Fathers,kings, and promises: Husserl and Reinach on the a priori

Internationale Akademie für Philosophie im Fürstentum LiechtensteinPrepared as part of the project The A Prlori in Austrian Philosophy of the Austrian Fonds zur Förderung der wissenschaftlichen Forschung. My special thanks for helpful comments and improvement suggestions go to the director of this project, Prof. Dr. Barry Smith, as well as to Roberto Casati, Agnieszka Lekka-Kowalik, Graham White, and to the participants of the advanced seminar for formal ontology at the International Academy for Philosophy in the Principality of Liechtenstein.     

The finite model property for BCI and related systems

We prove the finite model property (fmp) for BCI and BCI with additive conjunction, which answers some open questions in Meyer and Ono [11]. We also obtain similar results for some restricted versions of these systems in the style of the Lambek calculus [10, 3]. The key tool is the method of barriers which was earlier introduced by the author to prove fmp for the product-free Lambek calculus [2] and the commutative product-free Lambek calculus [4].Presented by H. Ono     

Gaifman's theorem on categorial grammars revisited

The equivalence of (classical) categorial grammars and context-free grammars, proved by Gaifman [4], is a very basic result of the theory of formal grammars (an essentially equivalent result is known as the Greibach normal form theorem [1], [14]). We analyse the contents of Gaifman's theorem within the framework of structure and type transformations. We give a new proof of this theorem which relies on the algebra of phrase structures and exhibit a possibility to justify the key construction used in Gaifman's proof by means of the Lambek calculus of syntactic types [15].     

A simple and general method of solving the finite axiomatizability problems for Lambek's syntactic calculi

In [4], I proved that the product-free fragment L of Lambek's syntactic calculus (cf. Lambek [2]) is not finitely axiomatizable if the only rule of inference admitted is Lambek's cut-rule. The proof (which is rather complicated and roundabout) was subsequently adapted by Kandulski [1] to the non-associative variant NL of L (cf. Lambek [3]). It turns out, however, that there exists an extremely simple method of non-finite-axiomatizability proofs which works uniformly for different subsystems of L (in particular, for NL). We present it below to the use of those who refer to the results of [1] and [4].     

Presuppositional completeness

Some notions of the logic of questions (presupposition of a question, validation, entailment) are used for defining certain kinds of completeness of elementary theories. Presuppositional completeness, closely related to -completeness ([3], [6]), is shown to be fulfilled by strong elementary theories like Peano arithmetic.     

The Face of the Chameleon: The Experience of Facial Mimicry for the Mimicker and the Mimickee

This research addressed three questions concerning facial mimicry: (a) Does the relationship between mimicry and liking characterize all facial expressions, or is it limited to specific expressions? (b) Is the relationship between facial mimicry and liking symmetrical for the mimicker and the mimickee? (c) Does conscious mimicry have consequences for emotion recognition? A paradigm is introduced in which participants interact over a computer setup with a confederate whose prerecorded facial displays of emotion are synchronized with participants’ behavior to create the illusion of social interaction. In Experiment 1, the confederate did or did not mimic participants’ facial displays of various subsets of basic emotions. Mimicry promoted greater liking for the confederate regardless of which emotions were mimicked. Experiment 2 reversed these roles: participants were instructed to mimic or not to mimic the confederate’s facial displays. Mimicry did not affect liking for the confederate but it did impair emotion recognition.     

A direct proof of the equivalence of free categorial grammars and simple phrase structure grammars

In [2], Bar-Hillel, Gaifman, and Shamir prove that the simple phrase structure grammars (SPGs) defined by Chomsky are equivalent in a certain sense to Bar-Hillel's bidirectional categorial grammars (BCGs). On the other hand, Cohen [3] proves the equivalence of the latter ones to what the calls free categorial grammars (FCGs). They are closely related to Lambek's syntactic calculus which, in turn, is based on the idea due to Ajdukiewicz [1]. For the reasons which will be discussed in the last section, Cohen's proof seems to be at least incomplete. This paper yields a direct proof of the equivalence ofFCGs andSPGs.Allatum est die S Marlii 1976     

Phenomenology,possible worlds and negation

I would like to thank Charles W. Harvey from the University of Central Arkansas and Leon Gumaski from the University of Toru in Poland for a number of useful criticisms of an earlier version of this paper.