On a property of BCK-identities

A BCK-algebra is an algebra in which the terms are generated by a set of variables, 1, and an arrow. We mean by aBCK-identity an equation valid in all BCK-algebras. In this paper using a syntactic method we show that for two termss andt, if neithers=1 nort=1 is a BCK-identity, ands=t is a BCK-identity, then the rightmost variables of the two terms are identical.This theorem was conjectured firstly in [5], and then in [3]. As a corollary of this theorem, we derive that the BCK-algebras do not form a variety, which was originally proved algebraically by Wroski ([4]).To prove the main theorem, we use a Gentzen-type logical system for the BCK-algebras, introduced by Komori, which consists of the identity axiom, the right and the left introduction rules of the implication, the exchange rule, the weakening rule and the cut. As noted in [2], the cut-elimination theorem holds for this system.Presented byJan Zygmunt     

A logical formalization of the OCC theory of emotions

In this paper, we provide a logical formalization of the emotion triggering process and of its relationship with mental attitudes, as described in Ortony, Clore, and Collins’s theory. We argue that modal logics are particularly adapted to represent agents’ mental attitudes and to reason about them, and use a specific modal logic that we call Logic of Emotions in order to provide logical definitions of all but two of their 22 emotions. While these definitions may be subject to debate, we show that they allow to reason about emotions and to draw interesting conclusions from the theory.     

Cut-elimination for Weak Grzegorczyk Logic Go

We present a syntactic proof of cut-elimination for weak Grzegorczyk logic Go. The logic has a syntactically similar axiomatisation to Gödel–Löb logic GL (provability logic) and Grzegorczyk’s logic Grz. Semantically, GL can be viewed as the irreflexive counterpart of Go, and Grz can be viewed as the reflexive counterpart of Go. Although proofs of syntactic cut-elimination for GL and Grz have appeared in the literature, this is the first proof of syntactic cut-elimination for Go. The proof is technically interesting, requiring a deeper analysis of the derivation structures than the proofs for GL and Grz. New transformations generalising the transformations for GL and Grz are developed here.     

An unlabeled bracketing solution to the problem of conjoined phrases in Montague's PTQ

Conclusions Although Montague claims that the system of The proper treatment of quantification in ordinary English includes some conjunction and disjunction, the rules for other grammatical constructions do not take conjunction or disjunction into account, and in general fail either syntactically or semantically when one of their arguments is so formed. Using an unlabeled bracketing of syntactic structure and recursive definitions, we have been able to rewrite the rules so that correct results are obtained.These results should provide a firmer basis for extension of PTQ.This research was supported in part by NSF Grants GS-31309 and BNS 76-23840. Our observations were made with the aid of several computer programs for PTQ: a sentence generator for the bracketed syntax, a parser, and a translator. I should like to thank Philip Tedeschi, David Warren, and David Lewis for helpful discussions. Warren is also acknowledged as co-author of the section on the semantic role of conjunction.     

A logical calculus for controlled monotonicity

In this paper we introduce a new deductive framework for analyzing processes displaying a kind of controlled monotonicity. In particular, we prove the cut-elimination theorem for a calculus involving series-parallel structures over partial orders which is built up from multi-level sequents, an interesting variant of Gentzen-style sequents. More broadly, our purpose is to provide a general, syntactical tool for grasping the combinatorics of non-monotonic processes.     

Denotation of contextual modal type theory (CMTT): Syntax and meta-programming

The modal logic S4 can be used via a Curry–Howard style correspondence to obtain a λ-calculus. Modal (boxed) types are intuitively interpreted as ‘closed syntax of the calculus’. This λ-calculus is called modal type theory—this is the basic case of a more general contextual modal type theory, or CMTT.CMTT has never been given a denotational semantics in which modal types are given denotation as closed syntax. We show how this can indeed be done, with a twist. We also use the denotation to prove some properties of the system.     

