Tomasz Kowalski | Jagiellonian University (original) (raw)

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Research paper thumbnail of Complexity and polymorphisms for digraph constraint problems under some basic constructions

The role of polymorphisms in determining the complexity of constraint satisfaction problems is we... more The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic constructions. As applications we observe a collapse in the applicability of algorithms for CSPs over directed graphs with both a total source and a total sink: the corresponding CSP is solvable by the "few subpowers algorithm" if and only if it is solvable by a local consistency check algorithm. Moreover, we find that the property of "strict width" and solvability by few subpowers are unstable under first order reductions. The analysis also yields a complete characterisation of the main polymorphism properties for digraphs whose symmetric closure is a complete graph.

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Research paper thumbnail of State Morphism MV-Algebras

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Research paper thumbnail of Digraph related constructions and the complexity of digraph homomorphism problems

ArXiv, 2013

The role of polymorphisms in determining the complexity of constraint satisfaction problems is we... more The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic constructions. As applications we prove the algebraic CSP dichotomy conjecture holds for digraphs whose symmetric closure is a complete graph, and observe a collapse in the applicability of algorithms for CSPs over directed graphs with both a total source and a total sink: the corresponding CSP is solvable by the "few subpowers algorithm" if and only if it is solvable by a local consistency check algorithm. Moreover, we find that the property of "strict width" and solvability by few subpowers are unstable under first order reductions.

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Research paper thumbnail of Coherence in Modal Logic

A variety is said to be coherent if the finitely generated subalgebras of its finitely presented ... more A variety is said to be coherent if the finitely generated subalgebras of its finitely presented members are also finitely presented. In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform deductive interpolation property for equational consequence in a variety, and a general criterion was given for the failure of coherence (and hence uniform deductive interpolation) in varieties of algebras with a term-definable semilattice reduct. In this paper, a more general criterion is obtained and used to prove the failure of coherence and uniform deductive interpolation for a broad family of modal logics, including K, KT, K4, and S4.

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Research paper thumbnail of Diassociativity is not finitely based relative to power associativity

We show that the variety of diassociative loops is not finitely based even relative to power asso... more We show that the variety of diassociative loops is not finitely based even relative to power associative loops with inverse property.

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Research paper thumbnail of Algebra Universalis Boolean-like algebras

Using Vaggione’s concept of central element in a double-pointed algebra, we introduce the notion ... more Using Vaggione’s concept of central element in a double-pointed algebra, we introduce the notion of Boolean-like variety as a generalisation of Boolean algebras to an arbitrary similarity type. Appropriately relaxing the requirement that every element be central in any member of the variety, we obtain the more general class of semi-Boolean-like varieties, which still retain many of the pleasing properties of Boolean algebras. We prove that a double-pointed variety is discriminator if and only if it is semi-Boolean-like, idempotent, and 0-regular. This theorem yields a new Maltsev-style characterisation of double-pointed discriminator varieties.

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Research paper thumbnail of Fraïssé–Hintikka theorem in institutions

Journal of Logic and Computation

We generalize the characterization of elementary equivalence by Ehrenfeucht–Fraïssé games to arbi... more We generalize the characterization of elementary equivalence by Ehrenfeucht–Fraïssé games to arbitrary institutions whose sentences are finitary. These include many-sorted first-order logic, higher-order logic with types, as well as a number of other logics arising in connection to specification languages. The gain for the classical case is that the characterization is proved directly for all signatures, including infinite ones.

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Research paper thumbnail of Varieties of semiassociative relation algebras and tense algebras

Algebra universalis

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Research paper thumbnail of Uniform Interpolation and Coherence

Annals of Pure and Applied Logic

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Research paper thumbnail of Complexity and polymorphisms for digraph constraint problems under some basic constructions

International Journal of Algebra and Computation, 2016

The role of polymorphisms in determining the complexity of constraint satisfaction problems is we... more The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context, we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic constructions. As applications we observe a collapse in the applicability of algorithms for CSPs over directed graphs with both a total source and a total sink: the corresponding CSP is solvable by the “few subpowers algorithm” if and only if it is solvable by a local consistency check algorithm. Moreover, we find that the property of “strict width” and solvability by few subpowers are unstable under first-order reductions. The analysis also yields a complete characterization of the main polymorphism properties for digraphs whose symmetric closure is a complete graph.

