Papers by Marco Volpe
2008 15th International Symposium on Temporal Representation and Reasoning, 2008
We give labeled natural deduction systems for a family of tense logics extending the basic linear... more We give labeled natural deduction systems for a family of tense logics extending the basic linear tense logic Kl . We prove that our systems are sound and complete with respect to the usual Kripke semantics, and that they possess a number of useful normalization properties (in particular, derivations reduce to a normal form that enjoys a subformula property). We also discuss how to extend our systems to capture richer logics like (fragments of) LTL.
The Distributed Temporal Logic DTL allows one to reason about temporal properties of a distribute... more The Distributed Temporal Logic DTL allows one to reason about temporal properties of a distributed system from the local point of view of the system’s agents, which are assumed to execute independently and to interact by means of event sharing. In this paper, we introduce the Quantum Branching Distributed Temporal Logic QBDTL , a variant of DTL able to represent quantum state transformations in an abstract, qualitative way. In QBDTL , each agent represents a distinct quantum bit (the unit of quantum information theory), which
evolves by means of quantum transformations and possibly interacts with other agents, and n-ary quantum operators act as communication/synchronization points between agents. We endow QBDTL with a DTL-style semantics, which fits the
intrinsically distributed nature of quantum computing, we formalize a labeled deduction system for QBDTL , and we prove the soundness of this deduction system with respect to the given semantics. Finally, we discuss possible extensions of our system in order to reason about entanglement phenomena.
We propose an approach for defining labeled natural deduction systems for the class of Peircean b... more We propose an approach for defining labeled natural deduction systems for the class of Peircean branching
temporal logics, seen as logics in their own right rather than as sublogics of Ockhamist systems. In particular, we give a system for the logic UB, i.e., the until-free fragment of CTL, and show that it is sound and complete. We also study normalization and discuss how derivations may reduce to a normal form using an appropriate management of proof contexts. Finally, we briefly discuss how to extend our system in order to capture full CTL.
Interpolation has been successfully applied in formal meth-
ods for model checking and test-case... more Interpolation has been successfully applied in formal meth-
ods for model checking and test-case generation for sequential programs.
Security protocols, however, exhibit such idiosyncrasies that make them unsuitable to the direct application of such methods. In this paper, we address this problem and present an interpolation-based method for security protocol verification. Our method starts from a formal protocol specification and combines Craig interpolation, symbolic execution and the standard Dolev-Yao intruder model to search for possible attacks on the protocol. Interpolants are generated as a response to search failure in order to prune possible useless traces and speed up the exploration.
We illustrate our method by means of a concrete example and discuss the results obtained by using a prototype implementation.
We present an extension of the mosaic method aimed at cap-
turing many-dimensional modal logics.... more We present an extension of the mosaic method aimed at cap-
turing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5 -like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique
not only in obtaining a proof of decidability and a proof of completeness for the corresponding Hilbert-style axiomatization, but also in the development of a mosaic-based tableau system. We further consider extensions
for dealing with the case when interactions between the two dimensions exist, thus covering a wide class of bundled Ockhamist branching-time logics, and present for them some partial results, such as a non-analytic version of the tableau system.
We give a sound and complete labelled natural deduction system for a bundled branching temporal l... more We give a sound and complete labelled natural deduction system for a bundled branching temporal logic, namely the until-free
version of BCTL* . The logic BCTL* is obtained by referring to a more general semantics than that of CTL*, where we
only require that the set of paths in a model is closed under taking suffixes (i.e. is suffix-closed) and is closed under putting
together a finite prefix of one path with the suffix of any other path beginning at the same state where the prefix ends (i.e. is
fusion-closed). In other words, this logic does not enjoy the so-called limit-closure property of the standard CTL* validity
semantics. We give both a classical and an intuitionistic version of our labelled natural deduction system for the until-free
version of BCTL*, and carry out a proof-theoretical analysis of the intuitionistic system: we prove that derivations reduce
to a normal form, which allows us to give a purely syntactical proof of consistency (for both the intuitionistic and classical
versions) of the deduction system.
A general procedure is presented for producing classic-like
cut-based tableau systems for finite... more A general procedure is presented for producing classic-like
cut-based tableau systems for finite-valued logics. In such systems, cut is the only branching rule, and formulas are accompanied by signs acting as syntactic proxies for the two classical truth-values. The systems produced are guaranteed to be sound, complete and analytic, and they are also seen to polinomially simulate the truth-table method, thus extending
the results in [6]. Lukasiewicz’s 3-valued logic is used throughout as a simple illustrative example.