Type Logics and Pregroups

We discuss the logic of pregroups, introduced by Lambek [34], and its connections with other type logics and formal grammars. The paper contains some new ideas and results: the cut-elimination theorem and a normalization theorem for an extended system of this logic, its P-TIME decidability, its interpretation in L1, and a general construction of (preordered) bilinear algebras and pregroups whose universe is an arbitrary monoid. Special Issue Categorial Grammars and Pregroups Edited by Wojciech Buszkowski and Anne Preller     

Meeting strength in substructural logics

This paper contributes to the theory of hybrid substructural logics, i.e. weak logics given by a Gentzen-style proof theory in which there is only alimited possibility to use structural rules. Following the literture, we use an operator to mark formulas to which the extra structural rules may be applied. New in our approach is that we do not see this as a modality, but rather as themeet of the marked formula with a special typeQ. In this way we can make the specific structural behaviour of marked formulas more explicit.The main motivation for our approach is that we can provide a nice, intuitive semantics for hybrid substructural logics. Soundness and completeness for this semantics are proved; besides this we consider some proof-theoretical aspects like cut-elimination and embeddings of the strong system in the hybrid one.Presented byMelvin Fitting     

Some differences between phonetic and auditory modes of perception

When third-formant transitions are appropriately incorporated into an acoustic syllable, they provide critical support for the phonetic percepts we call [d] and [g], but when presented in isolation they are perceived as time-varying ‘chirps’. In the present experiment, both modes of perception were made available simultaneously by presenting the third-format transitions to one ear and the remainder of the acoustic syllable to the other. On the speech side of this duplex percept, where the transitions supported the perception of stop-vowel syllables, perception was categorical and influenced by the presence of a preposed [al] or [ar]. On the nonspeech side, where the same transitions were heard as ‘chirps’, perception was continuous and free of influence from the preposed syllables. As both differences occurred under conditions in which the acoustic input was constant, we should suppose that they reflect the different properties of auditory and phonetic modes of perception.     

Does syntax contribute to the function of duets in a parrot, Amazona auropalliata?

Complex acoustic signals in many animal species are characterized by a syntax that governs how different notes are combined, but the importance of syntax to the communicative function of signals is not well understood. Mated pairs of yellow-naped amazons, Amazona auropalliata, produce coordinated vocal duets that are used for territory maintenance and defense. These duets follow rules that specify the ordering of notes within duets, such as a strict alternation of sex-specific notes and a defined progression of note types through each duet. These syntactical rules may function to define sex-specific roles, improve coordination, and allow individuals to combine calls into meaningful sequences. As a first step toward understanding the functional significance of syntax, we conducted two separate audio playback experiments in which we presented nesting pairs with normal duets and duets with broken syntax (i.e., one of the syntactic rules was broken). In Experiment One, we reversed the order of female and male notes within note pairs while retaining the typical progression of note types through a duet. In Experiment Two we reversed the order of note types across a whole duet while retaining the typical female-male ordering within note pairs. We hypothesized that duets with broken syntax would be less-effective signals than duets with normal syntax and predicted that pairs would respond less to broken syntax than to normal duets. Contrary to predictions, we did not observe differences in response between treatments for any variables except latency to approach the speaker. After we combined data across experiments post hoc, we observed longer latencies to approach the speakers after playbacks of broken syntax duets, suggesting that pairs could differentiate between playbacks. These responses suggest that breaking one rule of duet syntax at a time does not result in detectable loss of signal efficacy in the context of territorial intrusions.     

When what you say about others says something about you: Language abstraction and inferences about describers’ attitudes and goals

According to the linguistic category model ( [Semin and Fiedler, 1988] and [Semin and Fiedler, 1991]), a person’s behavior can be described at varying levels of abstraction from concrete (e.g., “Lisa slaps Ann”) to abstract (e.g., “Lisa is aggressive”). Research has shown that language abstraction conveys information about the person whose behavior is described (Wigboldus, Semin, & Spears, 2000). However to date, little research has examined the information that language abstraction may convey about describers themselves. In this paper, we report three experiments demonstrating that describers who use relatively abstract language to describe others’ behaviors are perceived to have biased attitudes and motives compared with those describers who use more concrete language.     

