C. Sernadas | Universidade de Lisboa (original) (raw)

Papers by C. Sernadas

The transference of preservation results between importing (a logic combination mechanism that su... more The transference of preservation results between importing (a logic combination mechanism that subsumes several asymmetrical mechanisms for combining logics like temporalization, modalization and globalization) and unconstrained fibring is investigated. For that purpose, a new (more convenient) formulation of fibring, called biporting, is introduced. The equivalence between fibring and biporting is established by showing that satisfaction and semantic consequence are preserved. In consequence, particular cases of importing, like temporalization, modalization and globalization are shown to be subsumed by fibring. As an illustration, the preservation of the finite model property by fibring is carried over to importing and then to globalization.

Logic Journal of the IGPL, 2018

A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)comp... more A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective measurements made on a given quantum state. Simultaneous measurements are assumed to imply that the underlying observables are compatible. A sound and weakly complete axiomatization is provided relying on the decidable first-order theory of real closed ordered fields. The proposed logic is proved to be a conservative extension of classical propositional logic.

Logic Journal of the IGPL, 2017

The ambition constrained validity and the model witness problems in the logic UCL, proposed in [1... more The ambition constrained validity and the model witness problems in the logic UCL, proposed in [10], for reasoning about circuits with unreliable gates are analyzed. Moreover, two additional problems, motivated by the applications, are studied. One consists of finding bounds on the reliability rate of the gates that ensure that a given circuit has an intended success rate. The other consists of finding a reliability rate of the gates that maximizes the success rate of a given circuit. Sound and complete algorithms are developed for these problems and their computational complexity is studied.

Lecture Notes in Computer Science, 1989

The notion of abstract object type (AOT) tends to overlay the already classical concept of abstra... more The notion of abstract object type (AOT) tends to overlay the already classical concept of abstract data type (ADT) in several fields of application. Objects, although much more complex than data, have the advantage of dealing with states and processes. For that reason, they become useful, for instance, in the design of database applications and in software engineering. The difficulty lies in finding a suitable formalism for the abstract definition of objects, at least as effective as the equational formalism has been in the definition of abstract data types. The purpose of this paper is to present and discuss the main features of such a formalism. Concepts, tools and techniques are provided for the abstract definition of objects. A primitive language is presented allowing structured and rather independent definitions of object types. Each object is described as a temporal entity that evolves because of the events that happen during its life. The interaction between objects is reduced~ to event sharing. Both liveness and safety requirements can be stated and verified. Two case studies arc presented for illustrating every aspect of the approach: the stack example which is very popular in the ADT area, thus allowing the comparison between the concepts of ADT and AOT, and the well known example of the eating philosophers which allows the discussion of the dynamic aspects.

Having in mind applications to the design and verification of logic circuits, a complete extensio... more Having in mind applications to the design and verification of logic circuits, a complete extension of classical propositional logic is presented for reasoning about circuits with possibly erroneous inputs. The pitfalls of extrapolating classical reasoning to such circuits are extensively illustrated. Redundancy is shown to be effective for improving the reliability of such circuits.

Journal of Logic, Language and Information, 2003

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. ... more Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can

Lecture Notes in Computer Science, 1997

Several mechanisms for combining logics have appeared in the literature. Synchronization is one o... more Several mechanisms for combining logics have appeared in the literature. Synchronization is one of the simplest: the language of the combined logic is the disjoint union of the given languages, but the class of models of the resulting logic is a subset of the cartesian product of the given classes of models (the interaction between the two logics is imposed by constraining the class of pairs of models). Herein, we give both a model-theoretic and a proof-theoretic account of synchronization as a categorial construction (using coproducts and cocartesian liftings). We also prove that soundness is preserved by possibly constrained synchronization and state su cient conditions for preservation of model existence and strong completeness. We provide an application to the combination of dynamic logic and linear temporal logic.

