D. Pigozzi | Iowa State University (original) (raw)
Papers by D. Pigozzi
A model theory for correct behavioral subtyping for abstract data types with immutable objects is... more A model theory for correct behavioral subtyping for abstract data types with immutable objects is developed within the framework of the behavior-realization adjunction. To allow for incomplete speci cations, proofs of correct behavioral subtyping are based on comparison to one of several paradigmatic models. For specications that are not term-generated, these results are the rst complete algebraic characterizations of behavioral subtyping.
A model theory for correct behavioral subtyping for abstract data types with immutable objects is... more A model theory for correct behavioral subtyping for abstract data types with immutable objects is developed within the framework of the behavior-realization adjunction. To allow for incomplete speci cations, proofs of correct behavioral subtyping are based on comparison to one of several paradigmatic models. For specications that are not term-generated, these results are the rst complete algebraic characterizations of behavioral subtyping.
Algebra Universalis, 2000
Recent studies of the algebraic properties of bilattices have provided insight into their interna... more Recent studies of the algebraic properties of bilattices have provided insight into their internal structures, and have led to practical results, especially in reducing the computational complexity of bilattice-based multi-valued logic programs. In this paper the representation theorem for interlaced bilattices with negation found in 18] and extended to arbitrary interlaced bilattices without negation in 2] is presented. A natural equivalence is then established between the category of interlaced bilattices and the cartesian square of the category of bounded lattices. As a consequence a dual natural equivalence is obtained between the category of distributive bilattices and the coproduct of the category of bounded Priestley spaces with itself. Some applications of these equivalences are given. The subdirectly irreducible interlaced bilattices are characterized in terms of subdirectly irreducible lattices. A known characterization of the join-irreducible elements of the \knowledge" lattice of an interlaced bilattice is used to establish a natural equivalence between the category of nite, distributive bilattices and the category of posets of the form P ? Q:
Studia Logica - An International Journal for Symbolic Logic, 2003
An in nite sequence = h n(x0; : : : ; xn?1; y; u) : n <
Studia Logica - An International Journal for Symbolic Logic, 2006
In this paper we consider the structure of the class FGModS of full generalized models of a deduc... more In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACSs A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these structures with tipically logical properties of the sentential logic S. The main algebraic properties we consider are the closure of FGModS under substructures and under reduced products, and the property that for any A the lattice FACSs A is a complete sublattice of the lattice of all algebraic closed-set systems over A. The logical properties are the existence of a fully adequate Gentzen system for S, the Local Deduction Theorem and the Deduction Theorem for S. Some of the results are established for arbitrary deductive systems, while some are found to hold only for deductive systems in more restricted classes like the protoalgebraic or the weakly algebraizable ones. The paper ends with a section on examples and counterexamples.
Reports on Mathematical Logic, 2001
An in nite sequence = h n(x0; : : : ; xn?1; y; u) : n <
Studia Logica - An International Journal for Symbolic Logic, 2009
A definition and some inaccurate cross-references in the paper A Survey of Abstract Algebraic Log... more A definition and some inaccurate cross-references in the paper A Survey of Abstract Algebraic Logic, which might confuse some readers, are clarified and corrected; a short discussion of the main one is included. We also update a dozen of bibliographic references.
Studia Logica - An International Journal for Symbolic Logic, 2003
data types, classes and objects; F.3.1 [Logics and Meanings of Programs] Specifying and Verifying... more data types, classes and objects; F.3.1 [Logics and Meanings of Programs] Specifying and Verifying and Reasoning about Programs | Logics of programs, speci - cation techniques; F.3.2 [Logics and Meanings of Programs] Semantics of Programming Languages | algebraic approaches to semantics; F.3.3 [Logics and Meanings of Programs] Studies of Program Constructs | object-oriented constructs; F.4.1 [Mathematical Logic and Formal Languages] Mathematical Logic | proof theory, model theory.
