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  1. Tomasz Kowalski (2014). BCK is Not Structurally Complete. Notre Dame Journal of Formal Logic 55 (2):197-204.
    We exhibit a simple inference rule, which is admissible but not derivable in BCK, proving that BCK is not structurally complete. The argument is proof-theoretical.
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  2. Robert Goldblatt & Tomasz Kowalski (2012). The Power of a Propositional Constant. Journal of Philosophical Logic (1):1-20.
    Monomodal logic has exactly two maximally normal logics, which are also the only quasi-normal logics that are Post complete, and they are complete for validity in Kripke frames. Here we show that addition of a propositional constant to monomodal logic allows the construction of continuum many maximally normal logics that are not valid in any Kripke frame, or even in any complete modal algebra. We also construct continuum many quasi-normal Post complete logics that are not normal. The set of extensions (...)
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  3. Bakhadyr Khoussainov & Tomasz Kowalski (2012). Computable Isomorphisms of Boolean Algebras with Operators. Studia Logica 100 (3):481-496.
    In this paper we investigate computable isomorphisms of Boolean algebras with operators (BAOs). We prove that there are examples of polymodal Boolean algebras with finitely many computable isomorphism types. We provide an example of a polymodal BAO such that it has exactly one computable isomorphism type but whose expansions by a constant have more than one computable isomorphism type. We also prove a general result showing that BAOs are complete with respect to the degree spectra of structures, computable dimensions, expansions (...)
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  4. Tomasz Kowalski, Francesco Paoli & Matthew Spinks (2011). Quasi-Subtractive Varieties. Journal of Symbolic Logic 76 (4):1261-1286.
    Varieties like groups, rings, or Boolean algebras have the property that, in any of their members, the lattice of congruences is isomorphic to a lattice of more manageable objects, for example normal subgroups of groups, two-sided ideals of rings, filters (or ideals) of Boolean algebras.algebraic logic can explain these phenomena at a rather satisfactory level of generality: in every member A of a τ-regular variety the lattice of congruences of A is isomorphic to the lattice of deductive filters on (...)
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  5. Franchesco Paoli & Tomasz Kowalski (2010). On Some Properties of Quasi MV Algebras and Square Root Quasi MV Algebras. Part III. Reports on Mathematical Logic:161-199.
     
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  6. Tomasz Kowalski (2008). Self-Implications in BCI. Notre Dame Journal of Formal Logic 49 (3):295-305.
    Humberstone asks whether every theorem of BCI provably implies $\phi\to\phi$ for some formula $\phi$. Meyer conjectures that the axiom $\mathbf{B}$ does not imply any such "self-implication." We prove a slightly stronger result, thereby confirming Meyer's conjecture.
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  7. Tomasz Kowalski & John Slaney (2008). A Finite Fragment Of S3. Reports on Mathematical Logic.
    It is shown that the pure implication fragment of the modal logic [3] , pp. 385--387) has finitely many non-equivalent formulae in one variable. The exact number of such formulae is not known. We show that this finiteness result is the best possible, since the analogous fragment of S4, and therefore of [3], in two variables has infinitely many non-equivalent formulae.
     
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  8. Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski & Hiroakira Ono (2007). Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Elsevier.
    This is also where we begin investigating lattices of logics and varieties, rather than particular examples.
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  9. Tomasz Kowalski (2007). Weakly Associative Relation Algebras Hold the Key to the Universe. Bulletin of the Section of Logic 36 (3/4):145-157.
  10. Yosuke Katoh, Tomasz Kowalski & Masaki Ueda (2006). Almost Minimal Varieties Related to Fuzzy Logic. Reports on Mathematical Logic.
     
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  11. Tomasz Kowalski & Sam Butchart (2006). A Note on Monothetic BCI. Notre Dame Journal of Formal Logic 47 (4):541-544.
    In "Variations on a theme of Curry," Humberstone conjectured that a certain logic, intermediate between BCI and BCK, is none other than monothetic BCI—the smallest extension of BCI in which all theorems are provably equivalent. In this note, we present a proof of this conjecture.
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  12. Tomasz Kowalski & Marcus Kracht (2006). Semisimple Varieties of Modal Algebras. Studia Logica 83 (1-3):351 - 363.
    In this paper we show that a variety of modal algebras of finite type is semisimple iff it is discriminator iff it is both weakly transitive and cyclic. This fact has been claimed already in [4] (based on joint work by the two authors) but the proof was fatally flawed.
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  13. Tomasz Kowalski (2004). Retraction Note for "Pdl has Interpolation". Journal of Symbolic Logic 69 (3):935-935.
  14. Tomasz Kowalski (2004). Semisimplicity, EDPC and Discriminator Varieties of Residuated Lattices. Studia Logica 77 (2):255 - 265.
    We prove that all semisimple varieties of FL ew-algebras are discriminator varieties. A characterisation of discriminator and EDPC varieties of FL ew-algebras follows. It matches exactly a natural classification of logics over FL ew proposed by H. Ono.
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  15. Tomasz Kowalski (2002). PDL has Interpolation. Journal of Symbolic Logic 67 (3):933-946.
    It is proved that free dynamic algebras superamalgamate. Craig interpolation for propositional dynamic logic and superamalgamation for the variety of dynamic algebras follow.
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  16. Tomasz Kowalski (2001). Propositional Dynamic Logic has Interpolation. Bulletin of the Section of Logic 30 (1):33-39.
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  17. Marcus Kracht & Tomasz Kowalski (2001). Atomic Incompleteness or How to Kill One Bird with Two Stones. Bulletin of the Section of Logic 30 (2):71-78.
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  18. Tomasz Kowalski & Hiroakira Ono (2000). Remarks on Splittings in the Variety of Residuated Lattices. Reports on Mathematical Logic:133-140.
     
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  19. Tomasz Kowalski & Hiroakira Ono (2000). The Variety Of Residuated Lattices Is Generated By Its Finite Simple Members. Reports on Mathematical Logic:59-77.
    We show that the variety of residuated lattices is generated by its finite simple members, improving upon a finite model property result of Okada and Terui. The reasoning is a blend of proof-theoretic and algebraic arguments.
     
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  20. Tomasz Kowalski (1999). Pretabular Varieties Of Equivalential Algebras. Reports on Mathematical Logic:3-10.
    It is shown that there are precisely two pretabular varieties of equivalential algebras.
     
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  21. Tomasz Kowalski (1998). Varieties Of Tense Algebras. Reports on Mathematical Logic:53-95.
    The paper has two parts preceded by quite comprehensive preliminaries.In the first part it is shown that a subvariety of the variety ${\cal T}$ of all tense algebras is discriminator if and only if it is semisimple. The variety ${\cal T}$ turns out to be the join of an increasing chain of varieties ${\cal D}_n$, which are discriminator varieties. The argument carries over to all finite type varieties of boolean algebras with operators satisfying some term conditions. In the case of (...)
     
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  22. Tomasz Kowalski (1995). The Bottom of the Lattice of BCK-Varieties. Reports on Mathematical Logic:87-93.
     
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  23. Tomasz Kowalski (1994). A Syntactic Proof Of A Conjecture Of Andrzej Wronski. Reports on Mathematical Logic:81-86.
    A syntactic derivation of Cornish identity from the axioms of HBCK is presented which amounts to a syntactic proof of Wronski's conjecture that naturally ordered BCK-algebras form a variety.
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