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Research paper thumbnail of Analytic Cut and Interpolation for Bi-Intuitionistic Logic

The Review of Symbolic Logic, 2016

We prove that certain natural sequent systems for bi-intuitionistic logic have the analytic cut p... more 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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Research paper thumbnail of CDMTCS Resear h Repor Ser Computable IsomorbleK of Boolean Algebr with Oper Bakhadyr Khoussainov

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Research paper thumbnail of The Variety of Residuated Lattices is Generated by its Finite Simple Members

Rml, 2000

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Research paper thumbnail of Varieties of Tense Algebras

Rml, 1998

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Research paper thumbnail of Pretabular Varieties of Equivalential Algebras

Rml, 1999

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Research paper thumbnail of Digraph related constructions and the complexity of digraph homomorphism problems

In this context we study the stability of CSP complexity and polymorphism properties under some b... more In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic constructions. As applications we observe a collapse in the applicability of algorithms for CSPs over directed graphs with both a total source and a total sink: the corresponding CSP is solvable by the "few subpowers algorithm" if and only if it is solvable by a local consistency check algorithm. Moreover, we find that the property of "strict width" and solvability by few subpowers are unstable under first order reductions. The analysis also yields a complete characterisation of the main polymorphism properties for digraphs whose symmetric closure is a complete graph.

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Research paper thumbnail of A Perzanowski’s hypothesis confirmed

The coincidence of J. Perzanowski’s logic of parasymmetry KP=K+L(A→LA)↔L(MA→A) and K4lb=K+(LA→LLA... more The coincidence of J. Perzanowski’s logic of parasymmetry KP=K+L(A→LA)↔L(MA→A) and K4lb=K+(LA→LLA)+L(A→LMA) is proved.

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Research paper thumbnail of Semisimple varieties of BAOs

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Research paper thumbnail of Sixth Annual Conference in Ordered Algebraic Structures

... Michael R. Darnel l-Metabelian Varieties of Lattice-Ordered Groups Costas Drossos Various ide... more ... Michael R. Darnel l-Metabelian Varieties of Lattice-Ordered Groups Costas Drossos Various ideas in MV-partitions. Manfred Droste Any group is the outer automorphism group of a simple group Nikolaos Galatos Generalized MV-algebras Javier Gómez-Pérez Order properties ...

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Research paper thumbnail of Blast 2008

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Research paper thumbnail of Complexity and polymorphisms for digraph constraint problems under some basic constructions

The role of polymorphisms in determining the complexity of constraint satisfaction problems is we... more The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic constructions. As applications we observe a collapse in the applicability of algorithms for CSPs over directed graphs with both a total source and a total sink: the corresponding CSP is solvable by the "few subpowers algorithm" if and only if it is solvable by a local consistency check algorithm. Moreover, we find that the property of "strict width" and solvability by few subpowers are unstable under first order reductions. The analysis also yields a complete characterisation of the main polymorphism properties for digraphs whose symmetric closure is a complete graph.

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Research paper thumbnail of State Morphism MV-Algebras

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Digraph related constructions and the complexity of digraph homomorphism problems

ArXiv, 2013

The role of polymorphisms in determining the complexity of constraint satisfaction problems is we... more The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic constructions. As applications we prove the algebraic CSP dichotomy conjecture holds for digraphs whose symmetric closure is a complete graph, and observe a collapse in the applicability of algorithms for CSPs over directed graphs with both a total source and a total sink: the corresponding CSP is solvable by the "few subpowers algorithm" if and only if it is solvable by a local consistency check algorithm. Moreover, we find that the property of "strict width" and solvability by few subpowers are unstable under first order reductions.

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Research paper thumbnail of Coherence in Modal Logic

A variety is said to be coherent if the finitely generated subalgebras of its finitely presented ... more A variety is said to be coherent if the finitely generated subalgebras of its finitely presented members are also finitely presented. In a recent paper by the authors it was shown that coherence forms a key ingredient of the uniform deductive interpolation property for equational consequence in a variety, and a general criterion was given for the failure of coherence (and hence uniform deductive interpolation) in varieties of algebras with a term-definable semilattice reduct. In this paper, a more general criterion is obtained and used to prove the failure of coherence and uniform deductive interpolation for a broad family of modal logics, including K, KT, K4, and S4.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Diassociativity is not finitely based relative to power associativity

We show that the variety of diassociative loops is not finitely based even relative to power asso... more We show that the variety of diassociative loops is not finitely based even relative to power associative loops with inverse property.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Algebra Universalis Boolean-like algebras