Frontiers of Combining Systems, 2002

We introduce a framework for presenting non-classical logics in a modular and uniform way as labe... more We introduce a framework for presenting non-classical logics in a modular and uniform way as labelled natural deduction systems. The use of algebras of truth-values as the labelling algebras of our systems allows us to give generalized systems for multiple-valued logics. More specifically, our framework generalizes previous work where labels represent worlds in the underlying Kripke structure: since we can take multiple-valued logics as meaning not only finitely or infinitely manyvalued logics but also power-set logics, our framework allows us to present also logics such as modal, intuitionistic and relevance logics, thus providing a first step towards fibring these logics with many-valued ones. Work partially supported by Fundação para a Ciência e a Tecnologia, Portugal.

Handbook of Philosophical Logic, 2nd Edition, 2005

It is a task of philosophy to explain the sense in which contemporary science uses the label "log... more It is a task of philosophy to explain the sense in which contemporary science uses the label "logics", specially through "logics in" (natural language, program verification, machine learning, knowledge representation, abductive and inductive reasoning, etc.) as well as "logics for" (hybrid reasoning systems, ontology, engineering, reasoning about cryptographic construction, defeasible argumentation, reasoning with uncertainty, reasoning under contradiction, reasoning about action, agents with bounded rationality, and so on) and even "logics that" (that characterize classes of finite structures as in finite model theory, that characterize formal grammars, that characterize processes, etc.) The Greek term logos (and ratio in Latin) from which "logic" and "reason" derive, with its original meaning of "to put together", and later "to speak about" is suggestive: it may be relevant for such domains to start by collecting peculiar concepts and thoughts, and then recompiling them in an orderly way using logical tools so that talking and reasoning about the resulting concepts becomes something practical and effective. Whether or not such usage favours logical pluralism (in the sense that there is more than one "real logic"') or just reflects isolated parts of the conception of reason as cosmic ordering, is also a matter for philosophy, as it is also to reconcile this practice with logic regarded as an epistemological enterprise or to Kant's transcendental deduction. But what is more: the contemporary usage of the term logic specializes from the formal logic (in the sense of abiding to the criteria of concept, judgment, and inference) not only towards using symbolic logic (i.e., a development of formal logic by means of mathematical concepts), but also by means of mechanized, computer-based concepts, or in other words, by means of the algorithmic side of logic. It is natural to think that the intense use of "logics in", "logics that" and even "logics" with no specifications can be combined again by mathematical methods, realizing a certain philosophers and logicians dream to building mechanisms where several different logics could interact and cooperate, instead of clashing. In this sense the project of reducing reasoning to symbolic computation is an old one. The philosopher and mathematician Bernard Bolzano born in Prague, Bohemia was not far from proposing the

Handbook of Quantum Logic and Quantum Structures, 2009

A decidable logic extending classical reasoning and supporting quantum reasoning is presented. Th... more A decidable logic extending classical reasoning and supporting quantum reasoning is presented. The quantum logic is obtained by applying the exogenous semantics approach to propositional logic. The design is guided by the postulates of quantum mechanics and inspired by applications in quantum computation and information. The models of the quantum logic are superpositions of classical valuations. In order to achieve decidability, the superpositions are taken in inner product spaces over algebraic closures of arbitrary real closed fields.

Theoretical Computer Science, 2003

The general theory of randomly timed automata is developed: starting with the practical motivatio... more The general theory of randomly timed automata is developed: starting with the practical motivation and presentation of the envisaged notion, the categorical theory of minimization, aggregation, encapsulation, interconnection and realization of such automata is worked out. All these constructions are presented universally: minimization and realization as adjunctions, aggregation as product, interconnection as cartesian lifting, and encapsulation as co-cartesian lifting. Stochastic timed automata are shown to be a particular case of randomly timed automata. The notion of stochastic timed automaton is shown to be too restrictive to establish a self contained theory of combination and realization. Contents

Logica Universalis, 2011

Combined connectives arise in combined logics. In fibrings, such combined connectives are known a... more Combined connectives arise in combined logics. In fibrings, such combined connectives are known as shared connectives and inherit the logical properties of each component. A new way of combining connectives (and other language constructors of propositional nature) is proposed by inheriting only the common logical properties of the components. A sound and complete calculus is provided for reasoning about the latter. The calculus is shown to be a conservative extension of the original calculus. Examples are provided contributing to a better understanding of what are the common properties of any two constructors, say disjunction and conjunction.

