Normal Natural Deduction Proofs (in classical logic)

Natural deduction (for short: nd-) calculi have not been used systematically as a basis for automated theorem proving in classical logic. To remove objective obstacles to their use we describe (1) a method that allows to give semantic proofs of normal form theorems for nd-calculi and (2) a framework that allows to search directly for normal nd-proofs. Thus, one can try to answer the question: How do we bridge the gap between claims and assumptions in heuristically motivated ways? This informal question motivates the formulation of intercalation calculi. Ic-calculi are the technical underpinnings for (1) and (2), and our paper focuses on their detailed presentation and meta-mathematical investigation in the case of classical predicate logic. As a central theme emerges the connection between restricted forms of nd-proofs and (strategies for) proof search: normal forms are not obtained by removing local "detours", but rather by constructing proofs that directly reflect proof-strategic considerations. That theme warrants further investigation.

     

Connectives and narrative text: The role of continuity

Connectives are text devices that signal the relation between adjacent sentences. Recently there has been a surge of research interest in the role played by connectives in on-line processing. The present research tested the hypothesis that connectives will impact on-line processing to the extent that they signal a text event that represents a departure from the continuity of the events stated in the text. In Experiment 1, participants generated sentences to follow a stimulus sentence. An additive, causal, or adversative connective (or no connective) was provided to serve as the first word of the participants’ sentence. Results showed that sentences generated in response to additive or causal connectives depicted text events that were continuous with the stimulus text. In contrast, sentences generated in response to adversative connectives depicted discontinuous text events. In Experiments 2 and 3, participants read coherent sentence pairs containing inappropriately placed additive, causal, or adversative connectives. Support for the continuity hypothesis was found when it was shown that adversative connectives led to the greatest amount of processing disruption, as measured by longer reading time on the postconnective sentence (Experiment 2) and lower ratings of coherence (Experiment 3). Future research in this area is discussed.     

On The Computational Consequences of Independence in Propositional Logic

Sandu and Pietarinen [Partiality and Games: Propositional Logic. Logic J. IGPL 9 (2001) 101] study independence friendly propositional logics. That is, traditional propositional logic extended by means of syntax that allow connectives to be independent of each other, although the one may be subordinate to the other. Sandu and Pietarinen observe that the IF propositional logics have exotic properties, like functional completeness for three-valued functions. In this paper we focus on one of their IF propositional logics and study its properties, by means of notions from computational complexity. This approach enables us to compare propositional logic before and after the IF make-over. We observe that all but one of the best-known decision problems experience a complexity jump, provided that the complexity classes at hand are not equal. Our results concern every discipline that incorporates some notion of independence such as computer science, natural language semantics, and game theory. A corollary of one of our theorems illustrates this claim with respect to the latter discipline.     

The Linguistic Formulation of Fallacies Matters: The Case of Causal Connectives

Argumentation - While the role of discourse connectives has long been acknowledged in argumentative frameworks, these approaches often take a coarse-grained approach to connectives, treating them...     

The Intertwinement of Propositional and Doxastic Justification

One important distinction in the debate over the nature of epistemic justification is the one between propositional and doxastic justification. Roughly, while doxastic justification is a property of beliefs, propositional justification is a property of propositions. On a rather common view, which accounts for doxastic justification in terms of propositional justification plus the so-called ‘basing relation’, propositional justification is seen as the prior notion, and doxastic justification is explained in terms of it. According to the opposing view, the direction of explanation needs to be reversed, and doxastic justification should be seen as primary. I distinguish between two notions of priority, and I argue that they give different verdicts with respect to the issue of which notion of justification comes first. The lesson may be taken to be that propositional and doxastic justification are in a relation of intertwinement.     

Attitude,Inference, Association: On the Propositional Structure of Implicit Bias

The overwhelming majority of those who theorize about implicit biases posit that these biases are caused by some sort of association. However, what exactly this claim amounts to is rarely specified. In this paper, I distinguish between different understandings of association, and I argue that the crucial senses of association for elucidating implicit bias are the cognitive structure and mental process senses. A hypothesis is subsequently derived: if associations really underpin implicit biases, then implicit biases should be modulated by counterconditioning or extinction but should not be modulated by rational argumentation or logical interventions. This hypothesis is false; implicit biases are not predicated on any associative structures or associative processes but instead arise because of unconscious propositionally structured beliefs. I conclude by discussing how the case study of implicit bias illuminates problems with popular dual‐process models of cognitive architecture.     