Using Vaggione’s concept of central element in a double-pointed algebra, we introduce the notion ... more Using Vaggione’s concept of central element in a double-pointed algebra, we introduce the notion of Boolean-like variety as a generalisation of Boolean algebras to an arbitrary similarity type. Appropriately relaxing the requirement that every element be central in any member of the variety, we obtain the more general class of semi-Boolean-like varieties, which still retain many of the pleasing properties of Boolean algebras. We prove that a double-pointed variety is discriminator if and only if it is semi-Boolean-like, idempotent, and 0-regular. This theorem yields a new Maltsev-style characterisation of double-pointed discriminator varieties.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Fraïssé–Hintikka theorem in institutions

Journal of Logic and Computation

We generalize the characterization of elementary equivalence by Ehrenfeucht–Fraïssé games to arbi... more We generalize the characterization of elementary equivalence by Ehrenfeucht–Fraïssé games to arbitrary institutions whose sentences are finitary. These include many-sorted first-order logic, higher-order logic with types, as well as a number of other logics arising in connection to specification languages. The gain for the classical case is that the characterization is proved directly for all signatures, including infinite ones.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Varieties of semiassociative relation algebras and tense algebras

Algebra universalis

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Uniform Interpolation and Coherence

Annals of Pure and Applied Logic

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Complexity and polymorphisms for digraph constraint problems under some basic constructions

International Journal of Algebra and Computation, 2016

The role of polymorphisms in determining the complexity of constraint satisfaction problems is we... more The role of polymorphisms in determining the complexity of constraint satisfaction problems is well established. In this context, we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic constructions. As applications we observe a collapse in the applicability of algorithms for CSPs over directed graphs with both a total source and a total sink: the corresponding CSP is solvable by the “few subpowers algorithm” if and only if it is solvable by a local consistency check algorithm. Moreover, we find that the property of “strict width” and solvability by few subpowers are unstable under first-order reductions. The analysis also yields a complete characterization of the main polymorphism properties for digraphs whose symmetric closure is a complete graph.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Analytic Cut and Interpolation for Bi-Intuitionistic Logic

The Review of Symbolic Logic, 2016

We prove that certain natural sequent systems for bi-intuitionistic logic have the analytic cut p... more 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.

Bookmarks Related papers MentionsView impact

Research paper thumbnail of CDMTCS Resear h Repor Ser Computable IsomorbleK of Boolean Algebr with Oper Bakhadyr Khoussainov

Bookmarks Related papers MentionsView impact

Research paper thumbnail of The Variety of Residuated Lattices is Generated by its Finite Simple Members

Rml, 2000

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Varieties of Tense Algebras

Rml, 1998

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Pretabular Varieties of Equivalential Algebras

Rml, 1999

Bookmarks Related papers MentionsView impact

Research paper thumbnail of Digraph related constructions and the complexity of digraph homomorphism problems

In this context we study the stability of CSP complexity and polymorphism properties under some b... more In this context we study the stability of CSP complexity and polymorphism properties under some basic graph theoretic constructions. As applications we observe a collapse in the applicability of algorithms for CSPs over directed graphs with both a total source and a total sink: the corresponding CSP is solvable by the "few subpowers algorithm" if and only if it is solvable by a local consistency check algorithm. Moreover, we find that the property of "strict width" and solvability by few subpowers are unstable under first order reductions. The analysis also yields a complete characterisation of the main polymorphism properties for digraphs whose symmetric closure is a complete graph.

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Research paper thumbnail of A Perzanowski’s hypothesis confirmed

The coincidence of J. Perzanowski’s logic of parasymmetry KP=K+L(A→LA)↔L(MA→A) and K4lb=K+(LA→LLA... more The coincidence of J. Perzanowski’s logic of parasymmetry KP=K+L(A→LA)↔L(MA→A) and K4lb=K+(LA→LLA)+L(A→LMA) is proved.

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Research paper thumbnail of Semisimple varieties of BAOs

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Research paper thumbnail of Sixth Annual Conference in Ordered Algebraic Structures

... Michael R. Darnel l-Metabelian Varieties of Lattice-Ordered Groups Costas Drossos Various ide... more ... Michael R. Darnel l-Metabelian Varieties of Lattice-Ordered Groups Costas Drossos Various ideas in MV-partitions. Manfred Droste Any group is the outer automorphism group of a simple group Nikolaos Galatos Generalized MV-algebras Javier Gómez-Pérez Order properties ...

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Research paper thumbnail of Blast 2008

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Research paper thumbnail of AN OUTLINE OF A TOPOGRAPHY OF TENSE LOGICS

My PhD Thesis. Despite the title it is about varieties of tense algebras.

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