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1993 | 28 | 1 | 67-94
Tytuł artykułu

Compactness and Löwenheim-Skolem properties in categories of pre-institutions

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The abstract model-theoretic concepts of compactness and Löwenheim-Skolem properties are investigated in the "softer" framework of pre-institutions [18]. Two compactness results are presented in this paper: a more informative reformulation of the compactness theorem for pre-institution transformations, and a theorem on natural equivalences with an abstract form of the first-order pre-institution. These results rely on notions of compact transformation, which are introduced as arrow-oriented generalizations of the classical, object-oriented notions of compactness. Furthermore, a notion of cardinal pre-institution is introduced, and a Löwenheim-Skolem preservation theorem for cardinal pre-institutions is presented.
Słowa kluczowe
Rocznik
Tom
28
Numer
1
Strony
67-94
Opis fizyczny
Daty
wydano
1993
Twórcy
  • University of Pisa, Dip. Informatica, Corso Italia 40, I-56125 Pisa, Italy
  • University of Twente, Fac., Informatica, P. O. Box 217, NL-7500AE Enschede, The Netherlands
Bibliografia
  • [1] H. Andréka, I. Németi and I. Sain, Abstract model theoretic approach to algebraic logic, manuscript, Mathematical Institute, Budapest, 1984.
  • [2] E. Astesiano and M. Cerioli, Commuting between institutions via simulation, Univ. of Genova, Formal Methods Group, Technical Report no. 2, 1990.
  • [3] G. Bernot and M. Bidoit, Proving the correctness of algebraically specified software: Modularity and Observability issues, in: M. Nivat, C. M. I. Rattray, T. Rus and G. Scollo (eds.), AMAST '91, Algebraic Methodology and Software Technology, Workshops in Computing, Springer, London 1992, 216-239.
  • [4] C. C. Chang and H. J. Keisler, Model Theory, third ed., North-Holland, Amsterdam 1990.
  • [5] H.-D. Ebbinghaus, Extended logics: the general framework, in: J. Barwise and S. Feferman (eds.), Model-Theoretic Logics, Springer, Berlin 1985, 25-76.
  • [6] H.-D. Ebbinghaus, J. Flum and W. Thomas, Mathematical Logic, Springer, New York 1984.
  • [7] H. Ehrig, M. Baldamus, F. Cornelius and F. Orejas, Theory of algebraic module specification including behavioural semantics and constraints, in: M. Nivat, C. M. I. Rattray, T. Rus and G. Scollo (eds.), AMAST '91, Algebraic Methodology and Software Technology, Workshops in Computing, Springer, London 1992, 145-172.
  • [8] A. J. M. van Gasteren, On the Shape of Mathematical Arguments, Lecture Notes in Comput. Sci. 445, Springer, Berlin 1990.
  • [9] J. A. Goguen and R. Burstall, Introducing institutions, in: E. Clarke and D. Kozen (eds.), Logics of Programs, Lecture Notes in Comput. Sci. 164, Springer, Berlin 1984, 221-256.
  • [10] S. MacLane, Categories for the Working Mathematician, Graduate Texts in Math. 5, Springer, New York 1971.
  • [11] J.-A. Makowski, Compactness, embeddings and definability, in: J. Barwise and S. Feferman (eds.), Model-Theoretic Logics, Springer, Berlin 1985, 645-716.
  • [12] V. Manca and A. Salibra, On the power of equational logic: applications and extensions, in: H. Andréka, J. D. Monk and I. Németi (eds.), Algebraic Logic, Colloq. Math. Soc. János Bolyai 54, North-Holland, Amsterdam 1991, 393-412.
  • [13] V. Manca, A. Salibra and G. Scollo, Equational type logic, Theoret. Comput. Sci. 77 (1990), 131-159.
  • [14] V. Manca, A. Salibra and G. Scollo, On the expressiveness of equational type logic, in: C. M. I. Rattray and R. G. Clark (eds.), The Unified Computation Laboratory: Modelling, Specifications and Tools, Oxford Univ. Press, Oxford 1992, 85-100.
  • [15] J. Meseguer, General logics, in: H.-D. Ebbinghaus et al. (eds.), Logic Colloquium '87, North-Holland, Amsterdam 1989, 275-329.
  • [16] M. P. Nivela and F. Orejas, Initial behaviour semantics for algebraic specifications, in: D. T. Sannella and A. Tarlecki (eds.), Recent Trends in Data Type Specification, Lecture Notes in Comput. Sci. 332, Springer, Berlin 1988, 184-207.
  • [17] F. Orejas, M. P. Nivela and H. Ehrig, Semantical constructions for categories of behavioural specifications, in: H. Ehrig, H. Herrlich, H.-J. Kreowski and G. Preuß (eds.), Categorical Methods in Computer Science - with Aspects from Topology, Lecture Notes in Comput. Sci. 393, Springer, Berlin 1989, 220-245.
  • [18] A. Salibra and G. Scollo, A soft stairway to institutions, in: M. Bidoit and C. Choppy (eds.), Recent Trends in Data Type Specification, Lecture Notes in Comput. Sci. 655, Springer, Berlin 1993, 310-329.
  • [19] D. T. Sannella and A. Tarlecki, Specifications in an arbitrary institution, Inform. and Comput. 76 (1988), 165-210.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv28z1p67bwm
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