Sequent-systems and groupoid models. I

The purpose of this paper is to connect the proof theory and the model theory of a family of propositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related toBCK algebras, and, finally, Johansson's and Heyting's logic. First, sequent-systems are given for these logics, and cut-elimination results are proved. In these sequent-systems the rules for the logical operations are never changed: all changes are made in the structural rules. Next, Hubert-style formulations are given for these logics, and algebraic completeness results are demonstrated with respect to residuated lattice-ordered groupoids. Finally, model structures related to relevant model structures (of Urquhart, Fine, Routley, Meyer, and Maksimova) are given for our logics. These model structures are based on groupoids parallel to the sequent-systems. This paper lays the ground for a kind of correspondence theory for axioms of logics with implication weaker than Heyting's, a correspondence theory analogous to the correspondence theory for modal axioms of normal modal logics.The first part of the paper, which follows, contains the first two sections, which deal with sequent-systems and Hubert-formulations. The second part, due to appear in the next issue of this journal, will contain the third section, which deals with groupoid models.     

“Put a Little Love in Your Heart”: Acceptance of Paternalistic and Ally Political Discourses Both Predict Pro-Roma Solidarity Intentions Through Moral Inclusion

The way politicians talk about minorities institutes the normative context of intergroup relations. We investigated how endorsement of different political discourses predicts donation and collective action intentions by majority members toward the Roma in five European countries. The survey was conducted online using samples demographically similar to the populations of Hungary, Slovakia, Romania, France, and Ireland (N = 5,054). First, results showed that accepting paternalistic discourse versus discourse promoting allyship were not distinguishable; both promoted higher moral inclusion which in turn predicted higher prosocial intentions. Second, donations (i.e., immediate relief) and collective action (i.e., social change action) were driven by identical factors. Third, acceptance of openly hostile political discourse neither predicted moral exclusion, nor lower prosocial intentions. In summary, our research provides important evidence that when it comes to Roma—non-Roma relations, the previously established distinction between solidarity intentions that aim to solidify status relations versus bring about social change is completely blurred, presumably because of the social context in which any positive message communicates moral inclusion challenging the hostile status quo.     

Reflections on “difficult” embeddings

The main purpose of this note is to present difficult embeddings of minimal and full intuitionistic logic into classical linear logic, and to prove their soundness and faithfulness. Moreover, it is also pointed out that Girard's translation of intuitionistic logic into classical linear logic is provably equivalent to one of the translations considered in this paper.     

Connectification forn-contraction

In this paper, we introduce connectification operators for intuitionistic and classical linear algebras corresponding to linear logic and to some of its extensions withn-contraction. In particular,n-contraction (n2) is a version of the contraction rule, wheren+1 occurrences of a formula may be contracted ton occurrences. Since cut cannot be eliminated from the systems withn-contraction considered most of the standard proof-theoretic techniques to investigate meta-properties of those systems are useless. However, by means of connectification we establish the disjunction property for both intuitionistic and classical affine linear logics withn-contraction.Presented byHiroakira Ono     

Comprehension of nonlexical categories in agrammatism

The focus of the paper is a proposal advanced by Grodzinsky (1984, 1986, 1990) concerning a possible syntactic deficit in agrammatism with respect to nonlexical categories. Eight native speakers of Serbo-Croatian, who presented a clinical picture of Broca's aphasia with agrammatism, were tested. Subject's sensitivity to traces and their knowledge of the inflectional and determiner system was investigated using a grammaticality judgment paradigm. The processing load was further minimized by use of short sentences that unequivocally exemplified different syntactic violations. These steps led to significant improvement in the performance of agrammatic aphasics, a result that is incompatible with the claim that the content of nonlexical elements is lost in agrammatism.A partial account of the findings was presented at the 31 st Meeting of the Academy of Aphasia, October 24–26, 1993. Tucson, Arizona. The authors gratefully acknowledge help in data collection from Mile Vukovi, Faculty of Defectology, University of Belgrade, and from Jovanka Jezdimirovi and Veronika Ispanovi-Radojkovi, the Institute for Mental Health in Belgrade. This research was supported in part by a grant (HD-01994) to Haskins Laboratories from the National Institute of Child Health and Human Development.     

Sensorimotor synchronization: Motor responses to pseudoregular auditory patterns

Musically trained and untrained subjects (N=30) were asked to synchronize their finger tapping with stimuli in auditory patterns. Each pattern comprised six successive tonal stimuli of the same duration, the first of which was accented by a different frequency. The duration of interstimulus onset intervals (ISIs) gradually increased or decreased in constant steps toward the end of the patterns. Four values of such steps were used in different trials: 20, 30, 45, and 60 msec. Various time-control mechanisms are hypothesized as being simultaneously responsible for subjects’ incorrect reproduction of the internal temporal ratios of the stimulus patterns. The mechanism of assimilation (of a central tendency) led subjects to enforce a regular (isochronous) structure on the patterns. The influence of other time-control mechanisms (distinction, subjective expression of an accent, sequential transfer) was expressed mainly in differences between intertap onset intervals (ITIs) and the corresponding ISIs at the beginning of the patterns. The duration of the first two ITIs was in the majority of the trials in an inverse ratio to the ratio of the respective ISIs. The distortions resulting from the timing mechanisms concerned were more pronounced in the performance of nonmusicians than in that of musicians.