Sequent-systems and groupoid models. II

The purpose of this paper is to connect the proof theory and the model theory of a family of prepositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related to BCK 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, Hilbert-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.Below is the sequel to the first part of the paper, which appeared in the previous issue of this journal (vol. 47 (1988), pp. 353–386). The first part contained sections on sequent-systems and Hilbert-formulations, and here is the third section on groupoid models. This second part is meant to be read in conjunction with the first part.     

Mathematical models of central pattern generators in locomotion: I. Current problems

As a background for subsequent studies of mathematical models of central pattern generators in locomotion (Stafford & Barnwell, 1985a, b) relevant aspects of the literature on locomotion are reviewed, concepts of locomotion discussed, and extant models considered. Advantages and disadvantages of present models are discussed, and the need for mathematical models is emphasized. It is shown that realistic models of pattern generation in locomotion must take numerous factors into account, including phases of step cycle, muscle sequencing, gait and interlimb coordination, initiation and cessation of locomotion, and many aspects of neuromuscular control and function.     

Logit models and logistic regressions for social networks: I. An introduction to Markov graphs andp

Spanning nearly sixty years of research, statistical network analysis has passed through (at least) two generations of researchers and models. Beginning in the late 1930's, the first generation of research dealt with the distribution of various network statistics, under a variety of null models. The second generation, beginning in the 1970's and continuing into the 1980's, concerned models, usually for probabilities of relational ties among very small subsets of actors, in which various simple substantive tendencies were parameterized. Much of this research, most of which utilized log linear models, first appeared in applied statistics publications.But recent developments in social network analysis promise to bring us into a third generation. The Markov random graphs of Frank and Strauss (1986) and especially the estimation strategy for these models developed by Strauss and Ikeda (1990; described in brief in Strauss, 1992), are very recent and promising contributions to this field. Here we describe a large class of models that can be used to investigate structure in social networks. These models include several generalizations of stochastic blockmodels, as well as models parameterizing global tendencies towards clustering and centralization, and individual differences in such tendencies. Approximate model fits are obtained using Strauss and Ikeda's (1990) estimation strategy.In this paper we describe and extend these models and demonstrate how they can be used to address a variety of substantive questions about structure in social networks.This research was supported by grants from the Australian Research Council and the National Science Foundation (#SBR93-10184). This paper was presented at the 1994 Annual Meeting of the Psychometric Society, Champaign, Illinois, June 1994. Special thanks go to Sarah Ardu for programming assistance, Laura Koehly and Garry Robins for help with this research, and to Shizuhiko Nishisato and three reviewers for their comments. INTERNETemail addresses:pattison@psych.unimelb.edu.au (PP);stanwass@uiuc.edu (SW). Affiliations: Department of Psychology, University of Melbourne (PP); Department of Psychology, Department of Statistics, and The Beckman Institute for Advanced Science and Technology, University of Illinois (SW).     

Pronoun resolution and discourse models.

Psychological investigations of pronoun resolution have implicitly assumed that the processes involved automatically provide a unique referent for every pronoun. We challenge this assumption and propose a new framework for studying pronoun resolution. Drawing on advances in discourse representation and global memory modeling, this framework suggests that automatic processes may not always identify a unique referent for a pronoun. In 9 experiments, we demonstrate that, unlike noun anaphors, pronouns sometimes do not produce relative facilitation of their referents in comparison with nonreferents. We argue that research on pronoun resolution must consider the discourse contexts in which pronouns are likely to occur.     

Meaning and Interpretation. I

The paper is an attempt at a logical explication of some crucial notions of current general semantics and pragmatics. A general, axiomatic, formal-logical theory of meaning and interpretation is outlined in this paper.In the theory, accordingto the token-type distinction of Peirce, language is formalised on two levels: first as a language of token-objects (understood as material, empirical, enduring through time-and space objects) and then – as a language of type-objects (understood as abstract objects, as classes of tokens). The basic concepts of the theory, i.e. the notions: meaning, denotation and interpretation of well-formed expressions (wfes) of the language are formalised on the type-level, by utilising some semantic-pragmatic primitive notions introduced on the token-level. The paper is divided into two parts.In Part Ia theoryof meaningand denotation is proposed, and in Part II - its expansion to the theory of meaning and interpretation is presented.The meaninga wfe is defined as an equivalence class of the relation possessing the same manner of using types (cf. Ajdukiewicz [1934], Wittgenstein [1953]). The concept of denotation is defined by means of the relation of referring which holds between wfe-types and objects of reality described by the given language. Presented by Wojciech Buszkowski     

Mental models and the fan effect.

Explanations of data from fan effect experiments have been based on propositional network models. This article presents findings not readily predicted by such models. In particular, in three experiments we found that, during a speeded-recognition test, subjects retrieved facts about several objects associated with a single location faster than facts about several locations associated with a single object. Indeed, there was no fan effect in the former case despite the fact that there were an equivalent number of associations among concepts in both conditions. We suggest that such data are consistent with a mental model representational account.     

Parameterization of connectionist models.

We present a method for estimating parameters of connectionist models that allows the model's output to fit as closely as possible to empirical data. The method minimizes a cost function that measures the difference between statistics computed from the model's output and statistics computed from the subjects' performance. An optimization algorithm finds the values of the parameters that minimize the value of this cost function. The cost function also indicates whether the model's statistics are significantly different from the data's. In some cases, the method can find the optimal parameters automatically. In others, the method may facilitate the manual search for optimal parameters. The method has been implemented in Matlab, is fully documented, and is available for free download from the Psychonomic Society Web archive at www.psychonomic.org/archive/.