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  1. Kosta Došen & Zoran Petrić (2013). Syntax for Split Preorders. Annals of Pure and Applied Logic 164 (4):443-481.
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  2. Kosta Dosen & Zoran Petric (2012). Isomorphic Formulae in Classical Propositional Logic. Mathematical Logic Quarterly 58 (1):5-17.
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  3. Kosta Došen & Zoran Petrić (2009). Coherence in Linear Predicate Logic. Annals of Pure and Applied Logic 158 (1):125-153.
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  4. Kosta Došen & Zoran Petrić (2008). Equality of Proofs for Linear Equality. Archive for Mathematical Logic 47 (6):549-565.
    This paper is about equality of proofs in which a binary predicate formalizing properties of equality occurs, besides conjunction and the constant true proposition. The properties of equality in question are those of a preordering relation, those of an equivalence relation, and other properties appropriate for an equality relation in linear logic. The guiding idea is that equality of proofs is induced by coherence, understood as the existence of a faithful functor from a syntactical category into a category whose arrows (...)
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  5. Kosta Dosen, Zoran Petric & Lutz Strassburger (2008). Proof-Net Categories. Bulletin of Symbolic Logic 14 (2).
     
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  6. Kosta Došen & Zoran Petrić (2007). Medial Commutativity. Annals of Pure and Applied Logic 146 (2):237-255.
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  7. Kosta Dosen (2006). Models of Deduction. Synthese 148 (3):639 - 657.
    In standard model theory, deductions are not the things one models. But in general proof theory, in particular in categorial proof theory, one finds models of deductions, and the purpose here is to motivate a simple example of such models. This will be a model of deductions performed within an abstract context, where we do not have any particular logical constant, but something underlying all logical constants. In this context, deductions are represented by arrows in categories involved in a general (...)
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  8. Kosta Došen & Zoran Petrć (2006). Associativity as Commutativity. Journal of Symbolic Logic 71 (1):217 - 226.
    It is shown that coherence conditions for monoidal categories concerning associativity are analogous to coherence conditions for symmetric strictly monoidal categories, where associativity arrows are identities. Mac Lane's pentagonal coherence condition for associativity is decomposed into conditions concerning commutativity, among which we have a condition analogous to naturality and a degenerate case of Mac Lane's hexagonal condition for commutativity. This decomposition is analogous to the derivation of the Yang-Baxter equation from Mac Lane's hexagon and the naturality of commutativity. The pentagon (...)
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  9. Kosta Došen & Zoran Petrić (2006). Coherence for Star-Autonomous Categories. Annals of Pure and Applied Logic 141 (1):225-242.
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  10. Lev D. Beklemishev, Stephen Cook, Olivier Lessmann, Simon Thomas, Jeremy Avigad, Arnold Beckmann, Tim Carlson, Robert L. Constable & Kosta Došen (2003). 2002 European Summer Meeting of the Association for Symbolic Logic Logic Colloquium'02. Bulletin of Symbolic Logic 9 (1):71.
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  11. Kosta Došen (2003). Identity of Proofs Based on Normalization and Generality. Bulletin of Symbolic Logic 9 (4):477-503.
    Some thirty years ago, two proposals were made concerning criteria for identity of proofs. Prawitz proposed to analyze identity of proofs in terms of the equivalence relation based on reduction to normal form in natural deduction. Lambek worked on a normalization proposal analogous to Prawitz's, based on reduction to cut-free form in sequent systems, but he also suggested understanding identity of proofs in terms of an equivalence relation based on generality, two derivations having the same generality if after generalizing maximally (...)
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  12. Kosta Došen & Zoran Petrić (2003). Generality of Proofs and its Brauerian Representation. Journal of Symbolic Logic 68 (3):740-750.
    The generality of a derivation is an equivalence relation on the set of occurrences of variables in its premises and conclusion such that two occurrences of the same variable are in this relation if and only if they must remain occurrences of the same variable in every generalization of the derivation. The variables in question are propositional or of another type. A generalization of the derivation consists in diversifying variables without changing the rules of inference. This paper examines in the (...)
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  13. Kosta Došen & Zoran Petrić (2002). Bicartesian Coherence. Studia Logica 71 (3):331 - 353.