The Journal of Symbolic Logic, 1988
Mathematical Structures in Computer Science, 2007
Object oriented (OO) programming techniques can be applied to equational specification logics by ... more Object oriented (OO) programming techniques can be applied to equational specification logics by distinguishing visible data from hidden data (i.e., by distinguishing the output of methods from the objects to which the methods apply), and then focusing on the behavioral equivalence of hidden data in the sense introduced by H. Reichel in 1984. Equational specification logics structured in this way are called hidden equational logics, HEL's. The central problem is how to extend the specification of a given HEL to a specification of behavioral equivalence in a computationally effective way. S. Buss and G. Roşu showed in 2000 that this is not possible in general, but much work has been done on the partial specification of behavioral equivalence for a wide class of HEL's. The OO connection suggests the use of coalgebraic methods, and J. Goguen and his collaborators have developed coinductive processes that depend on an appropriate choice of a cobasis, a special set of contexts that generates a subset of the behavioral equivalence relation. In this paper the theoretical aspects of coinduction are investigated, specifically its role as a supplement to standard equational logic for determining behavioral equivalence. Various forms of coinduction are explored. A simple characterization is given of those HEL's that are behaviorally specifiable. Those sets of conditional equations that constitute a complete, finite cobasis for a HEL are characterized in terms of the HEL's specification. Behavioral equivalence, in the form of logical equivalence, is also an important concept for single-sorted logics, e.g., sentential logics such as the classical propositional logic. The paper is an application of the methods of the extensive work that has been done in this area to HEL's, and to a broader class of logics that encompasses both sentential logics and HEL's.
MEMOIRS of the American Mathematical Society SUBMISSION. This journal is designed particularly fo... more MEMOIRS of the American Mathematical Society SUBMISSION. This journal is designed particularly for long research papers (and groups of cognate papers) in pure and applied mathematics. The papers, in general, are longer than those in the TRANSACTIONS of the American ...
Reports on Mathematical Logic
An in nite sequence = h n(x0; : : : ; xn?1; y; u) : n <
A model theory for correct behavioral subtyping for abstract data types with immutable objects is... more A model theory for correct behavioral subtyping for abstract data types with immutable objects is developed within the framework of the behavior-realization adjunction. To allow for incomplete speci cations, proofs of correct behavioral subtyping are based on comparison to one of several paradigmatic models. For specications that are not term-generated, these results are the rst complete algebraic characterizations of behavioral subtyping.
A model theory for correct behavioral subtyping for abstract data types with immutable objects is... more A model theory for correct behavioral subtyping for abstract data types with immutable objects is developed within the framework of the behavior-realization adjunction. To allow for incomplete speci cations, proofs of correct behavioral subtyping are based on comparison to one of several paradigmatic models. For specications that are not term-generated, these results are the rst complete algebraic characterizations of behavioral subtyping.
Algebra Universalis, 2000
Recent studies of the algebraic properties of bilattices have provided insight into their interna... more Recent studies of the algebraic properties of bilattices have provided insight into their internal structures, and have led to practical results, especially in reducing the computational complexity of bilattice-based multi-valued logic programs. In this paper the representation theorem for interlaced bilattices with negation found in 18] and extended to arbitrary interlaced bilattices without negation in 2] is presented. A natural equivalence is then established between the category of interlaced bilattices and the cartesian square of the category of bounded lattices. As a consequence a dual natural equivalence is obtained between the category of distributive bilattices and the coproduct of the category of bounded Priestley spaces with itself. Some applications of these equivalences are given. The subdirectly irreducible interlaced bilattices are characterized in terms of subdirectly irreducible lattices. A known characterization of the join-irreducible elements of the \knowledge" lattice of an interlaced bilattice is used to establish a natural equivalence between the category of nite, distributive bilattices and the category of posets of the form P ? Q:
Studia Logica - An International Journal for Symbolic Logic, 2003
An in nite sequence = h n(x0; : : : ; xn?1; y; u) : n <
Studia Logica - An International Journal for Symbolic Logic, 2006
In this paper we consider the structure of the class FGModS of full generalized models of a deduc... more In this paper we consider the structure of the class FGModS of full generalized models of a deductive system S from a universal-algebraic point of view, and the structure of the set of all the full generalized models of S on a fixed algebra A from the lattice-theoretical point of view; this set is represented by the lattice FACSs A of all algebraic closed-set systems C on A such that (A, C) ε FGModS. We relate some properties of these structures with tipically logical properties of the sentential logic S. The main algebraic properties we consider are the closure of FGModS under substructures and under reduced products, and the property that for any A the lattice FACSs A is a complete sublattice of the lattice of all algebraic closed-set systems over A. The logical properties are the existence of a fully adequate Gentzen system for S, the Local Deduction Theorem and the Deduction Theorem for S. Some of the results are established for arbitrary deductive systems, while some are found to hold only for deductive systems in more restricted classes like the protoalgebraic or the weakly algebraizable ones. The paper ends with a section on examples and counterexamples.
