Fundamenta Informaticae - Volume 6, issue 3-4

Article Type: Other

DOI: 10.3233/FI-1983-63-401

Citation: Fundamenta Informaticae, vol. 6, no. 3-4, pp. i-vi, 1983

Authors: Orlicki, Andrzej

Article Type: Research Article

Abstract: We try to define effective numberings of the logic of effective definitional schemes which has been defined in Tiuryn [4]. It turns out that a reasonable way of doing it leads us to the functions which are not surjective. Therefore in the traditional sense they are not effective numberings. However, these functions induce “good” numberings of the set of functions computable by effective definitional schemes.

Keywords: effective definitional schemes, Godol quasi-numbering, complete numbering set

DOI: 10.3233/FI-1983-63-402

Citation: Fundamenta Informaticae, vol. 6, no. 3-4, pp. 235-245, 1983

Authors: Orłowska, Ewa

Article Type: Research Article

Abstract: In the paper we consider dependencies of attributes in Pawlak’s model of information systems. We develop a logic which enables us to express and to prove dependencies. We present a Gentzen-style deduction system for the logic.

Keywords: information system, dependencies of attributes, propositional logic, lattice

DOI: 10.3233/FI-1983-63-403

Citation: Fundamenta Informaticae, vol. 6, no. 3-4, pp. 247-256, 1983

Authors: Skandalis, Kostas

Article Type: Research Article

Abstract: In this paper we compare two notions of effectiveness in the ordered field of real numbers. The first one is introduced using the notion of program in the sense of algorithmic logic. The second is the recursiveness in Baire space. After an identification of the Baire space with the set of reals using an effective and natural mapping it turns out that these two notions are different. We also study a natural notion of effectiveness extending both these notions.

Keywords: recursive, real function, programmable function, algorithmic logic

DOI: 10.3233/FI-1983-63-404

Citation: Fundamenta Informaticae, vol. 6, no. 3-4, pp. 257-274, 1983

Authors: Pasztor, Ana

Article Type: Research Article

Abstract: We prove that the category of ω -continuous algebras of any fixed (infinitary) signature is a variety of the category of partial algebras of an adequate signature. This enables us to derive properties of ω -continuous algebras from the thoroughly investigated properties of partial algebras.

Keywords: Continuous algebras, variety, partial algebras

DOI: 10.3233/FI-1983-63-405

Citation: Fundamenta Informaticae, vol. 6, no. 3-4, pp. 275-288, 1983

Authors: Novotný, Miroslav | Pawlak, Zdzisław

Article Type: Research Article

Abstract: Rought sets are investigated as a tool for expressing uncertainty of the relation “to be an element of”. We give some representation theorems for rough sets expressed in terms of information systems.

Keywords: approximation space, upper approximation, lower approximation, rough top equality, rough bottom equality, rough equality, upper rough set, lower rough set, information system

DOI: 10.3233/FI-1983-63-406

Citation: Fundamenta Informaticae, vol. 6, no. 3-4, pp. 289-296, 1983

Authors: Dańko, Wiktor

Article Type: Research Article

Abstract: In this paper, similarly to [1,4,17,20,21,29,30], abstract data types are understood as formalized many-sorted theories based on algorithmic languages (e.g. a language of algorithmic logic [2,16] or a language of dynamic logic [11,29]). Operations on data types, leading from (more) primitive types to compound types, are defined in terms of the interpretability theory (cf. Szczerba [25]). The approach proposed here to defining new types accords with the methods of introducing new classes of objects in programming languages like Simula 67, Pascal, Loglan, Ada.

Keywords: logics of programs, formalized algorithmic theories, data structures, interpretations between theories

DOI: 10.3233/FI-1983-63-407

Citation: Fundamenta Informaticae, vol. 6, no. 3-4, pp. 297-332, 1983

Authors: Goeman, H.J.M. | Groenewegen, L.P.J. | Kleijn, H.C.M. | Rozenberg, G.

Article Type: Research Article

Abstract: This paper continues the investigation froll1 [Goeman et al.] concerning the use of sets of places of a Petri net as additional (to input places) constraints for granting concession. Now interpretations of more general constraints are considered and expressed as Boolean expressions. This gives rise to various classes of constrained Petri nets. These are compared in the language theoretical framework introduced in [Goeman et al.]. An upperbound for the language defining power is found in the class of context-free programmed languages.

Keywords: Petri nets, constraints, Boolean expressions, Petri net languages

DOI: 10.3233/FI-1983-63-408

Citation: Fundamenta Informaticae, vol. 6, no. 3-4, pp. 333-374, 1983

Authors: Jaegermann, Michał | Lipski Jr., Witold

Article Type: Research Article

Abstract: We consider the problem of answering numerical queries, i.e. queries involving cardinalities of sets of objects with specified conditions, in a data base where information is incomplete. We give an algorithm to compute a lower bound and an upper bound on the response to a numerical query. The bounds proceduced by the algorithm are the best logically derivable from the information available in the data base.

Keywords: incomplete information, query languages, data bases

DOI: 10.3233/FI-1983-63-409

Citation: Fundamenta Informaticae, vol. 6, no. 3-4, pp. 375-391, 1983