28 found
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  1.  30
    Residuated Lattices: An Algebraic Glimpse at Substructural Logics.Nikolaos Galatos, Peter Jipsen, Tomasz Kowalski & Hiroakira Ono - 2007 - Elsevier.
    This is also where we begin investigating lattices of logics and varieties, rather than particular examples.
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  2.  18
    Analytic Cut and Interpolation for Bi-Intuitionistic Logic.Tomasz Kowalski & Hiroakira Ono - 2017 - Review of Symbolic Logic 10 (2):259-283.
    We prove that certain natural sequent systems for bi-intuitionistic logic have the analytic cut property. In the process we show that the (global) subformula property implies the (local) analytic cut property, thereby demonstrating their equivalence. Applying a version of Maehara technique modified in several ways, we prove that bi-intuitionistic logic enjoys the classical Craig interpolation property and Maximova variable separation property; its Halldén completeness follows.
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  3.  30
    Semisimplicity, EDPC and Discriminator Varieties of Residuated Lattices.Tomasz Kowalski - 2004 - 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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  4.  26
    Semisimple Varieties of Modal Algebras.Tomasz Kowalski & Marcus Kracht - 2006 - 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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  5. On Some Properties of Quasi MV Algebras and Square Root Quasi MV Algebras. Part III.Franchesco Paoli & Tomasz Kowalski - 2010 - Reports on Mathematical Logic:161-199.
     
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  6.  9
    Weakly Associative Relation Algebras Hold the Key to the Universe.Tomasz Kowalski - 2007 - Bulletin of the Section of Logic 36 (3/4):145-157.
  7.  8
    BCK is Not Structurally Complete.Tomasz Kowalski - 2014 - 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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  8.  27
    Quasi-Subtractive Varieties.Tomasz Kowalski, Francesco Paoli & Matthew Spinks - 2011 - 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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  9.  9
    Computable Isomorphisms of Boolean Algebras with Operators.Bakhadyr Khoussainov & Tomasz Kowalski - 2012 - 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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  10. Varieties Of Tense Algebras.Tomasz Kowalski - 1998 - 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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  11. A Syntactic Proof Of A Conjecture Of Andrzej Wronski.Tomasz Kowalski - 1994 - 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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  12.  10
    Self-Implications in BCI.Tomasz Kowalski - 2008 - 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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  13. The Variety Of Residuated Lattices Is Generated By Its Finite Simple Members.Tomasz Kowalski & Hiroakira Ono - 2000 - 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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  14. A Finite Fragment Of S3.Tomasz Kowalski & John Slaney - 2008 - 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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  15.  7
    A Note on Monothetic BCI.Tomasz Kowalski & Sam Butchart - 2006 - 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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  16.  13
    An Abelian Rule for BCI—and Variations.Tomasz Kowalski & Lloyd Humberstone - 2016 - Notre Dame Journal of Formal Logic 57 (4):551-568.
    We show the admissibility for BCI of a rule form of the characteristic implicational axiom of abelian logic, this rule taking us from →β to α. This is done in Section 8, with surrounding sections exploring the admissibility and derivability of various related rules in several extensions of BCI.
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  17.  15
    Propositional Dynamic Logic has Interpolation.Tomasz Kowalski - 2001 - Bulletin of the Section of Logic 30 (1):33-39.
  18.  16
    Atomic Incompleteness or How to Kill One Bird with Two Stones.Marcus Kracht & Tomasz Kowalski - 2001 - Bulletin of the Section of Logic 30 (2):71-78.
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  19.  28
    Retraction Note for "Pdl has Interpolation".Tomasz Kowalski - 2004 - Journal of Symbolic Logic 69 (3):935-935.
  20. The Bottom of the Lattice of BCK-Varieties.Tomasz Kowalski - 1995 - Reports on Mathematical Logic:87-93.
  21.  21
    The Power of a Propositional Constant.Robert Goldblatt & Tomasz Kowalski - 2012 - 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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  22.  19
    PDL has Interpolation.Tomasz Kowalski - 2002 - 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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  23.  2
    The Power of a Propositional Constant.Robert Goldblatt & Tomasz Kowalski - 2014 - Journal of Philosophical Logic 43 (1):133-152.
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  24. Almost Minimal Varieties Related to Fuzzy Logic.Yosuke Katoh, Tomasz Kowalski & Masaki Ueda - 2006 - Reports on Mathematical Logic.
     
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  25. Pdl Has Interpolation.Tomasz Kowalski - 2002 - Journal of Symbolic Logic 67 (3):933-946.
    It is proved that free dynamic algebras superamalgamate. Craig interpolation for proposi- tional dynamic logic and superamalgamation for the variety of dynamic algebras follow.
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  26. Pretabular Varieties Of Equivalential Algebras.Tomasz Kowalski - 1999 - Reports on Mathematical Logic:3-10.
    It is shown that there are precisely two pretabular varieties of equivalential algebras.
     
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  27. Retraction Note for “PDL has Interpolation”.Tomasz Kowalski - 2004 - Journal of Symbolic Logic 69 (3):935-935.
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  28. Remarks on Splittings in the Variety of Residuated Lattices.Tomasz Kowalski & Hiroakira Ono - 2000 - Reports on Mathematical Logic:133-140.
     
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