Reports on Mathematical Logic, 2001
An in nite sequence = h n(x0; : : : ; xn?1; y; u) : n <
Studia Logica - An International Journal for Symbolic Logic, 2009
A definition and some inaccurate cross-references in the paper A Survey of Abstract Algebraic Log... more A definition and some inaccurate cross-references in the paper A Survey of Abstract Algebraic Logic, which might confuse some readers, are clarified and corrected; a short discussion of the main one is included. We also update a dozen of bibliographic references.
Studia Logica - An International Journal for Symbolic Logic, 2003
data types, classes and objects; F.3.1 [Logics and Meanings of Programs] Specifying and Verifying... more data types, classes and objects; F.3.1 [Logics and Meanings of Programs] Specifying and Verifying and Reasoning about Programs | Logics of programs, speci - cation techniques; F.3.2 [Logics and Meanings of Programs] Semantics of Programming Languages | algebraic approaches to semantics; F.3.3 [Logics and Meanings of Programs] Studies of Program Constructs | object-oriented constructs; F.4.1 [Mathematical Logic and Formal Languages] Mathematical Logic | proof theory, model theory.
The Journal of Symbolic Logic, 1988
Mathematical Structures in Computer Science, 2007
Object oriented (OO) programming techniques can be applied to equational specification logics by ... more Object oriented (OO) programming techniques can be applied to equational specification logics by distinguishing visible data from hidden data (i.e., by distinguishing the output of methods from the objects to which the methods apply), and then focusing on the behavioral equivalence of hidden data in the sense introduced by H. Reichel in 1984. Equational specification logics structured in this way are called hidden equational logics, HEL's. The central problem is how to extend the specification of a given HEL to a specification of behavioral equivalence in a computationally effective way. S. Buss and G. Roşu showed in 2000 that this is not possible in general, but much work has been done on the partial specification of behavioral equivalence for a wide class of HEL's. The OO connection suggests the use of coalgebraic methods, and J. Goguen and his collaborators have developed coinductive processes that depend on an appropriate choice of a cobasis, a special set of contexts that generates a subset of the behavioral equivalence relation. In this paper the theoretical aspects of coinduction are investigated, specifically its role as a supplement to standard equational logic for determining behavioral equivalence. Various forms of coinduction are explored. A simple characterization is given of those HEL's that are behaviorally specifiable. Those sets of conditional equations that constitute a complete, finite cobasis for a HEL are characterized in terms of the HEL's specification. Behavioral equivalence, in the form of logical equivalence, is also an important concept for single-sorted logics, e.g., sentential logics such as the classical propositional logic. The paper is an application of the methods of the extensive work that has been done in this area to HEL's, and to a broader class of logics that encompasses both sentential logics and HEL's.
MEMOIRS of the American Mathematical Society SUBMISSION. This journal is designed particularly fo... more MEMOIRS of the American Mathematical Society SUBMISSION. This journal is designed particularly for long research papers (and groups of cognate papers) in pure and applied mathematics. The papers, in general, are longer than those in the TRANSACTIONS of the American ...
Reports on Mathematical Logic
An in nite sequence = h n(x0; : : : ; xn?1; y; u) : n <