    Coherence is demonstrated for categories with binary products and sums, but without the terminal and the initial object, and without distribution. This coherence amounts to the existence of a faithful functor from a free category with binary products and sums to the category of relations on finite ordinals. This result is obtained with the help of proof-theoretic normalizing techniques. When the terminal object is present, coherence may still be proved if of binary sums we keep just their bifunctorial properties. It (...)
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  14. Kosta Došen (2001). Restall Greg. An Introduction to Substructural Logics. Routledge, London and New York 2000, Xiv+ 381 Pp. [REVIEW] Bulletin of Symbolic Logic 7 (4):527-530.
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  15. Kosta Dosen (2001). Review: Greg Restall, An Introduction to Substructural Logics. [REVIEW] Bulletin of Symbolic Logic 7 (4):527-530.
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  16. Kosta Došen (1999). Cut Elimination in Adjuncion. Bulletin of the Section of Logic 28 (2):61-73.
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  17. Kosta Došen & Zoran Petrić (1999). Cartesian Isomorphisms Are Symmetric Monoidal: A Justification of Linear Logic. Journal of Symbolic Logic 64 (1):227-242.
    It is proved that all the isomorphisms in the cartesian category freely generated by a set of objects (i.e., a graph without arrows) can be written in terms of arrows from the symmetric monoidal category freely generated by the same set of objects. This proof yields an algorithm for deciding whether an arrow in this free cartesian category is an isomorphism.
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  18. Kosta Došen (1996). Deductive Completeness. Bulletin of Symbolic Logic 2 (3):243-283.
    This is an exposition of Lambek's strengthening and generalization of the deduction theorem in categories related to intuitionistic propositional logic. Essential notions of category theory are introduced so as to yield a simple reformulation of Lambek's Functional Completeness Theorem, from which its main consequences can be readily drawn. The connections of the theorem with combinatory logic, and with modal and substructural logics, are briefly considered at the end.
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  19. Kosta Dosen & Zoran Petric (1996). Modal Functional Completeness. In H. Wansing (ed.), Proof Theory of Modal Logic. Kluwer.
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  20. Kosta Došen (1993). Rudimentary Kripke Models for the Intuitionistic Propositional Calculus. Annals of Pure and Applied Logic 62 (1):21-49.
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  21. Kosta Došen (1992). A Brief Survey of Frames for the Lambek Calculus. Mathematical Logic Quarterly 38 (1):179-187.
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  22. Kosta Došen (1992). Modal Logic as Metalogic. Journal of Logic, Language and Information 1 (3):173-201.
    The goal of this paper is to show how modal logic may be conceived as recording the derived rules of a logical system in the system itself. This conception of modal logic was propounded by Dana Scott in the early seventies. Here, similar ideas are pursued in a context less classical than Scott's.First a family of propositional logical systems is considered, which is obtained by gradually adding structural rules to a variant of the nonassociative Lambek calculus. In this family one (...)
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  23. Kosta Došen (1992). Modal Translations in Substructural Logics. Journal of Philosophical Logic 21 (3):283 - 336.
    Substructural logics are logics obtained from a sequent formulation of intuitionistic or classical logic by rejecting some structural rules. The substructural logics considered here are linear logic, relevant logic and BCK logic. It is proved that first-order variants of these logics with an intuitionistic negation can be embedded by modal translations into S4-type extensions of these logics with a classical, involutive, negation. Related embeddings via translations like the double-negation translation are also considered. Embeddings into analogues of S4 are obtained with (...)
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  24. Kosta Došen (1992). The First Axiomatization of Relevant Logic. Journal of Philosophical Logic 21 (4):339 - 356.
    This is a review, with historical and critical comments, of a paper by I. E. Orlov from 1928, which gives the oldest known axiomatization of the implication-negation fragment of the relevant logic R. Orlov's paper also foreshadows the modal translation of systems with an intuitionistic negation into S4-type extensions of systems with a classical, involutive, negation. Orlov introduces the modal postulates of S4 before Becker, Lewis and Gödel. Orlov's work, which seems to be nearly completely ignored, is related to the (...)
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  25. Kosta Došen (1991). Ancestral Kripke Models and Nonhereditary Kripke Models for the Heyting Propositional Calculus. Notre Dame Journal of Formal Logic 32 (4):580-597.
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  26. Kosta Došen (1990). Addenda and Corrigenda to "Sequent-Systems and Groupoid Models". Studia Logica 49 (4):614 -.