Language, thought, and real nouns

We test the claim that acquiring a mass-count language, like English, causes speakers to think differently about entities in the world, relative to speakers of classifier languages like Japanese. We use three tasks to assess this claim: object-substance rating, quantity judgment, and word extension. Using the first two tasks, we present evidence that learning mass-count syntax has little effect on the interpretation of familiar nouns between Japanese and English, and that speakers of these languages do not divide up referents differently along an individuation continuum, as claimed in some previous reports [Gentner, D., & Boroditsky, L. (2001). Individuation, relativity, and early word learning. In M. Bowerman, & S. Levinson (Eds.), Language acquisition and conceptual development (pp. 215-256). Cambridge University Press]. Instead, we argue that previous cross-linguistic differences [Imai, M., & Gentner, D. (1997). A cross-linguistic study of early word meaning: Universal ontology and linguistic influence. Cognition, 62, 169-200] are attributable to “lexical statistics” [Gleitman, L., & Papafragou, A. (2005). Language and thought. In K. Holyoak, & R. Morrison (Eds.), Cambridge handbook of thinking and reasoning (pp. 633-661). Cambridge University Press]. Speakers of English are more likely to think that a novel ambiguous expression like “the blicket” refers to a kind of object (relative to speakers of Japanese) because speakers of English are likely to assume that “blicket” is a count noun rather than a mass noun, based on the relative frequency of each kind of word in English. This is confirmed by testing Mandarin-English bilinguals with a word extension task. We find that bilinguals tested in English with mass-count ambiguous syntax extend novel words like English monolinguals (and assume that a word like “blicket” refers to a kind of object). In contrast, bilinguals tested in Mandarin are significantly more likely to extend novel words by material. Thus, online lexical statistics, rather than non-linguistic thought, mediate cross-linguistic differences in word extension. We suggest that speakers of Mandarin, English, and Japanese draw on a universal set of lexical meanings, and that mass-count syntax allows speakers of English to select among these meanings.     

Synchronized Linear-Time Temporal Logic

A new combined temporal logic called synchronized linear-time temporal logic (SLTL) is introduced as a Gentzen-type sequent calculus. SLTL can represent the n-Cartesian product of the set of natural numbers. The cut-elimination and completeness theorems for SLTL are proved. Moreover, a display sequent calculus ??SLTL is defined.     

Busting a Myth about Leśniewski and Definitions

A theory of definitions which places the eliminability and conservativeness requirements on definitions is usually called the standard theory. We examine a persistent myth which credits this theory to Le?niewski, a Polish logician. After a brief survey of its origins, we show that the myth is highly dubious. First, no place in Le?niewski's published or unpublished work is known where the standard conditions are discussed. Second, Le?niewski's own logical theories allow for creative definitions. Third, Le?niewski's celebrated ‘rules of definition’ lay merely syntactical restrictions on the form of definitions: they do not provide definitions with such meta-theoretical requirements as eliminability or conservativeness. On the positive side, we point out that among the Polish logicians, in the 1920s and 1930s, a study of these meta-theoretical conditions is more readily found in the works of ?ukasiewicz and Ajdukiewicz.     

A Bayesian Model For The Estimation Of Latent Interaction And Quadratic Effects When Latent Variables Are Non-Normally Distributed

Structural equation models with interaction and quadratic effects have become a standard tool for testing nonlinear hypotheses in the social sciences. Most of the current approaches assume normally distributed latent predictor variables. In this article, we present a Bayesian model for the estimation of latent nonlinear effects when the latent predictor variables are nonnormally distributed. The nonnormal predictor distribution is approximated by a finite mixture distribution. We conduct a simulation study that demonstrates the advantages of the proposed Bayesian model over contemporary approaches (Latent Moderated Structural Equations [LMS], Quasi-Maximum-Likelihood [QML], and the extended unconstrained approach) when the latent predictor variables follow a nonnormal distribution. The conventional approaches show biased estimates of the nonlinear effects; the proposed Bayesian model provides unbiased estimates. We present an empirical example from work and stress research and provide syntax for substantive researchers. Advantages and limitations of the new model are discussed.     

A note on the proof theory the λII-calculus

The II-calculus, a theory of first-order dependent function types in Curry-Howard-de Bruijn correspondence with a fragment of minimal first-order logic, is defined as a system of (linearized) natural deduction. In this paper, we present a Gentzen-style sequent calculus for the II-calculus and prove the cut-elimination theorem.The cut-elimination result builds upon the existence of normal forms for the natural deduction system and can be considered to be analogous to a proof provided by Prawitz for first-order logic. The type-theoretic setting considered here elegantly illustrates the distinction between the processes of normalization in a natural deduction system and cut-elimination in a Gentzen-style sequent calculus.We consider an application of the cut-free calculus, via the subformula property, to proof-search in the II-calculus. For this application, the normalization result for the natural deduction calculus alone is inadequate, a (cut-free) calculus with the subformula property being required.This paper was written whilst the author was affiliated to the University of Edinburgh, Scotland, U.K. and revised for publication whilst he was affiliated to the University of Birmingham, England, U.K.Presented byDaniele Mundici     

