Strukturalna teoria automatów skończonych określonych za pomocą matryc

Praca przedstawiona Radzie Wydziau Matematyki, Fizyki i Chemii Uniwersytetu Wrocawskiego w celu uzyskania stopnia doktora nauk matematycznych.Allatum est die 11 Aprilis 1964     

Finite axiomatization for some intermediate logics

LetN. be the set of all natural numbers (except zero), and letD _n ^* = {k ∈N ∶k|n} ∪ {0} wherek¦n if and only ifn=k.x f or somex∈N. Then, an ordered setD _n ^* = 〈D _n ^* , ? _n , wherex? _ny iffx¦y for anyx, y∈D _n ^* , can easily be seen to be a pseudo-boolean algebra. In [5], V.A. Jankov has proved that the class of algebras {D _n ^* ∶n∈B}, whereB =,{k ∈N∶ ? \(\mathop \exists \limits_{n \in N} \) (n > 1 ≧n ² k)is finitely axiomatizable. The present paper aims at showing that the class of all algebras {D _n ^* ∶n∈B} is also finitely axiomatizable. First, we prove that an intermediate logic defined as follows: $$LD = Cn(INT \cup \{ p_3 \vee [p_3 \to (p_1 \to p_2 ) \vee (p_2 \to p_1 )]\} )$$ finitely approximatizable. Then, defining, after Kripke, a model as a non-empty ordered setH = 〈K, ?〉, and making use of the set of formulas true in this model, we show that any finite strongly compact pseudo-boolean algebra ? is identical with. the set of formulas true in the Kripke modelH _B = 〈P(?), ?〉 (whereP(?) stands for the family of all prime filters in the algebra ?). Furthermore, the concept of a structure of divisors is defined, and the structure is shown to beH D _n ^* = 〈P (D _n ^* ), ?〉for anyn∈N. Finally, it is proved that for any strongly compact pseudo-boolean algebraU satisfying the axiomp ₃∨ [p ₃→(p₁→p₂)∨(p₂→p₁)] there is a structure of divisorsD _* ⁿ such that it is possible to define a strong homomorphism froomiH D _n ^* ontoH D _U . Exploiting, among others, this property, it turns out to be relatively easy to show that \(LD = \mathop \cap \limits_{n \in N} E(\mathfrak{D}_n^* )\) .     

Analityczne komponenty definicji arbitralnych

Tre: Wstp. I. Definicje arbitralne. II. Syntetyczne konsekwencje definicji arbitralnych III. Analityczne i rzeczowe komponenty definicji arbitralnych. IV. Zdania analityczne.Artyku ten w nieznacznym tylko stopniu róni si od pracy doktorskiej, któr przedstawiem w 1962 r. Jak najuprzejmiej dzikuj Prof. Dr M. Kokoszyskiej-Lutman, Prof. Dr J. Supeckiemu oraz Doc. Dr M. Przeckiemu za szereg uwag i wskazówek, z których tak wiele skorzystaem przygotowujc ostateczn redakcj pracy.     

Constraints and Preferences in Inductive Learning: An Experimental Study of Human and Machine Performance

The paper examines constraints and preferences employed by people in learning decision rules from preclassified examples. Results from four experiments with human subjects were analyzed and compared with artificial intelligence (AI) inductive learning programs. The results showed the people's rule inductions tended to emphasize category validity (probability of some property, given a category) more than cue validity (probability that an entity is a member of a category given that it has some property) to a greater extent than did the AI programs. Although the relative proportions of different rule types (e.g., conjunctive vs. disjunctive) changed across experiments, a single process model provided a good account of the data from each study. These observations are used to argue for describing constraints in terms of processes embodied in models rather than in terms of products or outputs. Thus AI induction programs become candidate psychological process models and results from inductive learning experiments can suggest new algorithms. More generally, the results show that human inductive generalizations tend toward greater specificity than would be expected if conceptual simplicity were the key constraint on inductions. This bias toward specificity may be due to the fact that this criterion both maximizes inferences that may be drawn from category membership and protects rule induction systems from developing over-generalizations.