Logical rules of visual brain: From anatomy through neurophysiology to cognition

Humans can easily recognize objects as complex as faces even if they have not seen them in such conditions or context before. It seems that perceptually we are insensitive to the exact properties of an object’s parts but the same parts in different configurations or contexts may introduce contradictory effects. From a computational point of view, we are often insensitive to changes of some symbols, but the same symbols may lead to different classification of the same object. In present work we are looking for the anatomical and neurophysiological basis of these perceptual effects. We describe interactions between parts and their configurations in different areas of the visual brain on the basis of a single cell electrophysiological activity in the thalamus, and cortical areas V1 and V4. Our model is based on feedforward (FF) and feedback (FB) interactions between these areas. In the retina and thalamus simple light spots are classified, V1 is the first area extracting edge orientation and V4 is the first area sensitive to simple shapes. The FF pathways combine properties extracted in each area into hypothetical objects. Area V1 presents concepts of orientations, while area V4 presents concepts of a simple shape. The FB pathways are responsible for comparison of the learned concepts with extracted object’s properties – they form predictions. In each area structure related predictions are tested against hypothesis. We formulate a theory in which different visual stimuli are described through their condition attributes: responses in LGN, V1, and V4 neurons are divided into several ranges and are treated as decision attributes. Applying rough set theory [Pawlak, Z. (1991). Rough sets – theoretical aspects of reasoning about data. Boston, London, Dordrecht: Kluwer Academic Publishers] we have divided our stimuli into area dependent equivalent classes. We propose that relationships between decision rules in each area are determined by two different logical rules: “driver logical rule” of FF and “modulator logical rule” of FB pathways. These interactions are proposed to be a neurophysiological basis of the object classification.     

Socratic Proofs for Quantifiers

First-order logic is formalized by means of tools taken from the logic of questions. A calculus of questions which is a counterpart of the Pure Calculus of Quantifiers is presented. A direct proof of completeness of the calculus is given. *Research for this paper was supported by The Foundation for Polish Science (both authors), and indirectly (in the case of the first author) by a bilateral exchange project funded by the Ministry of the Flemish Community (project BIL 01/80) and the State Committee for Scientific Research, Poland.     

Deconstructing Differentiation: Self Regulation, Interdependent Relating, and Well-Being in Adulthood

This study examined underlying similarities between the Personal Authority in the Family System Questionnaire (PAFS; Bray, Williamson, & Malone, 1984a) and the Differentiation of Self Inventory (DSI; Skowron & Friedlander, 1998). Generalized least-squares factor analysis yielded two related factors, Self Regulation and Interdependent Relating, accounting for 60% of the variance in the solution. Greater Self Regulation—comprised of DSI scales characterized by less emotional reactivity and the ability to take an I position in relationships—and Interdependent Relating—marked by greater personal authority, intergenerational intimacy and less intergenerational fusion on the PAFS and less emotional cutoff on the DSI—predicted well-being among both women and men. Implications for family therapy and suggestions for future research are discussed.     

A conjunction in closure spaces

This paper is closely related to investigations of abstract properties of basic logical notions expressible in terms of closure spaces as they were begun by A. Tarski (see [6]). We shall prove many properties of ω-conjunctive closure spaces (X is ω-conjunctive provided that for every two elements of X their conjunction in X exists). For example we prove the following theorems:

1. For every closed and proper subset of an ω-conjunctive closure space its interior is empty (i.e. it is a boundary set).
2. If X is an ω-conjunctive closure space which satisfies the ω-compactness theorem and \(\hat P\) [X] is a meet-distributive semilattice (see [3]), then the lattice of all closed subsets in X is a Heyting lattice.
3. A closure space is linear iff it is an ω-conjunctive and topological space.
4. Every continuous function preserves all conjunctions.

     

Erotetic arguments: A preliminary analysis

The concept of erotetic argument is introduced. Two relations between sets of declarative sentences and questions are analysed; and two classes of erotetic arguments are characterized.     

Undecidability without Arithmetization

In the present paper the well-known Gödels – Churchs argument concerning the undecidability of logic (of the first order functional calculus) is exhibited in a way which seems to be philosophically interestingfi The natural numbers are not used. (Neither Chinese Theorem nor other specifically mathematical tricks are applied.) Only elementary logic and very simple set-theoretical constructions are put into the proof. Instead of the arithmetization I use the theory of concatenation (formalized by Alfred Tarski). This theory proves to be an appropriate tool. The decidability is defined directly as the property of graphical discernibility of formulas.