Paolo Agliano - Academia.edu (original) (raw)

Papers by Paolo Agliano

Fuzzy Sets and Systems, 2022

A characterization of all the simple (in the universal algebraci sense) combinatorial inverse sem... more A characterization of all the simple (in the universal algebraci sense) combinatorial inverse semigroups, as well as of the monolith of the subdirectly irreducible ones, is obtained. Then the ideal of varieties of combinatorial inverse semigroups is studied and a theorem is proved, which states that the variety of semilattices has a unique upper cover

Varieties generated by a two-element algebra (here called two-generated varieties) have long cons... more Varieties generated by a two-element algebra (here called two-generated varieties) have long constituted a surprisingly varied source of examples of algebraic properties. In this vein, we show that they have varied congruence intersection properties as well. A classification is given. It is found that for these varieties filtrality is equivalent to congruence distributivity

"Invited Papers Logic of Proofs with Complexity Operators, S. ArtEmov and A. Chuprina Beyond... more "Invited Papers Logic of Proofs with Complexity Operators, S. ArtEmov and A. Chuprina Beyond the s-Semantics: A Theory of Observables, M. Comini and G. Levi The Logic of Commuting Equivalence Relations, D. Finberg, M. Mainetti, and G.-C. Rota Proof-Nets: The Parallel Syntax for Proof-theory, J.-Y. Girard Magari and Others on GOdel's Ontological Proof, P. Hajek Finitely Generated Magari Algebras and Arithmetic, L. Hendriks and D. de Jongh The Butterfly and the Serpent, J. Lambek Adjoints in and Among Bicategories, F. William Lawvere Exponential Algebra, A. Macintyre Categorical Equivalences for Varieties, R. McKenzie Boolean Universal Algebra, A.F. Pixley Restructuring Mathematical Logic: An Approach Based on Peirce's Pragmatism, R. Wille The Development of Research in Algebra in Italy from 1850 to 1940, G. Zappa Contributed Papers A Criterion to Decide the Semantic Match Problem, G. Aguzzi and U. Modigliani Remarks on Magari Algebras of PA and IDelta0+EXP, L. Beklemishev Undecidability in Weak Membership Theories, D. BellE and F. Parlamento Infinite Lambda-Calculus and Non-sensible Models, A. Berarducci A Computer Study of 3-Element Groupoids, J. Bremen and S.N. Burris Ideal Properties of Congruencies, I. Chajda Dualisability in General and Endodualisability in Particular, B.A. Davey Hyperordinals and Nonstandard Alpha-Models, M. Di Nasso Some Notes on Subword Quantification and Induction Thereof, F. Ferreira Research in Automated Deduction as a Basis for a Probabilistic Proof-theory, P. Forcheri, P. Gentilini, and M.T. Molfino Idempotent Simple Algebras, K. Kearnes A Revision of the Mathematical Part of Magari's Paper on "Introduction to Metamorality", R. Magari and G. Simi Some Aspects of the Categorical Semantics for the Polymorphic Lambda-Calculus, M.E. Maietti Reflection Using the Derivability Conditions, S. Matthews and A.K. Simpson Stone Bases, Alias the Constructive Content of Stone Representation, S. Negri On k-Permutability for Categories of T-Algebras, M.C. Pedicchio Weak vs. Strong Boethius' Thesis: A Problem in the Analysis of Consequential Implication, C. Pizzi A New and Elementary Method to Represent Every Complete Boolean Algebra, G. Sambin On Finite Intersections of Intermediate Predicate Logics, D. Skvortsov A Completeness Theorem for Formal Topologies, A. Valentini "

Fuzzy Sets and Systems, 2021

Fuzzy Sets and Systems, 2019

Abstract We study and characterize splitting algebras in varieties of integral residuated (semi)l... more Abstract We study and characterize splitting algebras in varieties of integral residuated (semi)lattices; the main result is a complete characterization of the splitting algebras in the variety of GBL e w -algebras, i.e. integral, bounded, commutative and divisible residuated lattices.

Fuzzy Sets and Systems, 2018

Abstract In this paper we continue our investigations on splitting algebras in varieties of resid... more Abstract In this paper we continue our investigations on splitting algebras in varieties of residuated (semi)lattices carried out in [2] and [3] ; the focus is on representable varieties of GBL-algebras, i.e. varieties generated by their totally ordered members. In this context several characterizations of splitting algebras are obtained.