We give labeled natural deduction systems for a family of tense logics extending the basic linear... more We give labeled natural deduction systems for a family of tense logics extending the basic linear tense logic Kl.
We prove that our systems are sound and complete with respect to the usual Kripke semantics, and that they possess a number of useful normalization properties (in particular, derivations reduce to a normal form that enjoys a subformula property). We also discuss how to extend our systems to capture richer logics like (fragments of) LTL.
We give a sound and complete labeled natural deduction system for an interesting fragment of CTL*... more We give a sound and complete labeled natural deduction system for an interesting fragment of CTL*, namely the until-free version of BCTL*. The logic BCTL* is obtained by referring to a more general semantics than that of CTL*, where we only require that the set of paths in a model is closed under taking suffixes (i.e. is suffix-closed) and is closed under putting together a finite prefix of one path with the suffix of any other path beginning at the same state where the prefix ends (i.e. is fusion-closed). In other words, this logic does not enjoy the so-called limit-closure property of the standard CTL* validity semantics.
Electronic Notes in Theoretical Computer Science, 2009
Until is a notoriously difficult temporal operator as it is both
existential and universal at th... more Until is a notoriously difficult temporal operator as it is both
existential and universal at the same time: AUB holds at the current time instant w iff either B holds at w or there exists a time instant w in the future at which B holds and such that A holds in all the time instants between the current one and w . This “ambivalent” nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and w . This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system for a linear-time logic endowed with the new history
operator and show that, via a proper translation, such a system is also sound and complete with respect to the linear temporal logic LTL with until.
Journal of Applied Non-classical Logics, 2010
Until is a notoriously difficult temporal operator as it is both existential and universal at the... more Until is a notoriously difficult temporal operator as it is both existential and universal at the same time: A U B holds at the current time instant w iff either B holds at w or there exists a time instant w ? in the future at which B holds and such that A holds in all the time instants between the current one and w ? . This “ambivalent” nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and w ? . This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system N(LTL ∇ ) for a linear-time logic LTL ∇ endowed with the new history operator. We show that LTL ∇ is equivalent to the linear temporal logic LTL with until, which follows by formalizing back and forth translations between the two logics. We also define an indirect translation from LTL ∇ into LTL via temporal logics with past operators; such a result
provides an upper bound to the problem of satisfiability for LTL ∇ formulas.
Thesis Chapters by Marco Volpe
Despite the great relevance of temporal logics in many applications of computer science, their th... more Despite the great relevance of temporal logics in many applications of computer science, their theoretical analysis is far from being concluded. In particular, we still lack a satisfactory proof theory for temporal logics and this is
especially true in the case of branching-time logics.
The main contribution of this thesis consists in presenting a modular approach to the definition of labeled (natural) deduction systems for a large class of temporal logics. We start by proposing a system for the minimal Priorean tense logic and show how to modularly enrich it in order to deal with more complex logics, like LTL. We also consider the extension to the branching case, focusing on the Ockhamist branching-time logics with a bundled semantics.
A detailed proof-theoretical analysis of the systems is performed. In particular, in the case of discrete-time logics, for which rules modeling an induction principle are required, we define a procedure of normalization inspired to those of systems for Heyting Arithmetic. As a consequence of normalization, we obtain a purely syntactical proof of the consistency of the systems.
Scientific Papers (Comp. Science, Math. Logic ) by Marco Volpe
In Proceedings of Wollic'14, Lecture Notes in Computer Science. In print., 2014
The Distributed Temporal Logic DTL allows one to reason about temporal properties of a distribute... more The Distributed Temporal Logic DTL allows one to reason about temporal properties of a distributed system from the local point of view of the system's agents, which are assumed to execute independently and to interact by means of event sharing. In this paper, we introduce the Quantum Branching Distributed Temporal Logic QBDTL, a variant of DTL able to represent quantum state transformations in an abstract, qualitative way. In QBDTL, each agent represents a distinct quantum bit (the unit of quantum information theory), which evolves by means of quantum transformations and possibly interacts with other agents, and n-ary quantum operators act as communication/synchronization points between agents. We endow QBDTL with a DTL-style semantics, which fits the intrinsically distributed nature of quantum computing, we formalize a labeled deduction system for QBDTL, and we prove the soundness of this deduction system with respect to the given semantics. Finally, we discuss possible extensions of our system in order to reason about entanglement phenomena.