Logic Journal of IGPL, 2007

Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formu... more Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way (e.g via Hilbert calculi). Heterogeneous fibring, allowing the original logics to have different presentations (e.g. one presented by a Hilbert calculus and the other by a sequent calculus), has been an open problem. Herein, consequence systems are shown to be a good solution for heterogeneous fibring when one of the logics is presented in a semantic way and the other by a calculus and also a solution for the heterogeneous fibring of calculi. The new notion of abstract proof system is shown to provide a better solution to heterogeneous fibring of calculi namely because derivations in the fibring keep the constructive nature of derivations in the original logics. Preservation of compactness and semi-decidability is investigated.

Journal of Logic and Computation, 2009

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving cha... more A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as an m-graph where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is an m-graph where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics, and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided.

Journal of Logic and Computation, 2009

A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, ... more A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with nondeterministic semantics, and subsume all logics endowed with an algebraic semantics.

Journal of Logic and Computation, 2002

We give a categorial characterization of how labelled deduction systems for logics with a proposi... more We give a categorial characterization of how labelled deduction systems for logics with a propositional basis behave under unconstrained fibring and under fibring that is constrained by symbol sharing. At the semantic level, we introduce a general semantics for our systems and then give a categorial characterization of fibring of models. Based on this, we establish the conditions under which our systems are sound and complete with respect to the general semantics for the corresponding logics, and establish requirements on logics and systems so that completeness is preserved by both forms of fibring.

Journal of Logic and Computation, 2012

When combining logics while imposing the sharing of connectives, the result is frequently inconsi... more When combining logics while imposing the sharing of connectives, the result is frequently inconsistent. In fact, in fibring, fusion and other forms of combination reported in the literature, each shared connective inherits the logical properties of each of its components. A new form of combining logics (meet-combination) is proposed where such a connective inherits only the common logical properties of its components. The conservative nature of the proposed combination is shown to hold without provisos. Preservation of soundness and completeness is also proved. Illustrations are provided involving classical, intuitionistic and modal logics.

Journal of Logic and Computation, 2013

A complete extension of classical propositional logic is proposed for reasoning about circuits wi... more A complete extension of classical propositional logic is proposed for reasoning about circuits with unreliable gates. The pitfalls of extrapolating classical reasoning to such unreliable circuits are extensively illustrated. Several metatheorems are shown to hold with additional provisos. Applications are provided in verification of logic circuits and improving their reliability.

Journal of Applied Non-Classical Logics, 2003

We introduce a general recipe for presenting non-classical logics in a modular and uniform way as... more We introduce a general recipe for presenting non-classical logics in a modular and uniform way as labelled deduction systems. Our recipe is based on a labelling mechanism where labels are general entities that are present, in one way or another, in all logics, namely truth-values. More specifically, the main idea underlying our approach is the use of algebras of truth-values, whose operators reflect the semantics we have in mind, as the labelling algebras of our labelled deduction systems. The "truth-values as labels" approach allows us to give generalized systems for multiplevalued logics within the same formalism: since we can take multiple-valued logics as meaning not only finitely or infinitely many-valued logics but also power-set logics, i.e. logics for which the denotation of a formula can be seen as a set of worlds, our recipe allows us to capture also logics such as modal, intuitionistic and relevance logics, thus providing a first step towards the fibring of these logics with many-valued ones.

The transference of preservation results between importing (a logic combination mechanism that su... more The transference of preservation results between importing (a logic combination mechanism that subsumes several asymmetrical mechanisms for combining logics like temporalization, modalization and globalization) and unconstrained fibring is investigated. For that purpose, a new (more convenient) formulation of fibring, called biporting, is introduced. The equivalence between fibring and biporting is established by showing that satisfaction and semantic consequence are preserved. In consequence, particular cases of importing, like temporalization, modalization and globalization are shown to be subsumed by fibring. As an illustration, the preservation of the finite model property by fibring is carried over to importing and then to globalization.