Studia Logica, 2007

A continuous t-norm is a continuous map * from [0, 1] 2 into [0, 1] such that [0, 1], * , 1 is a ... more A continuous t-norm is a continuous map * from [0, 1] 2 into [0, 1] such that [0, 1], * , 1 is a commutative totally ordered monoid. Since the natural ordering on [0, 1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and [0, 1], * , →, 1 becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras [0, 1], * , →, 1 , where * is a continuous t-norm. In this paper we investigate the structure of the variety of basic hoops and some of its subvarieties. In particular we provide a complete description of the finite subdirectly irreducible basic hoops, and we show that the variety of basic hoops is generated as a quasivariety by its finite algebras. We extend these results to Hájek's BL-algebras, and we give an alternative proof of the fact that the variety of BL-algebras is generated by all algebras arising from continuous t-norms on [0, 1] and their residua. The last part of the paper is devoted to the investigation of the subreducts of BL-algebras, of Gödel algebras and of product algebras.

Semigroup Forum, 1991

The one-block property is stated and it is proved that, whenever it holds for a class closed unde... more The one-block property is stated and it is proved that, whenever it holds for a class closed under homomorphic images, it implies congruence semimodularity for the whole class. An equational characterization of regular varieties having the one-block property is obtained. Some characterization is obtained also for irregular varieties of semigroups having the one-block property.

Journal of the Australian Mathematical Society, 1989

We consider the lattice of pseudovarieties contained in a given pseudovariety P. It is shown that... more We consider the lattice of pseudovarieties contained in a given pseudovariety P. It is shown that if the lattice L of subpseudovarieties of P has finite height, then L is isomorphic to the lattice of subvarieties of a locally finite variety. Thus not every finite lattice is isomorphic to a lattice of subpseudovarieties. Moreover, the lattice of subpseudovarieties of P satisfies every positive universal sentence holding in all lattice of subvarieties of varieties V(A) ganarated by algebras A ε P.

Journal of the Australian Mathematical Society, 1999

It is shown that a variety ν has distributive congruence lattices if and only if the intersection... more It is shown that a variety ν has distributive congruence lattices if and only if the intersection of two principal congruence relations is definable by equations involving terms with parameters. The nature of the terms involved then provides a useful classification of congruence distributive varieties. In particular, the classification puts into proper perspective two stronger properties. A variety is said to have the Principal Intersection Property if the intersection of any two principal congruence relations is principal, or the Compact Intersection Property if the intersection of two compact congruence relations is compact. For non-congruence-distributive varieties, it is shown that some useful constuctions are nevertheless possible.

Journal of the Australian Mathematical Society, 2001

In this paper we investigate subtractive varieties of algebras that are congruence quasi-orderabl... more In this paper we investigate subtractive varieties of algebras that are congruence quasi-orderable. Though this concept has its origin in abstract algebraic logic, it seems to be worth investigating in a purely algebraic fashion. Besides clarifying the algebraic meaning of this notion, we obtain several structure theorems about such varieties. Also several examples are provided to illustrate the theory.

Journal of the Australian Mathematical Society, 1992

In the general context of ideals in universal algebras, we study varietal properties connected wi... more In the general context of ideals in universal algebras, we study varietal properties connected with ideals that are equivalent both to Ma'cev conditions and congruence properties such as 0-regularity, 0-permutability, etc.

Journal of Pure and Applied Algebra, 2003

... GI Zapata, Functional Analysis, Holomorphy, and Approximation Theory 84 ... Republic Wroclaw ... more ... GI Zapata, Functional Analysis, Holomorphy, and Approximation Theory 84 ... Republic Wroclaw University, Poland Universitat Hannover, Germany Universita La Sapienza, Roma, Italy ... Ralph McKenzie Giancarlo Meloni Franco Migliorini Franco Montagna Daniela Monteverdi Ugo ...

Algebra Universalis, 1997

ABSTRACT This paper deals with notions of (equational) definability of principal ideals in subtra... more ABSTRACT This paper deals with notions of (equational) definability of principal ideals in subtractive varieties. These notions are first characterized in several different ways. The strongest notion (EDPI) is then further investigated. We introduce the variety of MINI algebras (a generalization of Hilbert algebras) and we show that they are a paradigm for subtractive EDPI varieties. Finally we deal with principal ideal operations, and in particular with the cases of meet and join of principal ideals being equationally definable.

Algebra Universalis, 1997

ABSTRACT As a sequel to [2] and [15] we investigate ideal properties focusing on subtractive vari... more ABSTRACT As a sequel to [2] and [15] we investigate ideal properties focusing on subtractive varieties. Here we probe the relations between congruences and ideals in subtractive varieties, in order to give some means to recover the congruence structure from the ideal structure. To do so we consider mainly two operators from the ideal lattice to the congruence lattice of a given algebra and we classify subtractive varieties according to various properties of these operators. In the last section several examples are discussed in details.

