions of subjective uncertainty should behave in dynamic, update-based semantic systems; then extant implementations of expressions of subjective uncertainty in such models are evaluated and found wanting; finally, a new update semantics is proposed. The desiderata at the heart of this paper center around the contention that expressions of subjective uncertainty express beliefs which are not persistent (i.e. beliefs that won’t necessarily survive the addition of new information that is compatible with all previous information), whereas propositions express beliefs that are persistent. I argue that if we make the move of treating updates in a dynamic semantics as Bayesian updates, i.e. as conditionalization, then expressions of subjective uncertainty will behave the way we want them to without altering the way propositions behave.     

State-trace analysis can be an appropriate tool for assessing the number of cognitive systems: A reply to Ashby (2014)

Ashby (2014) has argued that state-trace analysis (STA) is not an appropriate tool for assessing the number of cognitive systems, because it fails in its primary goal of distinguishing single-parameter and multiple-parameter models. We show that this is based on a misunderstanding of the logic of STA, which depends solely on nearly universal assumptions about psychological measurement and clearly supersedes inferences based on functional dissociation and the analysis of interactions in analyses of variance. We demonstrate that STA can be used to draw inferences concerning the number of latent variables mediating the effects of a set of independent variables on a set of dependent variables. We suggest that STA is an appropriate tool to use when making arguments about the number of cognitive systems that must be posited to explain behavior. However, no statistical or inferential procedure is able to provide definitive answers to questions about the number of cognitive systems, simply because the concept of a “system” is not defined in an appropriate way.