Logic Journal of the IGPL, 2018

A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)comp... more A probabilistic propositional logic, endowed with an epistemic component for asserting (non-)compatibility of diagonizable and bounded observables, is presented and illustrated for reasoning about the random results of projective measurements made on a given quantum state. Simultaneous measurements are assumed to imply that the underlying observables are compatible. A sound and weakly complete axiomatization is provided relying on the decidable first-order theory of real closed ordered fields. The proposed logic is proved to be a conservative extension of classical propositional logic.

Logic Journal of the IGPL, 2017

The ambition constrained validity and the model witness problems in the logic UCL, proposed in [1... more The ambition constrained validity and the model witness problems in the logic UCL, proposed in [10], for reasoning about circuits with unreliable gates are analyzed. Moreover, two additional problems, motivated by the applications, are studied. One consists of finding bounds on the reliability rate of the gates that ensure that a given circuit has an intended success rate. The other consists of finding a reliability rate of the gates that maximizes the success rate of a given circuit. Sound and complete algorithms are developed for these problems and their computational complexity is studied.

Lecture Notes in Computer Science, 1989

The notion of abstract object type (AOT) tends to overlay the already classical concept of abstra... more The notion of abstract object type (AOT) tends to overlay the already classical concept of abstract data type (ADT) in several fields of application. Objects, although much more complex than data, have the advantage of dealing with states and processes. For that reason, they become useful, for instance, in the design of database applications and in software engineering. The difficulty lies in finding a suitable formalism for the abstract definition of objects, at least as effective as the equational formalism has been in the definition of abstract data types. The purpose of this paper is to present and discuss the main features of such a formalism. Concepts, tools and techniques are provided for the abstract definition of objects. A primitive language is presented allowing structured and rather independent definitions of object types. Each object is described as a temporal entity that evolves because of the events that happen during its life. The interaction between objects is reduced~ to event sharing. Both liveness and safety requirements can be stated and verified. Two case studies arc presented for illustrating every aspect of the approach: the stack example which is very popular in the ADT area, thus allowing the comparison between the concepts of ADT and AOT, and the well known example of the eating philosophers which allows the discussion of the dynamic aspects.

Having in mind applications to the design and verification of logic circuits, a complete extensio... more Having in mind applications to the design and verification of logic circuits, a complete extension of classical propositional logic is presented for reasoning about circuits with possibly erroneous inputs. The pitfalls of extrapolating classical reasoning to such circuits are extensively illustrated. Redundancy is shown to be effective for improving the reliability of such circuits.

Journal of Logic, Language and Information, 2003

Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. ... more Fibring has been shown to be useful for combining logics endowed withtruth-functional semantics. However, the techniques used so far are unableto cope with fibring of logics endowed with non-truth-functional semanticsas, for example, paraconsistent logics. The first main contribution of thepaper is the development of a suitable abstract notion of logic, that mayalso encompass systems with non-truth-functional connectives, and wherefibring can

Lecture Notes in Computer Science, 1997

Several mechanisms for combining logics have appeared in the literature. Synchronization is one o... more Several mechanisms for combining logics have appeared in the literature. Synchronization is one of the simplest: the language of the combined logic is the disjoint union of the given languages, but the class of models of the resulting logic is a subset of the cartesian product of the given classes of models (the interaction between the two logics is imposed by constraining the class of pairs of models). Herein, we give both a model-theoretic and a proof-theoretic account of synchronization as a categorial construction (using coproducts and cocartesian liftings). We also prove that soundness is preserved by possibly constrained synchronization and state su cient conditions for preservation of model existence and strong completeness. We provide an application to the combination of dynamic logic and linear temporal logic.

Frontiers of Combining Systems, 2002

We introduce a framework for presenting non-classical logics in a modular and uniform way as labe... more We introduce a framework for presenting non-classical logics in a modular and uniform way as labelled natural deduction systems. The use of algebras of truth-values as the labelling algebras of our systems allows us to give generalized systems for multiple-valued logics. More specifically, our framework generalizes previous work where labels represent worlds in the underlying Kripke structure: since we can take multiple-valued logics as meaning not only finitely or infinitely manyvalued logics but also power-set logics, our framework allows us to present also logics such as modal, intuitionistic and relevance logics, thus providing a first step towards fibring these logics with many-valued ones. Work partially supported by Fundação para a Ciência e a Tecnologia, Portugal.

