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"Abstract logics" and "Classical abstract logics"

Seria
Rozprawy Matematyczne tom/nr w serii: 102 wydano: 1973
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CONTENTS
Preface......................................................................................................................................................... 5
ABSTRACT LOGICS (by D. J. Brown and E. Suszko)
Introduction.................................................................................................................................................. 9
I. Elementary properties of closure systems and closure operations............................................. 10
II. Some properties of closure operators and closure systems....................................................... 12
III. Basic concepts of closure spaces.................................................................................................... 14
IV. Galois connections and dual spaces............................................................................................... 16
V. Abstract logics........................................................................................................................................ 19
VI. Projective generation of abstract logics........................................................................................... 20
VII. Inductive generation of abstract logics............................................................................................ 23
VIII. Logical congruences and bi-logical morphisms......................................................................... 24
IX. The structure of $Θ_ℒ$....................................................................................................................... 26
X. Logical matrices.................................................................................................................................... 28
XI. Generating logics by matrices .......................................................................................................... 29
XII. Structurality and invariance................................................................................................................ 31
XIII. Adequacy and completeness........................................................................................................... 33
XIV. Some applications to mathematical logic..................................................................................... 35
References.................................................................................................................................................. 40

CLASSICAL ABSTRACT LOGICS (by S.L. Bloom and D. J. Brown)
1. Introduction............................................................................................................................................. 43
2. Preliminaries.......................................................................................................................................... 43
3. The category of classical logics.......................................................................................................... 45
4. The characterization theorems........................................................................................................... 48
References.................................................................................................................................................. 52
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 102
Liczba stron
52
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CII
Daty
wydano
1973
Twórcy
autor
autor
autor
autor
Bibliografia
  • [1] D. J. Brown, Abstract Logics, Ph. D. Thesis, Stevens Institute of Technology 1960.
  • [1] P. M. Cohn, Universal Algebra, Harper and Row 1965.
  • [1] G. Birkhoff, Lattice theory, Amer. Math. Soc. Colloq. Publ. 25, third edition, Amer. Math. Soc. (1967).
  • [2] G. Birkhoff, On the combination of topologies, Fund. Math. 26 (1936), pp. 156-166.
  • [1] S. Bloom and R. Suszko, Investigations into sentential calculus with identity, Notre Dame Journal of Formal Logic 13 (1972), pp. 289-308.
  • [2] S. Bloom and R. Suszko, Semantics for SCI, Studia Logica 28 (1971), pp. 77-81.
  • [1] G. Boole, An Investigation of the Laws of Thought, New York 1864.
  • [1] E. Cech, Topological Spaces, Revised, edition by Z. Frolík and M. Katetov, New York 1966.
  • [1] P. M. Cohn, Universal Algebra, New York 1965.
  • [1] C. J. Everett, Closure operators and Galois theory in lattices, Trans. Amer. Math. Soc. 55 (1944), pp. 514-525.
  • [1] G. Graetzer, Universal Algebra, Princeton 1968.
  • [1] P. Halmos, The basic concepts of algebraic logic, Amer. Math, Monthly 63 (I960), pp. 363-387.
  • [1] C. Kuratowski, Topologie I (1958) and II (1961), Warszawa.
  • [1] J. Łoś, O matrycach logicznych (On logical matrices), Travaux de la Société des Sciences et des Lettres de Wrocław, Ser. B 19 (1949).
  • [1] J. Łoś and R. Suszko, Remarks on sentential logics, Indag. Math. 20 (2) (1968), pp. 178-183.
  • [1] J. Łukasiewicz and A. Tarski, Untersuchungen über den Aussagenkalkül, C. R. Soc. Sci. Varsovie, Cl. Ill, 23 (1930), pp. 30-50.
  • [1] E. H. Moore, Introduction to a form of general analysis, AMS Colloq. Publ. 2, New Haven 1910.
  • [1] B. H. Neumann, Algebra, Lecture Notes, New York 1962.
  • [1] O. Ore, Combinations of closure relations, Annals of Math. 44 (1943), pp. 514-533.
  • [2] O. Ore, Galois connexions, Trans. Amer. Math. Soc. 55 (1944), pp. 493-513.
  • [1] R. S. Pierce, Introduction to the Theory of Abstract Algebras, New York 1968.
  • [1] J. Porte, Recherches sur la Théorie générale des systèmes formels et sur les systèmes connectives, Paris 1965.
  • [1] H. Rasiowa and R. Sikorski, The Mathematics of the Metamathematics, Warszawa 1963.
  • [1] R. Suszko, On analytic axioms and logical rules of inference, The Poznan Society of Friends of Science, Philosophical Section 7 (5) (1949), pp. 1-30.
  • [2] R. Suszko, Formal theory of logical values I, Studia Logica 4 (1967), pp. 145-236.
  • [3] R. Suszko, Concerning the method of logical schemes, the notion of logical calculus and the role of consequence relations, Studia Logica 11 (1961), pp. 185-214.
  • [1] A. Tarski, Logic, Semantics, Metamathematics, translation by J. H. Woodger of selected papers by Tarski, Oxford 1956.
  • [1] R. Wójcicki, Some remarks on the consequence operation in sentential logics, Fund. Math. 68 (1970), pp. 269-279.
  • [1] W. Zandarowska, O związkach pomiędzy wynikaniem, sprzecznością, i zupełnością (Connections between consequence, inconsistency and completeness), Studia Logica 18 (1966), pp. 165-174.
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