Abstract
Building on the work of Goguen and Burstall on institutions and on Tarski's notion of deductive system, a categorial framework for manipulating theories in an arbitrary logic is presented. Its main contribution is the formalisation of the semantics of theory-building operations on top of a consequence relation. For that purpose, the notion of π-institution is proposed as an alternative to the notion of institution, replacing the notions of model and satisfaction by a primitive consequence operator in the definition of a logic. The resulting approach to the semantics of specification languages is intrinsically different from the original one in the sense that the ultimate denotation of a specification is taken herein to be a class of theories (sets of formulae closed for the consequence relation) and not a class of models of that logic. Adopting this point of view, the semantics of Clear-like specification building operations is analysed.
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M.Arbib and E.Manes, Arrows, Structures, and Functors, Academic Press 1975
A.Avron, "Simple Consequence Relations", Report ECS-LFCS-87-30, Edinburgh, June 1987
J.Barwise, "Axioms for Abstract Model Theory", Annals of Mathematical Logic 7, 1974
W.Blok and D.Pigozzi, "A Characterization of Algebraizable Logics", Internal Report, Univ. Illinois at Chicago, January 1986
R.Burstall and J.Goguen, "The Semantics of Clear, a Specification Language", in LNCS 86, Proc. 1979 Copenhagen Winter School on Abstract Software Specification, Springer-Verlag 1980, 292–332
R.Burstall and J.Goguen, "An Informal Introduction to Specifications using Clear", in The Correctness Problem in Computer Science, R. Boyer and J. Moore (eds), Academic Press 1981, 185–213
H.-D. Ehrich, "On the Teory of Specification, Implementation and Parametrization of Abstract Data Types", Journal of the ACM, 29(1), January 1982, 206–227
H.Ehrig e B.Mahr, Fundamentals of Algebraic Specifications 1, EATCS Monographs on Computer Science, Springer-Verlag 1985
H.Enderton, A Mathematical Introduction to Logic, Academic Press 1972
J.Fiadeiro and A.Sernadas, "Structuring Theories on Consequence" — extended version, INESC, 1987
D.Gabbay, Semantical Investigations in Heyting's Intuitionistic Logic, Reidel, 1981
J. Goguen and R. Burstall, "Institutions: Abstract Model Theory for Computer Science", CSLI-85-30, Stanford University, 1985 (preliminary version in LNCS 164, Proc. Logics of Programming Workshop, E. Clarke and D. Kozen (eds), Springer-Verlag 1984, 221–256)
J. Goguen and R. Burstall, "A Study in the Foundations of Programming Methodology: Specifications, Institutions, Charters and Parchments", in LNCS 240, Proc. Conference on Computer Science and Category Theory, D. Pitt et al (eds), Springer-Verlag 1986, 313–333
J.Goguen, J.Thatcher, E.Wagner and J.Wright, "Abstract Data Types as Initial Algebras and the Correctness of Data Representations", in Computer Graphics, Pattern Recognition and Data Structures, IEEE 1975, 89–93
I. Hacking, "What is Logic?", The Journal of Philosophy 76, 1979, 285–318
R.Harper, F.Honsell and G.Plotkin, "A Framework for Defining Logics", Proc. 2 nd Annual Conference on Logic in Computer Science, Ithaca, NY, June 1987
S.MacLane, Categories for the Working Mathematician, Springer Verlag 1971
D. MacQueen and D. Sannella, "Completeness of Proof Systems for Equational Specifications", IEEE Transactions on Software Engineering 11, 1985, 454–461
T. Maibaum, P. Veloso and M. Sadler, "A Theory of Abstract Data Types for Program Development: Bridging the Gap?", in LNCS 186, Mathematical Foundations of Software Development, vol 2, Springer-Verlag 1985, 214–230
T. Maibaum, "Role of Abstraction in Program Development", in Information Processing 86, H.-J. Kugler (ed), North-Holand 1986, 135–142
J.Meseguer and J.Goguen, "Initiality, Induction and Computability", in Algebraic Methods in Semantics, M. Nivat and J. Reynolds (eds), Cambridge University Press 1985, 459–540
D.Pitt, S.Abramski, A.Poigné and D.Rydeheard (eds), Category Theory and Computer Programming, LNCS 240, Springer Verlag, 1986
D. Sannella and A. Tarlecki, "Specifications in an Arbitrary Institution", in LNCS 173, Proc. Int. Symposium on Semantics of Data Types, Springer-Verlag 1984, 337–356
D. Sannella and A. Tarlecki, "Toward Formal Development of Programs From Algebraic Specifications: Implementations Revisited", in LNCS 249, Proc. TAPSOFT '87, vol 1, Springer-Verlag 1987, 96–110 (an extended version will appear in Acta Informatica)
D. Scott, "Rules and Derived Rules", in Logical Theory and Semantical Analysis, S. Stenlund (ed), Reidel, Dordrecht, 1974, 147–161
A.Sernadas, J.Fiadeiro, C.Sernadas and H.-D.Ehrich, "Abstract Object Types: A Temporal Perspective", Colloquium on Temporal Logic and Specification, A.Pnueli et al (eds), Springer-Verlag 1988
A. Tarlecki, "On the Existence of Free Models in Abstract Algebraic Institutions", Theoretical Computer Science, 37(3), 1985, 269–304
A.Tarlecki, "Bits and Pieces of the Theory of Institutions", in [Pitt et al 86], 334–363
A. Tarski, "Fundamentale Begriffe der Methodologie der Deduktiven Wissenschaften" French translation in Logique, Sémantique, Métamathématique, vol 1, Armand Colin 1972, 67–116
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Fiadeiro, J., Sernadas, A. (1988). Structuring theories on consequence. In: Sannella, D., Tarlecki, A. (eds) Recent Trends in Data Type Specification. ADT 1987. Lecture Notes in Computer Science, vol 332. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50325-0_3
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DOI: https://doi.org/10.1007/3-540-50325-0_3
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