Categorical Abstract Algebraic Logic: Local Characterization Theorems for Classes of Systems

REFERENCES

• Barr , M. , Wells , C. ( 1999 ). Category Theory for Computing Science. , 3rd ed. Montreal : Les Publications CRM .
   Google Scholar
• Blok , W. J. , Pigozzi , D. ( 1986 ). Protoalgebraic logics . Studia Logica 45 : 337 – 369 .
   Google Scholar
• Blok , W. J. , Pigozzi , D. ( 1989 ). Algebraizable logics . Memoirs of the American Mathematical Society 77 ( 396 ).
   Web of Science ®Google Scholar
• Blok , W. J. , Pigozzi , D. ( 1992 ). Algebraic semantics for universal horn logic without equality . In: Romanowska , A. , Smith , J. D. H. , eds. Universal Algebra and Quasigroup Theory . Berlin : Heldermann Verlag .
   Google Scholar
• Bloom , S. L. ( 1975 ). Some theorems on structural consequence operations . Studia Logica 34 : 1 – 9 .
   Google Scholar
• Casanovas , E. , Dellunde , P. , Jansana , R. ( 1996 ). On elementary equivalence for equality-free logic . Notre Dame Journal of Formal Logic 37 ( 3 ): 506 – 522 .
   Google Scholar
• Czelakowski , J. ( 1981 ). Equivalential logics I, II . Studia Logica 40 : 227 – 236 , 355 – 372 .
   Google Scholar
• Czelakowski , J. ( 2001 ). Protoalgebraic Logics . Dordtrecht : Kluwer Academic Publishers .
   Google Scholar
• Czelakowski , J. , Elgueta , R. ( 1999 ). Local Characterization theorems for some classes of structures . Acta Scientarium Mathematicarum 65 : 19 – 32 .
   Google Scholar
• Dellunde , P. (1999). Equality-free logic: the method of diagrams and preservation theorems. Logic Journal of the IGPL 7(6):717–732.
   Google Scholar
• Dellunde , P. ( 2000 ). On definability of the equality in classes of algebras with an equivalence relation . Studia Logica 64 : 345 – 353 .
   Google Scholar
• Dellunde , P. , Jansana , R. ( 1996 ). Some characterization theorems for infinitary universal horn logic without equality . The Journal of Symbolic Logic 61 : 1242 – 1260 .
   Google Scholar
• Elgueta , R. ( 1997 ). Characterizing classes defined without equality . Studia Logica 58 : 357 – 394 .
   Google Scholar
• Elgueta , R. ( 1998 ). Subdirect representation theory for classes without equality . Algebra Universalis 40 : 201 – 246 .
   Web of Science ®Google Scholar
• Elgueta , R. ( 1999a ). Algebraic characterizations for universal fragments of logic . Mathematical Logic Quarterly 45 : 385 – 398 .
   Google Scholar
• Elgueta , R. ( 1999b ). Freeness in classes without equality . The Journal of Symbolic Logic 64 ( 3 ): 1159 – 1194 .
   Google Scholar
• Elgueta , R. , Jansana , R. ( 1999c ). Definability of Leibniz equality . Studia Logica 63 : 223 – 243 .
   Google Scholar
• Fiadeiro , J. , Sernadas , A. ( 1988 ). Structuring theories on consequence . In: Sannella , D. , Tarlecki , A. , eds. Recent Trends in Data Type Specification . Lecture Notes in Computer Science . Vol. 332 . New York : Springer-Verlag , pp. 44 – 72 .
   Google Scholar
• Font , J. M. , Jansana , R. ( 1996 ). A General Algebraic Semantics for Sentential Logics . Lecture Notes in Logic . Vol. 7 . Berlin Heidelberg : Springer-Verlag .
   Google Scholar
• Goguen , J. A. , Burstall , R. M. ( 1984 ). Introducing institutions . In: Clarke , E. , Kozen , D. , eds. Proceedings of the Logic of Programming Workshop, Lecture Notes in Computer Science . Vol. 164 . New York : Springer-Verlag , pp. 221 – 256 .
   Google Scholar
• Goguen , J. A. , Burstall , R. M. ( 1992 ). Institutions: abstract model theory for specification and programming . Journal of the Association for Computing Machinery 39 ( 1 ): 95 – 146 .
   Web of Science ®Google Scholar
• Gorbunov , V. A. ( 1994 ). The structure of the lattice of quasivarieties . Algebra Universalis 32 : 493 – 530 .
   Google Scholar
• Gorbunov , V. A. , Tumanov , V. I. ( 1982 ). The structure of lattices of quasivarieties . In: Mathematical Logic and the Theory of Algorithms . Trudy Inst. Mat. Sib. Otd. Akad. Nauk SSSR 2 . Nauka : Novosibirsk , pp. 12 – 44 .
   Google Scholar
• Mal'cev , A. I. ( 1971 ). The Metamathematics of Algebraic Systems . Collected Papers: 1936–1937 . Studies in Logic and the Foundations of Mathematics . Vol. 66 . Amsterdam : North-Holland .
   Google Scholar
• Voutsadakis , G. Categorical abstract algebraic logic: tarski congruence systems, logical morphisms and logical quotients . Submitted to the Annals of Pure and Applied Logic , Preprint available at http://www.voutsadakis.com/RESEARCH/papers.html
   Google Scholar
• Voutsadakis , G. ( 2005a ). Categorical abstract algebraic logic: models of π-institutions . Notre Dame Journal of Formal Logic 46 ( 4 ): 439 – 460 .
   Google Scholar
• Voutsadakis , G. ( 2005b ). Categorical abstract algebraic logic: (ℐ, N)-algebraic systems . Applied Categorical Structures 13 ( 3 ): 265 – 280 .
   Web of Science ®Google Scholar
• Voutsadakis , G. ( 2006a ). Categorical abstract algebraic logic: Leibniz equality and homomorphism theorems . Applied Categorical Structures 14 ( 4 ): 357 – 376 .
   Google Scholar
• Voutsadakis , G. ( 2006b ). Categorical abstract algebraic logic: operators on classes of structure systems . Scientiae Mathematicae Japonicae 19 : 1009 – 1023 .
   Google Scholar
• Voutsadakis , G. ( 2007a ). Categorical abstract algebraic logic: prealgebraicity and protoalgebraicity . Studia Logica 85 ( 2 ): 217 – 251 .
   Google Scholar
• Voutsadakis , G. ( 2007b ). Categorical abstract algebraic logic: structure systems and {\L}o' theorem . Far East Journal of Mathematical Sciences 24 ( 1 ): 73 – 98 .
   Google Scholar
• Voutsadakis , G. ( 2007c ). Categorical abstract algebraic logic: the diagram and the reduction operator lemmas . Mathematical Logic Quarterly 53 ( 2 ): 147 – 161 .
   Google Scholar
• Communicated by I. Swanson.
   Google Scholar