ORCID Profile
0000-0003-3095-4043
Current Organisations
Jagiellonian University
,
Universidade Lusófona
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Mathematical Logic, Set Theory, Lattices and Universal Algebra | Pure Mathematics |
Publisher: Springer Science and Business Media LLC
Date: 22-09-2011
Publisher: Springer Science and Business Media LLC
Date: 06-2011
Publisher: Elsevier BV
Date: 03-2023
Publisher: Oxford University Press (OUP)
Date: 13-12-2021
Abstract: Lindström’s theorem characterizes first-order logic in terms of its essential model theoretic properties. One cannot gain expressive power extending first-order logic without losing at least one of compactness or downward Löwenheim–Skolem property. We cast this result in an abstract framework of institution theory, which does not assume any internal structure either for sentences or for models, so it is more general than the notion of abstract logic usually used in proofs of Lindström’s theorem indeed, it can be said that institutional model theory is both syntax and semantics free. Our approach takes advantage of the methods of institutional model theory to provide a structured proof of Lindström’s theorem at a level of abstraction applicable to any logical system that is strong enough to describe its own concept of isomorphism and its own concept of elementary equivalence. We apply our results to some logical systems formalized as institutions and widely used in computer science practice.
Publisher: World Scientific Pub Co Pte Lt
Date: 05-2014
DOI: 10.1142/S0218196714500179
Abstract: We generalize the notion of discriminator variety in such a way as to capture several varieties of algebras arising mainly from fuzzy logic. After investigating the extent to which this more general concept retains the basic properties of discriminator varieties, we give both an equational and a purely algebraic characterization of quasi-discriminator varieties. Finally, we completely describe the lattice of subvarieties of the pure pointed quasi-discriminator variety, providing an explicit equational base for each of its members.
Publisher: Duke University Press
Date: 07-2008
Publisher: Springer Science and Business Media LLC
Date: 06-2012
Publisher: Springer Science and Business Media LLC
Date: 12-2000
Publisher: WORLD SCIENTIFIC
Date: 24-07-2016
Publisher: Oxford University Press (OUP)
Date: 28-05-2014
Publisher: Informa UK Limited
Date: 02-03-2016
DOI: 10.1080/07315724.2015.1058198
Abstract: It is important for highly active in iduals to easily and accurately assess their hydration level. Bioelectrical impedance (BIA) can potentially meet these needs but its validity in active in iduals is not well established. We aim to validate total body water (TBW), extracellular water (ECW), and intracellular water (ICW) estimates obtained from 50 kHz BIA, bioelectrical impedance spectroscopy (BIS), and BIA-based models against dilution techniques in 2 populations: active adults and elite athletes. Active males (N = 28, 20-39 years) involved in recreational sports and elite athletes (females: N = 57, 16-35 years males: N = 127, 16-38 years) participated in this study. TBW and ECW were assessed with deuterium and bromide dilution, respectively. ICW was assessed as their difference. Body water compartments were also assessed by BIA (BIA-101), BIS (model 4200), and BIA-based equations. Small but significant differences were observed between alternative methods and the criterion in all subs les. In female athletes, r(2) > 0.69, r(2) > 0.57, and r(2) > 0.65 were observed between methods in the TBW, ECW, and ICW estimates. In males, r(2) > 0.75, r(2) > 0.65, and r(2) > 0.68 were found between alternative and reference methods in the TBW, ECW, and ICW estimates, respectively, whereas for male recreational exercisers, r(2) > 0.58, r(2) > 0.73, and r(2) > 0.75 were observed. Pure errors ranged between 0.19 to 3.32 kg for TBW, 0.64 to 1.63 for ECW, and 1.98 to 2.64 in ICW. The highest limits of agreement (LoA) were observed in Van Loan and Mayclin equation and the BIA method, respectively, for TBW and ECW assessment and the lowest LoA were observed in BIS for both TBW and ECW estimates. The higher accuracy of BIS in predicting in idual TBW, ECW, and ICW highlights its utility in water assessment of recreational and elite athletes.
Publisher: Elsevier BV
Date: 29-09-2009
Publisher: Springer Science and Business Media LLC
Date: 2000
Publisher: Oxford University Press (OUP)
Date: 03-09-2020
Abstract: 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.
Publisher: Elsevier BV
Date: 07-2019
Publisher: Springer Science and Business Media LLC
Date: 31-01-2013
Publisher: University of Chicago Press
Date: 09-1999
Publisher: Springer Science and Business Media LLC
Date: 16-12-2012
Publisher: World Scientific Pub Co Pte Lt
Date: 06-2021
DOI: 10.1142/S021819672150034X
Abstract: We study splittings or lack of them, in lattices of subvarieties of some logic-related varieties. We present a general lemma, the non-splitting lemma, which when combined with some variety-specific constructions, yields each of our negative results: the variety of commutative integral residuated lattices contains no splitting algebras, and in the varieties of double Heyting algebras, dually pseudocomplemented Heyting algebras and regular double [Formula: see text]-algebras the only splitting algebras are the two-element and three-element chains.