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  27. Kosta Došen (1989). Duality Between Modal Algebras and Neighbourhood Frames. Studia Logica 48 (2):219 - 234.
    This paper presents duality results between categories of neighbourhood frames for modal logic and categories of modal algebras (i.e. Boolean algebras with an additional unary operation). These results extend results of Goldblatt and Thomason about categories of relational frames for modal logic.
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  28. Kosta Došen (1989). Sequent-Systems and Groupoid Models. II. Studia Logica 48 (1):41 - 65.
    The purpose of this paper is to connect the proof theory and the model theory of a family of prepositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related to BCK algebras, and, finally, Johansson's and Heyting's logic. First, sequent-systems are given for these logics, and cut-elimination results are proved. In these sequent-systems the rules for the logical operations are never changed: all changes are made in the (...)
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  29. Kosta Došen (1989). Logical Constants as Punctuation Marks. Notre Dame Journal of Formal Logic 30 (3):362-381.
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  30. Kosta Došen (1988). Sequent-Systems and Groupoid Models. I. Studia Logica 47 (4):353 - 385.
    The purpose of this paper is to connect the proof theory and the model theory of a family of propositional logics weaker than Heyting's. This family includes systems analogous to the Lambek calculus of syntactic categories, systems of relevant logic, systems related toBCK algebras, and, finally, Johansson's and Heyting's logic. First, sequent-systems are given for these logics, and cut-elimination results are proved. In these sequent-systems the rules for the logical operations are never changed: all changes are made in the structural (...)
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  31. Kosta Došen & Peter Schroeder-Heister (1988). Uniqueness, Definability and Interpolation. Journal of Symbolic Logic 53 (2):554-570.
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  32. Kosta Došen (1987). A Note on Gentzen's Decision Procedure for Intuitionistic Propositional Logic. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 33 (5):453-456.
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  33. Kosta Došen (1985). A Completeness Theorem for the Lambek Calculus of Syntactic Categories. Mathematical Logic Quarterly 31 (14‐18):235-241.
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  34. Kosta Došen (1985). Models for Stronger Normal Intuitionistic Modal Logics. Studia Logica 44 (1):39 - 70.
    This paper, a sequel to Models for normal intuitionistic modal logics by M. Boi and the author, which dealt with intuitionistic analogues of the modal system K, deals similarly with intuitionistic analogues of systems stronger than K, and, in particular, analogues of S4 and S5. For these prepositional logics Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given, and soundness and completeness are proved with respect to these models. It is shown how the holding of (...)
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  35. Kosta Došen (1985). Sequent-Systems for Modal Logic. Journal of Symbolic Logic 50 (1):149-168.
    The purpose of this work is to present Gentzen-style formulations of S5 and S4 based on sequents of higher levels. Sequents of level 1 are like ordinary sequents, sequents of level 1 have collections of sequents of level 1 on the left and right of the turnstile, etc. Rules for modal constants involve sequents of level 2, whereas rules for customary logical constants of first-order logic with identity involve only sequents of level 1. A restriction on Thinning on the right (...)
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  36. Kosta Došen (1985). An Intuitionistic Sheffer Function. Notre Dame Journal of Formal Logic 26 (4):479-482.
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  37. Milan Božić & Kosta Došen (1984). Models for Normal Intuitionistic Modal Logics. Studia Logica 43 (3):217 - 245.
    Kripke-style models with two accessibility relations, one intuitionistic and the other modal, are given for analogues of the modal systemK based on Heyting's prepositional logic. It is shown that these two relations can combine with each other in various ways. Soundness and completeness are proved for systems with only the necessity operator, or only the possibility operator, or both. Embeddings in modal systems with several modal operators, based on classical propositional logic, are also considered. This paper lays the ground for (...)
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  38. Milan Bozic & Kosta Došen (1983). Axiomatizations of Intuitionistic Double Negation. Bulletin of the Section of Logic 12 (2):99-102.
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  39. Kosta Došen (1981). A Reduction of Classical Propositional Logic to the Conjunction-Negation Fragment of an Intuitionistic Relevant Logic. Journal of Philosophical Logic 10 (4):399 - 408.
  40. Kosta Došen (1978). A Note on the Law of Identity and the Converse Parry Property. Notre Dame Journal of Formal Logic 19 (1):174-176.
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