Marco Volpe

Quantum State Transformations and Branching Distributed Temporal Logic

The Distributed Temporal Logic DTL allows one to reason about temporal properties of a distributed system from the local point of view of the systems 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

Bivalent semantics, generalized compositionality and analytic classic-like tableaux for finite-valued logics

\textsf{QBDTL}

A Labeled Deduction System for the Logic UB

, a variant of DTL able to represent quantum state transformations in an abstract, qualitative way. In

Labelled natural deduction for a bundled branching temporal logic

\textsf{QBDTL}

Labeled Natural Deduction Systems for a Family of Tense Logics

, 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

A Labeled Natural Deduction System for a Fragment of CTL

\textsf{QBDTL}

Classic-Like Cut-Based Tableau Systems for Finite-Valued Logics

with a DTL-style semantics, which fits the intrinsically distributed nature of quantum computing, we formalize a labeled deduction system for

Using Interpolation for the Verification of Security Protocols

\textsf{QBDTL}

Certification of Prefixed Tableau Proofs for Modal Logic.

, 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.

On the Mosaic Method for Many-Dimensional Modal Logics: A Case Study Combining Tense and Modal Operators

The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) a mechanism for producing a classic-like description of them in terms of an effective variety of bivalent semantics; (ii) a mechanism for extracting, from the bivalent semantics so obtained, uniform (classically-labeled) cut-free standard analytic tableaux with possibly branching invertible rules and paired with proof strategies designed to guarantee termination of the associated proof procedure; (iii) a mechanism to also provide, for the same logics, uniform cut-based tableau systems with linear rules. The latter tableau systems are shown to be adequate even when restricted to analytic cuts, and they are also shown to polynomially simulate truth-tables, a feature that is not enjoyed by the former standard type of tableau systems (not even in the 2-valued case). The results are based on useful generalizations of the notions of analyticity and compositionality, and illustrate a theory that applies to many other classes of non-classical logics.