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Papers by Marco Volpe
evolves by means of quantum transformations and possibly interacts with other agents, and n-ary quantum operators act as communication/synchronization points between agents. We endow QBDTL with a DTL-style semantics, which fits the
intrinsically distributed nature of quantum computing, we formalize a labeled deduction system for QBDTL , and we prove the soundness of this deduction system with respect to the given semantics. Finally, we discuss possible extensions of our system in order to reason about entanglement phenomena.
temporal logics, seen as logics in their own right rather than as sublogics of Ockhamist systems. In particular, we give a system for the logic UB, i.e., the until-free fragment of CTL, and show that it is sound and complete. We also study normalization and discuss how derivations may reduce to a normal form using an appropriate management of proof contexts. Finally, we briefly discuss how to extend our system in order to capture full CTL.
ods for model checking and test-case generation for sequential programs.
Security protocols, however, exhibit such idiosyncrasies that make them unsuitable to the direct application of such methods. In this paper, we address this problem and present an interpolation-based method for security protocol verification. Our method starts from a formal protocol specification and combines Craig interpolation, symbolic execution and the standard Dolev-Yao intruder model to search for possible attacks on the protocol. Interpolants are generated as a response to search failure in order to prune possible useless traces and speed up the exploration.
We illustrate our method by means of a concrete example and discuss the results obtained by using a prototype implementation.
turing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5 -like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique
not only in obtaining a proof of decidability and a proof of completeness for the corresponding Hilbert-style axiomatization, but also in the development of a mosaic-based tableau system. We further consider extensions
for dealing with the case when interactions between the two dimensions exist, thus covering a wide class of bundled Ockhamist branching-time logics, and present for them some partial results, such as a non-analytic version of the tableau system.
version of BCTL* . The logic BCTL* is obtained by referring to a more general semantics than that of CTL*, where we
only require that the set of paths in a model is closed under taking suffixes (i.e. is suffix-closed) and is closed under putting
together a finite prefix of one path with the suffix of any other path beginning at the same state where the prefix ends (i.e. is
fusion-closed). In other words, this logic does not enjoy the so-called limit-closure property of the standard CTL* validity
semantics. We give both a classical and an intuitionistic version of our labelled natural deduction system for the until-free
version of BCTL*, and carry out a proof-theoretical analysis of the intuitionistic system: we prove that derivations reduce
to a normal form, which allows us to give a purely syntactical proof of consistency (for both the intuitionistic and classical
versions) of the deduction system.
cut-based tableau systems for finite-valued logics. In such systems, cut is the only branching rule, and formulas are accompanied by signs acting as syntactic proxies for the two classical truth-values. The systems produced are guaranteed to be sound, complete and analytic, and they are also seen to polinomially simulate the truth-table method, thus extending
the results in [6]. Lukasiewicz’s 3-valued logic is used throughout as a simple illustrative example.
We prove that our systems are sound and complete with respect to the usual Kripke semantics, and that they possess a number of useful normalization properties (in particular, derivations reduce to a normal form that enjoys a subformula property). We also discuss how to extend our systems to capture richer logics like (fragments of) LTL.
existential and universal at the same time: AUB holds at the current time instant w iff either B holds at w or there exists a time instant w in the future at which B holds and such that A holds in all the time instants between the current one and w . This “ambivalent” nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and w . This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system for a linear-time logic endowed with the new history
operator and show that, via a proper translation, such a system is also sound and complete with respect to the linear temporal logic LTL with until.
provides an upper bound to the problem of satisfiability for LTL ∇ formulas.
Thesis Chapters by Marco Volpe
especially true in the case of branching-time logics.
The main contribution of this thesis consists in presenting a modular approach to the definition of labeled (natural) deduction systems for a large class of temporal logics. We start by proposing a system for the minimal Priorean tense logic and show how to modularly enrich it in order to deal with more complex logics, like LTL. We also consider the extension to the branching case, focusing on the Ockhamist branching-time logics with a bundled semantics.
A detailed proof-theoretical analysis of the systems is performed. In particular, in the case of discrete-time logics, for which rules modeling an induction principle are required, we define a procedure of normalization inspired to those of systems for Heyting Arithmetic. As a consequence of normalization, we obtain a purely syntactical proof of the consistency of the systems.