Handbook of Philosophical Logic, 2nd Edition, 2005

It is a task of philosophy to explain the sense in which contemporary science uses the label "log... more It is a task of philosophy to explain the sense in which contemporary science uses the label "logics", specially through "logics in" (natural language, program verification, machine learning, knowledge representation, abductive and inductive reasoning, etc.) as well as "logics for" (hybrid reasoning systems, ontology, engineering, reasoning about cryptographic construction, defeasible argumentation, reasoning with uncertainty, reasoning under contradiction, reasoning about action, agents with bounded rationality, and so on) and even "logics that" (that characterize classes of finite structures as in finite model theory, that characterize formal grammars, that characterize processes, etc.) The Greek term logos (and ratio in Latin) from which "logic" and "reason" derive, with its original meaning of "to put together", and later "to speak about" is suggestive: it may be relevant for such domains to start by collecting peculiar concepts and thoughts, and then recompiling them in an orderly way using logical tools so that talking and reasoning about the resulting concepts becomes something practical and effective. Whether or not such usage favours logical pluralism (in the sense that there is more than one "real logic"') or just reflects isolated parts of the conception of reason as cosmic ordering, is also a matter for philosophy, as it is also to reconcile this practice with logic regarded as an epistemological enterprise or to Kant's transcendental deduction. But what is more: the contemporary usage of the term logic specializes from the formal logic (in the sense of abiding to the criteria of concept, judgment, and inference) not only towards using symbolic logic (i.e., a development of formal logic by means of mathematical concepts), but also by means of mechanized, computer-based concepts, or in other words, by means of the algorithmic side of logic. It is natural to think that the intense use of "logics in", "logics that" and even "logics" with no specifications can be combined again by mathematical methods, realizing a certain philosophers and logicians dream to building mechanisms where several different logics could interact and cooperate, instead of clashing. In this sense the project of reducing reasoning to symbolic computation is an old one. The philosopher and mathematician Bernard Bolzano born in Prague, Bohemia was not far from proposing the

Handbook of Quantum Logic and Quantum Structures, 2009

A decidable logic extending classical reasoning and supporting quantum reasoning is presented. Th... more A decidable logic extending classical reasoning and supporting quantum reasoning is presented. The quantum logic is obtained by applying the exogenous semantics approach to propositional logic. The design is guided by the postulates of quantum mechanics and inspired by applications in quantum computation and information. The models of the quantum logic are superpositions of classical valuations. In order to achieve decidability, the superpositions are taken in inner product spaces over algebraic closures of arbitrary real closed fields.

Theoretical Computer Science, 2003

The general theory of randomly timed automata is developed: starting with the practical motivatio... more The general theory of randomly timed automata is developed: starting with the practical motivation and presentation of the envisaged notion, the categorical theory of minimization, aggregation, encapsulation, interconnection and realization of such automata is worked out. All these constructions are presented universally: minimization and realization as adjunctions, aggregation as product, interconnection as cartesian lifting, and encapsulation as co-cartesian lifting. Stochastic timed automata are shown to be a particular case of randomly timed automata. The notion of stochastic timed automaton is shown to be too restrictive to establish a self contained theory of combination and realization. Contents

Logica Universalis, 2011

Combined connectives arise in combined logics. In fibrings, such combined connectives are known a... more Combined connectives arise in combined logics. In fibrings, such combined connectives are known as shared connectives and inherit the logical properties of each component. A new way of combining connectives (and other language constructors of propositional nature) is proposed by inheriting only the common logical properties of the components. A sound and complete calculus is provided for reasoning about the latter. The calculus is shown to be a conservative extension of the original calculus. Examples are provided contributing to a better understanding of what are the common properties of any two constructors, say disjunction and conjunction.