The study of religion(s) in Western Europe (II): Institutional developments after World War II

This essay discusses main features and developments of the study of religion(s) in Western Europe. It attempts a historical, geographical, and thematic synthesis. Part II sketches institutional developments after World War II in several countries and the emergence of professional associations (international as well as national). In the post World War II growth of the field, social-scientific approaches to the study of religion(s) became increasingly prominent. The article sketches the institutional developments and main scholarly concerns of the psychology, sociology, and anthropology of religions respectively. It then moves on to consider the Eranos conferences as a specific forum for scholarship. The final sections discuss religious changes in Western Europe and their reflections in the study of religion(s).     

Generalized Break Equivalence II: Contextual Control Over A Generalized Pattern of Stimulus Relations

The Psychological Record - In an earlier work (Gomez, Barnes-Holmes, & Luciano, 2001), it was found that although generalized break equivalence was achieved for 3 subjects (i.e., responding...     

"命题推理"的心理学研究综述

本文在对“如果…,那么…”规则、“四卡问题”和“THOG”等三种有关“命题推理”领域的研究作了简要综述。     

The Rationality of Belief and Some Other Propositional Attitudes

In this paper, I explore the question of whether the expectedconsequences of holding a belief can affect the rationality ofdoing so. Special attention is given to various ways in whichone might attempt to exert some measure of control over whatone believes and the normative status of the beliefs thatresult from the successful execution of such projects. I arguethat the lessons which emerge from thinking about the case ofbelief have important implications for the way we should thinkabout the rationality of a number of other propositional attitudes,such as regret, desire, and fear. Finally,I suggest that a lack of clarity with respect to the relevant issueshas given rise to a number of rather serious philosophical mistakes.     

Performance and Learning of Generalized Motor Programs: Relative (GMP) and Absolute (Parameter) Errors

The effects of practice (Experiment 1) and parameter variability (Experiment 2) on the learning of generalized motor programs (GMPs) and movement parameterization were investigated In each experiment, 2 tasks with different relative force-time structures were tested. Participants (N = 32, Experiment (N = 40, Experiment 2) attempted to exert a pattern of force that resembled in force and time a waveform that was displayed on a computer monitor. In both experiments, the analysis suggested that the GMP, although refined over practice, was relatively stable (i.e., resistant to decay and interference), even early in practice (after 20 trials). In addition, the results indicated that constant and variable parameter practice did not differentially affect GMP learning but did degrade the learning of the parameter that was not varied. The data provided additional evidence for the dissociation of the GMP and the parameterization processes proposed in GMP theory. Contrary to schema theory, the present data suggest an interdependence between the force and the time parameters: The manipulation of 1 of the parameters has a negative effect on the learning of the other parameter.     

Partially-Ordered (Branching) Generalized Quantifiers: A General Definition

Following Henkins discovery of partially-ordered (branching) quantification (POQ) with standard quantifiers in 1959, philosophers of language have attempted to extend his definition to POQ with generalized quantifiers. In this paper I propose a general definition of POQ with 1-place generalized quantifiers of the simplest kind: namely, predicative, or cardinality quantifiers, e.g., most, few, finitely many, exactly , where is any cardinal, etc. The definition is obtained in a series of generalizations, extending the original, Henkin definition first to a general definition of monotone-increasing (M) POQ and then to a general definition of generalized POQ, regardless of monotonicity. The extension is based on (i) Barwises 1979 analysis of the basic case of M POQ and (ii) my 1990 analysis of the basic case of generalized POQ. POQ is a non-compositional 1st-order structure, hence the problem of extending the definition of the basic case to a general definition is not trivial. The paper concludes with a sample of applications to natural and mathematical languages.     

Propositional Epistemic Logics with Quantification Over Agents of Knowledge (An Alternative Approach)

Studia Logica - In the previous paper with a similar title (see Shtakser in Stud Log 106(2):311–344, 2018), we presented a family of propositional epistemic logics whose languages are...     

On Pretabular Logics in NExtK4 (Part II)

In this paper we prove the pretabularity criteria for the logics of infinite depth in NExtK4. Then we use the criteria to resolve the problems of pretabular logics in NExtQ4 and prove that there is a continuum of pretabular logics in NExtQ4 just like NExtK4.