Cut elimination for a logic with induction and co-induction

Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles are based on a proof-theoretic (rather than set-theoretic) notion of definition (Hallnäs, 1991 [18], Eriksson, 1991 [11], Schroeder-Heister, 1993 [38], McDowell and Miller, 2000 [22]). Definitions are akin to logic programs, where the left and right rules for defined atoms allow one to view theories as “closed” or defining fixed points. The use of definitions and free equality makes it possible to reason intensionally about syntax. We add in a consistent way rules for pre- and post-fixed points, thus allowing the user to reason inductively and co-inductively about properties of computational system making full use of higher-order abstract syntax. Consistency is guaranteed via cut-elimination, where we give a direct cut-elimination procedure in the presence of general inductive and co-inductive definitions via the parametric reducibility technique.     

Grounding compositional symbols: no composition without discrimination

The classical computational conception of meaning has been challenged by the idea that symbols must be grounded on sensorimotor processes. A difficult question arises from the fact that grounding representations cannot be symbolic themselves but, in order to support compositionality, should work as primitives. This implies that they should be precisely identifiable and strictly connected with discriminable perceptual features. Ideally, each representation should correspond to a single discriminable feature. The present study was aimed at exploring whether feature discrimination is a fundamental requisite for grounding compositional symbols. We studied this problem by using Integral stimuli, composed of two interacting and not separable features. Such stimuli were selected in Experiment 1 as pictures whose component features are easily or barely discriminable (Separable or Integral) on the basis of psychological distance metrics (City-block or Euclidean) computed from similarity judgments. In Experiment 2, either each feature was associated with one word of a two-word expression, or the whole stimulus with a single word. In Experiment 3, the procedure was reversed and words or expressions were associated with whole pictures or separate features. Results support the hypothesis that single words are best grounded by Integral stimuli and composite expressions by Separable stimuli, where a strict association of single words with discriminated features is possible.     

The Meaning of Category Theory for 21st Century Philosophy

Among the main concerns of 20th century philosophy was that of the foundations of mathematics. But usually not recognized is the relevance of the choice of a foundational approach to the other main problems of 20th century philosophy, i.e., the logical structure of language, the nature of scientific theories, and the architecture of the mind. The tools used to deal with the difficulties inherent in such problems have largely relied on set theory and its “received view”. There are specific issues, in philosophy of language, epistemology and philosophy of mind, where this dependence turns out to be misleading. The same issues suggest the gain in understanding coming from category theory, which is, therefore, more than just the source of a “non-standard” approach to the foundations of mathematics. But, even so conceived, it is the very notion of what a foundation has to be that is called into question. The philosophical meaning of mathematics is no longer confined to which first principles are assumed and which “ontological” interpretation is given to them in terms of some possibly updated version of logicism, formalism or intuitionism. What is central to any foundational project proper is the role of universal constructions that serve to unify the different branches of mathematics, as already made clear in 1969 by Lawvere. Such universal constructions are best expressed by means of adjoint functors and representability up to isomorphism. In this lies the relevance of a category-theoretic perspective, which leads to wide-ranging consequences. One such is the presence of functorial constraints on the syntax–semantics relationships; another is an intrinsic view of (constructive) logic, as arises in topoi and, subsequently, in more general fibrations. But as soon as theories and their models are described accordingly, a new look at the main problems of 20th century’s philosophy becomes possible. The lack of any satisfactory solution to these problems in a purely logical and set-theoretic setting is the result of too circumscribed an approach, such as a static and punctiform view of objects and their elements, and a misconception of geometry and its historical changes before, during, and after the foundational “crisis”, as if algebraic geometry and synthetic differential geometry – not to mention algebraic topology – were secondary sources for what concerns foundational issues. The objectivity of basic geometrical intuitions also acts against the recent version of structuralism proposed as ‘the’ philosophy of category theory. On the other hand, the need for a consistent and adequate conceptual framework in facing the difficulties met by pre-categorical theories of language and scientific knowledge not only provides the basic concepts of category theory with specific applications but also suggests further directions for their development (e.g., in approaching the foundations of physics or the mathematical models in the cognitive sciences). This ‘virtuous’ circle is by now largely admitted in theoretical computer science; the time is ripe to realise that the same holds for classical topics of philosophy. Text of a talk given at the Workshop and Symposium on the Ramifications of Category Theory, Florence, November 18–22, 2003. For further documentation on the conference, see     

Incest and professional boundaries: Confidentiality versus mandatory reporting

The mandatory reporting of an incest case by a mental health professional, sets in motion a chain of events which raise conflict for all involved. Typically, attorneys, the courts, health service providers, as well as primary treatment team become involved. This article discusses some of the relevant dilemmas that are raised by the personal and professional mandatory report of incest.     