Using logical relevance for question answering

We propose a novel method of determining the appropriateness of an answer to a question through a proof of logical relevance rather than a logical proof of truth. We define logical relevance as the idea that answers should not be considered as absolutely true or false in relation to a question, but should be considered true more flexibly in a sliding scale of aptness. This enables us to reason rigorously about the appropriateness of an answer even in cases where the sources we are getting answers from are incomplete or inconsistent or contain errors. We show how logical relevance can be implemented through the use of measured simplification, a form of constraint relaxation, in order to seek a logical proof than an answer is in fact an answer to a particular question. We then give an example of such an implementation providing a set of specific rules for this purpose.     

Narcissism,identification, and longitudinal change in psychological health: Dynamic predictions

The narcissist has been described as “dependent on others to provide confirmation of the grandiose ego ideal” (American Psychiatric Association. (1994). Diagnostic and statistical manual of mental disorders (4th ed.). Washington, DC: Author.). The present study shows how the combination of dependent identification and unhealthy narcissism leads to decreasing psychological health across 42 years of adulthood. Change in psychological health is studied in 156 participants of the Intergenerational Studies, Institute of Human Development, University of California, Berkeley. We predicted that longitudinal decline in psychological health, as assessed by longitudinal hierarchical linear modeling analyses of the California Personality Inventory v3 scale [Gough, H. G., & Bradley, P. (1996). California Psychological Inventory. Palo Alto, CA: Consulting Psychologists Press], would be predicted by the joint presence in early adulthood of maladaptive narcissism [Wink, P. (1992). Three narcissism scales for the California Q-set. Journal of Personality Assessment, 58, 51–66] and defensive identification [Cramer, P. (1991a). The development of defense mechanisms: Theory, research and assessment. New York: Springer-Verlag]. In contrast, we predicted healthy narcissism would be positively related to psychological health throughout adulthood. Predictions were confirmed via regression analyses including interaction terms, and are explained by the insoluble conflict that occurs when narcissistic gratification is dependent on the admiration of others, but the tie to others interferes with independent growth and accomplishment.     

Borderline personality disorder features and cognitive,emotional, and predicted behavioral reactions to teasing

Borderline personality disorder (BPD) involves interpersonal dysfunction. It is unknown to what extent these problems are due to perceptual biases, emotional reactivity, or impulsivity above and beyond emotional reactions. The present study experimentally tested these mechanisms in the context of predicted reactions to teasing. Participants completed the Personality Assessment Inventory-Borderline Features scale [PAI-BOR; Morey, L. C. (1991). Personality assessment inventory: Professional manual. Odessa, FL: Psychological Assessment Resources], and the Rejection Sensitivity Questionnaire [Downey, G., & Feldman, S. I. (1996). Implications of rejection sensitivity for intimate relationships. Journal of Personality and Social Psychology, 70(6), 1327–1343], and imagined a scenario that involved teasing. Participants rated the teaser and their own predicted emotional and behavioral reactions. Analysis of Covariance results indicated that individuals who endorsed more BPD features showed elevated emotional reactions and predicted behavioral reactions to teasing, but not perceptual biases. Ratings of predicted behavioral responses could be accounted for by emotional responses, supporting the emotional reactivity perspectives of BPD [Linehan, M. M. (1993). Cognitive-behavioral treatment of borderline personality disorder. New York: Guilford].     

Logical Cornestones of Judaic Argumentation Theory

In this paper, the four Judaic inference rules: qal wa- ? omer, gezerah ? awah, heqe ?, binyan ’av are considered from the logical point of view and the pragmatic limits of applying these rules are symbolic-logically explicated. According to the Talmudic sages, on the one hand, after applying some inference rules we cannot apply other inference rules. These rules are weak. On the other hand, there are rules after which we can apply any other. These rules are strong. This means that Judaic inference rules have different pragmatic meanings and this fact differs Judaic logic from other ones. The Judaic argumentation theory built up on Judaic logic also contains pragmatic limits for proofs as competitive communication when different Rabbis claim different opinions in respect to the same subject. In order to define these limits we build up a special kind of syllogistics, the so-called Judaic pragmatic-syllogistics, where it is defined whose opinion should be choosen in a dispute.