Publisher: Victoria University of Wellington Library
Date: 24-04-2020
Abstract: A sequent system is used to give alternative proofs of two well known properties of free lattices: Whitman’s condition and semidistributivity. It demonstrates usefulness of such proof systems outside logic.
Publisher: Elsevier BV
Date: 03-2022
Publisher: Duke University Press
Date: 10-2006
Publisher: Duke University Press
Date: 2016
Publisher: Springer Science and Business Media LLC
Date: 25-07-2013
Publisher: Cambridge University Press (CUP)
Date: 09-2002
Abstract: It is proved that free dynamic algebras superamalgamate. Craig interpolation for propositional dynamic logic and superamalgamation for the variety of dynamic algebras follow.
Publisher: Elsevier BV
Date: 11-2011
Publisher: Cambridge University Press (CUP)
Date: 09-2004
Publisher: Springer Science and Business Media LLC
Date: 02-09-2009
Publisher: Walter de Gruyter GmbH
Date: 15-05-2011
DOI: 10.2478/S12175-011-0014-5
Abstract: We show that under some conditions, imposed on coatoms and maximal idempotents of a pseudo BL-algebra, we can decompose a pseudo BL-algebra M as an ordinal sum and we show that then M is linearly ordered. We investigate pseudo BL-algebras with a unique coatom a and with a maximal idempotent, and analyze two main situations: either a n = a n+1 holds for some n ≥ 1, or a n a n+1 hold for any n ≥ 1. We note that there exist (subdirectly irreducible) algebras with two coatoms that are not linearly ordered, so the restriction to a single coatom is natural.
Publisher: Cambridge University Press (CUP)
Date: 06-12-2016
DOI: 10.1017/S175502031600040X
Abstract: 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.
Publisher: Springer Science and Business Media LLC
Date: 12-08-2015
Publisher: Springer Science and Business Media LLC
Date: 31-03-2020
Publisher: Springer Science and Business Media LLC
Date: 06-2012
Publisher: World Scientific Pub Co Pte Lt
Date: 11-2016
DOI: 10.1142/S0218196716500600
Abstract: 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.
Publisher: Springer Science and Business Media LLC
Date: 16-05-2010
Publisher: Duke University Press
Date: 2014
Publisher: Springer Science and Business Media LLC
Date: 08-07-2008
Publisher: Springer Science and Business Media LLC
Date: 13-06-2023
DOI: 10.1007/S10801-023-01251-5
Abstract: Conventional Ramsey-theoretic investigations for edge-colourings of complete graphs are framed around avoidance of certain configurations. Motivated by considerations arising in the field of Qualitative Reasoning, we explore edge colourings that in addition to forbidding certain triangle configurations also require others to be present. These conditions have natural combinatorial interest in their own right, but also correspond to qualitative representability of certain nonassociative relation algebras , which we will call chromatic .
Publisher: Springer Science and Business Media LLC
Date: 06-06-2022
Publisher: Springer Science and Business Media LLC
Date: 21-03-2014
Publisher: Elsevier BV
Date: 05-2019
Publisher: Elsevier BV
Date: 02-2010
Publisher: Cambridge University Press (CUP)
Date: 12-2011
Abstract: 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 ex le normal subgroups of groups, two-sided ideals of rings, filters (or ideals) of Boolean algebras. Abstract 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 A of the τ -assertional logic of . Moreover, if has a constant 1 in its type and is 1-subtractive, the deductive filters on A ∈ of the 1-assertional logic of coincide with the -ideals of A in the sense of Gumm and Ursini, for which we have a manageable concept of ideal generation. However, there are isomorphism theorems, for ex le, in the theories of residuated lattices, pseudointerior algebras and quasi-MV algebras that cannot be subsumed by these general results. The aim of the present paper is to appropriately generalise the concepts of subtractivity and τ -regularity in such a way as to shed some light on the deep reason behind such theorems. The tools and concepts we develop hereby provide a common umbrella for the algebraic investigation of several families of logics, including substructural logics, modal logics, quantum logics, and logics of constructive mathematics.
Publisher: Springer Science and Business Media LLC
Date: 10-2010
Publisher: Springer Science and Business Media LLC
Date: 18-06-2011
Start Date: 03-2011
End Date: 03-2015
Amount: $650,082.00
Funder: Australian Research Council
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