Scientific Papers (Comp. Science, Math. Logic ) by Marco Volpe
evolves by means of quantum transformations and possibly interacts with other agents, and n-ary quantum operators act as communication/synchronization points between agents. We endow QBDTL with a DTL-style semantics, which fits the
intrinsically distributed nature of quantum computing, we formalize a labeled deduction system for QBDTL , and we prove the soundness of this deduction system with respect to the given semantics. Finally, we discuss possible extensions of our system in order to reason about entanglement phenomena.
temporal logics, seen as logics in their own right rather than as sublogics of Ockhamist systems. In particular, we give a system for the logic UB, i.e., the until-free fragment of CTL, and show that it is sound and complete. We also study normalization and discuss how derivations may reduce to a normal form using an appropriate management of proof contexts. Finally, we briefly discuss how to extend our system in order to capture full CTL.
ods for model checking and test-case generation for sequential programs.
Security protocols, however, exhibit such idiosyncrasies that make them unsuitable to the direct application of such methods. In this paper, we address this problem and present an interpolation-based method for security protocol verification. Our method starts from a formal protocol specification and combines Craig interpolation, symbolic execution and the standard Dolev-Yao intruder model to search for possible attacks on the protocol. Interpolants are generated as a response to search failure in order to prune possible useless traces and speed up the exploration.
We illustrate our method by means of a concrete example and discuss the results obtained by using a prototype implementation.
turing many-dimensional modal logics. As a proof-of-concept, we define the method for logics arising from the combination of linear tense operators with an “orthogonal” S5 -like modality. We show that the existence of a model for a given set of formulas is equivalent to the existence of a suitable set of partial models, called mosaics, and apply the technique
not only in obtaining a proof of decidability and a proof of completeness for the corresponding Hilbert-style axiomatization, but also in the development of a mosaic-based tableau system. We further consider extensions
for dealing with the case when interactions between the two dimensions exist, thus covering a wide class of bundled Ockhamist branching-time logics, and present for them some partial results, such as a non-analytic version of the tableau system.
version of BCTL* . The logic BCTL* is obtained by referring to a more general semantics than that of CTL*, where we
only require that the set of paths in a model is closed under taking suffixes (i.e. is suffix-closed) and is closed under putting
together a finite prefix of one path with the suffix of any other path beginning at the same state where the prefix ends (i.e. is
fusion-closed). In other words, this logic does not enjoy the so-called limit-closure property of the standard CTL* validity
semantics. We give both a classical and an intuitionistic version of our labelled natural deduction system for the until-free
version of BCTL*, and carry out a proof-theoretical analysis of the intuitionistic system: we prove that derivations reduce
to a normal form, which allows us to give a purely syntactical proof of consistency (for both the intuitionistic and classical
versions) of the deduction system.
cut-based tableau systems for finite-valued logics. In such systems, cut is the only branching rule, and formulas are accompanied by signs acting as syntactic proxies for the two classical truth-values. The systems produced are guaranteed to be sound, complete and analytic, and they are also seen to polinomially simulate the truth-table method, thus extending
the results in [6]. Lukasiewicz’s 3-valued logic is used throughout as a simple illustrative example.
We prove that our systems are sound and complete with respect to the usual Kripke semantics, and that they possess a number of useful normalization properties (in particular, derivations reduce to a normal form that enjoys a subformula property). We also discuss how to extend our systems to capture richer logics like (fragments of) LTL.
existential and universal at the same time: AUB holds at the current time instant w iff either B holds at w or there exists a time instant w in the future at which B holds and such that A holds in all the time instants between the current one and w . This “ambivalent” nature poses a significant challenge when attempting to give deduction rules for until. In this paper, in contrast, we make explicit this duality of until by introducing a new temporal operator ∇ that allows us to formalize the “history” of until, i.e., the “internal” universal quantification over the time instants between the current one and w . This approach provides the basis for formalizing deduction systems for temporal logics endowed with the until operator. For concreteness, we give here a labeled natural deduction system for a linear-time logic endowed with the new history
operator and show that, via a proper translation, such a system is also sound and complete with respect to the linear temporal logic LTL with until.
provides an upper bound to the problem of satisfiability for LTL ∇ formulas.
especially true in the case of branching-time logics.
The main contribution of this thesis consists in presenting a modular approach to the definition of labeled (natural) deduction systems for a large class of temporal logics. We start by proposing a system for the minimal Priorean tense logic and show how to modularly enrich it in order to deal with more complex logics, like LTL. We also consider the extension to the branching case, focusing on the Ockhamist branching-time logics with a bundled semantics.
A detailed proof-theoretical analysis of the systems is performed. In particular, in the case of discrete-time logics, for which rules modeling an induction principle are required, we define a procedure of normalization inspired to those of systems for Heyting Arithmetic. As a consequence of normalization, we obtain a purely syntactical proof of the consistency of the systems.