Fuzzy Sets and Systems, 2022

A characterization of all the simple (in the universal algebraci sense) combinatorial inverse sem... more A characterization of all the simple (in the universal algebraci sense) combinatorial inverse semigroups, as well as of the monolith of the subdirectly irreducible ones, is obtained. Then the ideal of varieties of combinatorial inverse semigroups is studied and a theorem is proved, which states that the variety of semilattices has a unique upper cover

Varieties generated by a two-element algebra (here called two-generated varieties) have long cons... more Varieties generated by a two-element algebra (here called two-generated varieties) have long constituted a surprisingly varied source of examples of algebraic properties. In this vein, we show that they have varied congruence intersection properties as well. A classification is given. It is found that for these varieties filtrality is equivalent to congruence distributivity

"Invited Papers Logic of Proofs with Complexity Operators, S. ArtEmov and A. Chuprina Beyond... more "Invited Papers Logic of Proofs with Complexity Operators, S. ArtEmov and A. Chuprina Beyond the s-Semantics: A Theory of Observables, M. Comini and G. Levi The Logic of Commuting Equivalence Relations, D. Finberg, M. Mainetti, and G.-C. Rota Proof-Nets: The Parallel Syntax for Proof-theory, J.-Y. Girard Magari and Others on GOdel's Ontological Proof, P. Hajek Finitely Generated Magari Algebras and Arithmetic, L. Hendriks and D. de Jongh The Butterfly and the Serpent, J. Lambek Adjoints in and Among Bicategories, F. William Lawvere Exponential Algebra, A. Macintyre Categorical Equivalences for Varieties, R. McKenzie Boolean Universal Algebra, A.F. Pixley Restructuring Mathematical Logic: An Approach Based on Peirce's Pragmatism, R. Wille The Development of Research in Algebra in Italy from 1850 to 1940, G. Zappa Contributed Papers A Criterion to Decide the Semantic Match Problem, G. Aguzzi and U. Modigliani Remarks on Magari Algebras of PA and IDelta0+EXP, L. Beklemishev Undecidability in Weak Membership Theories, D. BellE and F. Parlamento Infinite Lambda-Calculus and Non-sensible Models, A. Berarducci A Computer Study of 3-Element Groupoids, J. Bremen and S.N. Burris Ideal Properties of Congruencies, I. Chajda Dualisability in General and Endodualisability in Particular, B.A. Davey Hyperordinals and Nonstandard Alpha-Models, M. Di Nasso Some Notes on Subword Quantification and Induction Thereof, F. Ferreira Research in Automated Deduction as a Basis for a Probabilistic Proof-theory, P. Forcheri, P. Gentilini, and M.T. Molfino Idempotent Simple Algebras, K. Kearnes A Revision of the Mathematical Part of Magari's Paper on "Introduction to Metamorality", R. Magari and G. Simi Some Aspects of the Categorical Semantics for the Polymorphic Lambda-Calculus, M.E. Maietti Reflection Using the Derivability Conditions, S. Matthews and A.K. Simpson Stone Bases, Alias the Constructive Content of Stone Representation, S. Negri On k-Permutability for Categories of T-Algebras, M.C. Pedicchio Weak vs. Strong Boethius' Thesis: A Problem in the Analysis of Consequential Implication, C. Pizzi A New and Elementary Method to Represent Every Complete Boolean Algebra, G. Sambin On Finite Intersections of Intermediate Predicate Logics, D. Skvortsov A Completeness Theorem for Formal Topologies, A. Valentini "

Fuzzy Sets and Systems, 2021

Fuzzy Sets and Systems, 2019

Abstract We study and characterize splitting algebras in varieties of integral residuated (semi)l... more Abstract We study and characterize splitting algebras in varieties of integral residuated (semi)lattices; the main result is a complete characterization of the splitting algebras in the variety of GBL e w -algebras, i.e. integral, bounded, commutative and divisible residuated lattices.

Fuzzy Sets and Systems, 2018

Abstract In this paper we continue our investigations on splitting algebras in varieties of resid... more Abstract In this paper we continue our investigations on splitting algebras in varieties of residuated (semi)lattices carried out in [2] and [3] ; the focus is on representable varieties of GBL-algebras, i.e. varieties generated by their totally ordered members. In this context several characterizations of splitting algebras are obtained.