The Structure of Affect in a Non-Western Culture: Evidence for Cross-Cultural Comparability

We investigated the structure of affect in the Filipino culture and compared our results to those in Western studies. Four samples of students (ns = 397 to 530) rated their mood for today, the past week, or in general, using near-comprehensive sets of Filipino mood adjectives. Results of exploratory and confirmatory factor analyses supported a hierarchical model of affect and the cross-cultural comparability of self-report mood dimensions (i.e., higher-order Positive and Negative Affect, plus specific affects corresponding to hypothesized universal or basic emotions). The results were more consistent with biological theories of affect than a strong social constructivist perspective.     

The Processing of Grammatical Gender and Number in Spanish

The aim of the present study is to explore the representation and processing of inflectional morphology in Spanish. Experiment 1 compared the access time for words from the same base morpheme contrasted by the surface frequency of the masculine and feminine form, i.e., masculine-dominant items and feminine-dominant items. The results showed a surface frequency effect in both types of items. Experiment 2 compared the access time for masculine words having the same surface frequency but differing in their summed frequency (masculine plus feminine forms), the results showing no significant effect of this parameter. Finally, experiment 3 compared the access time for words from the same stem and contrasting by the surface frequencies for the singular and plural forms, i.e., singular-dominant and plural-dominant words. A clear frequency effect was observed for the singular-dominant words but not for plural-dominant ones. These results suggest that gender information is stored in the corresponding lexical entry and accessed from the full word form whereas the information about number is accessed from the stem corresponding to the singular form.     

Systematic Monitoring of the Implementation of a Case Management Model

A systematic approach for monitoring case management service provision and the results obtained when this approach was applied to a program for community-dwelling elders with severe mental illness are presented. A detailed, closed-ended, daily service log was used to collect data on 713 client-contact days. Participants (N = 24) were predominantly female (71%), were White (63%) or African American (37%), and tended to have diagnoses of either schizophrenia (42%) or major depression (21%). Services were delivered most frequently in the client's home (47%), the program office (35%), or by phone (27%); most frequent activities were monitoring psychiatric symptoms/medications (62 %), and monitoring physical symptoms or medications or both (54%). Service characteristics did not differ with regard to demographics but did vary with living situation and psychiatric diagnosis. The findings point to the need for flexible programs capable of meeting diverse service needs as well as the utility of a daily service log in studying case management.     

History of the unconscious in Soviet Russia: from its origins to the fall of the Soviet Union

Russia accepted the notion of the unconscious and psychoanalysis before many Western countries. The first Russian Psychoanalytic Society was established in 1911. After World War I and the Russian Revolution, for a short happy period, the following psychoanalysts were active: Sabina Spielrein, Tatiana Rosenthal, Moshe Wulff, Nikolai Osipov and Ivan Ermakov. Scholars associated with Soviet ideas participated too, including Aleksandr Luria, Michail Rejsner and Pavel Blonskij. Lev Vygotskij himself dealt with the unconscious. A second psychoanalytical society was set up in Kazan. Unfortunately, at the end of the 1920s, repression dissolved the psychoanalytic movement. Even the word 'psychoanalysis' was banned for decades. Nonetheless, interest in the unconscious, as distinct from psychoanalytic theory, survived in the work of the Georgian leader D. Uznadze. His followers organized the 1979 International Symposium on the Unconscious, in Tbilisi, Georgia, which marked the breaking of an ideological barrier. Since then, many medical, psychological, philosophical and sociological scholars have taken an interest in the unconscious, a subject both feared, for its ideological implications, and desired.Since the 1980s, psychoanalytic ideas have been published in the scientific press and have spread in society. The fall of the USSR in 1991 liberalized the scientific and institutional development of psychoanalysis.