Logic Journal of IGPL, 2007

Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formu... more Fibring is a meta-logical constructor that applied to two logics produces a new logic whose formulas allow the mixing of symbols. Homogeneous fibring assumes that the original logics are presented in the same way (e.g via Hilbert calculi). Heterogeneous fibring, allowing the original logics to have different presentations (e.g. one presented by a Hilbert calculus and the other by a sequent calculus), has been an open problem. Herein, consequence systems are shown to be a good solution for heterogeneous fibring when one of the logics is presented in a semantic way and the other by a calculus and also a solution for the heterogeneous fibring of calculi. The new notion of abstract proof system is shown to provide a better solution to heterogeneous fibring of calculi namely because derivations in the fibring keep the constructive nature of derivations in the original logics. Preservation of compactness and semi-decidability is investigated.

Journal of Logic and Computation, 2009

A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving cha... more A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as an m-graph where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is an m-graph where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an m-graph whose nodes are language expressions and the m-edges represent the inference rules of the two original systems. The sobriety of the approach is confirmed by proving that all the fibring notions are universal constructions. This graph-theoretic view is general enough to accommodate very different fibrings of propositional based logics encompassing logics with non-deterministic semantics, logics with an algebraic semantics, logics with partial semantics, and substructural logics, among others. Soundness and weak completeness are proved to be preserved under very general conditions. Strong completeness is also shown to be preserved under tighter conditions. In this setting, the collapsing problem appearing in several combinations of logic systems can be avoided.

Journal of Logic and Computation, 2009

A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, ... more A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the approach our results apply to very different logics encompassing, among others, substructural logics as well as logics with nondeterministic semantics, and subsume all logics endowed with an algebraic semantics.

Journal of Logic and Computation, 2002

We give a categorial characterization of how labelled deduction systems for logics with a proposi... more We give a categorial characterization of how labelled deduction systems for logics with a propositional basis behave under unconstrained fibring and under fibring that is constrained by symbol sharing. At the semantic level, we introduce a general semantics for our systems and then give a categorial characterization of fibring of models. Based on this, we establish the conditions under which our systems are sound and complete with respect to the general semantics for the corresponding logics, and establish requirements on logics and systems so that completeness is preserved by both forms of fibring.

Journal of Logic and Computation, 2012

When combining logics while imposing the sharing of connectives, the result is frequently inconsi... more When combining logics while imposing the sharing of connectives, the result is frequently inconsistent. In fact, in fibring, fusion and other forms of combination reported in the literature, each shared connective inherits the logical properties of each of its components. A new form of combining logics (meet-combination) is proposed where such a connective inherits only the common logical properties of its components. The conservative nature of the proposed combination is shown to hold without provisos. Preservation of soundness and completeness is also proved. Illustrations are provided involving classical, intuitionistic and modal logics.

Journal of Logic and Computation, 2013

A complete extension of classical propositional logic is proposed for reasoning about circuits wi... more A complete extension of classical propositional logic is proposed for reasoning about circuits with unreliable gates. The pitfalls of extrapolating classical reasoning to such unreliable circuits are extensively illustrated. Several metatheorems are shown to hold with additional provisos. Applications are provided in verification of logic circuits and improving their reliability.

Journal of Applied Non-Classical Logics, 2003

We introduce a general recipe for presenting non-classical logics in a modular and uniform way as... more We introduce a general recipe for presenting non-classical logics in a modular and uniform way as labelled deduction systems. Our recipe is based on a labelling mechanism where labels are general entities that are present, in one way or another, in all logics, namely truth-values. More specifically, the main idea underlying our approach is the use of algebras of truth-values, whose operators reflect the semantics we have in mind, as the labelling algebras of our labelled deduction systems. The "truth-values as labels" approach allows us to give generalized systems for multiplevalued logics within the same formalism: since we can take multiple-valued logics as meaning not only finitely or infinitely many-valued logics but also power-set logics, i.e. logics for which the denotation of a formula can be seen as a set of worlds, our recipe allows us to capture also logics such as modal, intuitionistic and relevance logics, thus providing a first step towards the fibring of these logics with many-valued ones.