Studia Logica, 2007

A continuous t-norm is a continuous map * from [0, 1] 2 into [0, 1] such that [0, 1], * , 1 is a ... more A continuous t-norm is a continuous map * from [0, 1] 2 into [0, 1] such that [0, 1], * , 1 is a commutative totally ordered monoid. Since the natural ordering on [0, 1] is a complete lattice ordering, each continuous t-norm induces naturally a residuation → and [0, 1], * , →, 1 becomes a commutative naturally ordered residuated monoid, also called a hoop. The variety of basic hoops is precisely the variety generated by all algebras [0, 1], * , →, 1 , where * is a continuous t-norm. In this paper we investigate the structure of the variety of basic hoops and some of its subvarieties. In particular we provide a complete description of the finite subdirectly irreducible basic hoops, and we show that the variety of basic hoops is generated as a quasivariety by its finite algebras. We extend these results to Hájek's BL-algebras, and we give an alternative proof of the fact that the variety of BL-algebras is generated by all algebras arising from continuous t-norms on [0, 1] and their residua. The last part of the paper is devoted to the investigation of the subreducts of BL-algebras, of Gödel algebras and of product algebras.

Semigroup Forum, 1991

The one-block property is stated and it is proved that, whenever it holds for a class closed unde... more The one-block property is stated and it is proved that, whenever it holds for a class closed under homomorphic images, it implies congruence semimodularity for the whole class. An equational characterization of regular varieties having the one-block property is obtained. Some characterization is obtained also for irregular varieties of semigroups having the one-block property.

Journal of the Australian Mathematical Society, 1989

We consider the lattice of pseudovarieties contained in a given pseudovariety P. It is shown that... more We consider the lattice of pseudovarieties contained in a given pseudovariety P. It is shown that if the lattice L of subpseudovarieties of P has finite height, then L is isomorphic to the lattice of subvarieties of a locally finite variety. Thus not every finite lattice is isomorphic to a lattice of subpseudovarieties. Moreover, the lattice of subpseudovarieties of P satisfies every positive universal sentence holding in all lattice of subvarieties of varieties V(A) ganarated by algebras A ε P.

Journal of the Australian Mathematical Society, 1999

It is shown that a variety ν has distributive congruence lattices if and only if the intersection... more It is shown that a variety ν has distributive congruence lattices if and only if the intersection of two principal congruence relations is definable by equations involving terms with parameters. The nature of the terms involved then provides a useful classification of congruence distributive varieties. In particular, the classification puts into proper perspective two stronger properties. A variety is said to have the Principal Intersection Property if the intersection of any two principal congruence relations is principal, or the Compact Intersection Property if the intersection of two compact congruence relations is compact. For non-congruence-distributive varieties, it is shown that some useful constuctions are nevertheless possible.

Journal of the Australian Mathematical Society, 2001

In this paper we investigate subtractive varieties of algebras that are congruence quasi-orderabl... more In this paper we investigate subtractive varieties of algebras that are congruence quasi-orderable. Though this concept has its origin in abstract algebraic logic, it seems to be worth investigating in a purely algebraic fashion. Besides clarifying the algebraic meaning of this notion, we obtain several structure theorems about such varieties. Also several examples are provided to illustrate the theory.

Journal of the Australian Mathematical Society, 1992

In the general context of ideals in universal algebras, we study varietal properties connected wi... more In the general context of ideals in universal algebras, we study varietal properties connected with ideals that are equivalent both to Ma'cev conditions and congruence properties such as 0-regularity, 0-permutability, etc.

Journal of Pure and Applied Algebra, 2003

... GI Zapata, Functional Analysis, Holomorphy, and Approximation Theory 84 ... Republic Wroclaw ... more ... GI Zapata, Functional Analysis, Holomorphy, and Approximation Theory 84 ... Republic Wroclaw University, Poland Universitat Hannover, Germany Universita La Sapienza, Roma, Italy ... Ralph McKenzie Giancarlo Meloni Franco Migliorini Franco Montagna Daniela Monteverdi Ugo ...

Algebra Universalis, 1997

ABSTRACT This paper deals with notions of (equational) definability of principal ideals in subtra... more ABSTRACT This paper deals with notions of (equational) definability of principal ideals in subtractive varieties. These notions are first characterized in several different ways. The strongest notion (EDPI) is then further investigated. We introduce the variety of MINI algebras (a generalization of Hilbert algebras) and we show that they are a paradigm for subtractive EDPI varieties. Finally we deal with principal ideal operations, and in particular with the cases of meet and join of principal ideals being equationally definable.

Algebra Universalis, 1997

ABSTRACT As a sequel to [2] and [15] we investigate ideal properties focusing on subtractive vari... more ABSTRACT As a sequel to [2] and [15] we investigate ideal properties focusing on subtractive varieties. Here we probe the relations between congruences and ideals in subtractive varieties, in order to give some means to recover the congruence structure from the ideal structure. To do so we consider mainly two operators from the ideal lattice to the congruence lattice of a given algebra and we classify subtractive varieties according to various properties of these operators. In the last section several examples are discussed in details.