
166Entanglement as a semantic resourceFoundations of Physics 40 (910): 14941518. 2010.The characteristic holistic features of the quantum theoretic formalism and the intriguing notion of entanglement can be applied to a field that is far from microphysics: logical semantics. Quantum computational logics are new forms of quantum logic that have been suggested by the theory of quantum logical gates in quantum computation. In the standard semantics of these logics, sentences denote quantum information quantities: systems of qubits (quregisters) or, more generally, mixtures of quregi…Read more

73MVAlgebras and Quantum ComputationStudia Logica 82 (2): 245270. 2006.We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasiMV algebras, we show that every quasiMV algebra is embeddable into the direct product of an MV algebra and a “flat” quasiMV algebra, and prove a completeness result w.r.t. a standard quasiMV algebra over the complex numbers.

71Expanding QuasiMV Algebras by a Quantum OperatorStudia Logica 87 (1): 99128. 2007.We investigate an expansion of quasiMV algebras ([10]) by a genuine quantum unary operator. The variety of such quasiMV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasiMV algebras generate ,we prove a standard completeness theorem for w.r.t. an algebra over the complex numbers.

36The ToffoliHadamard Gate System: an Algebraic ApproachJournal of Philosophical Logic 42 (3): 467481. 2013.Shi and Aharonov have shown that the Toffoli gate and the Hadamard gate give rise to an approximately universal set of quantum computational gates. The basic algebraic properties of this system have been studied in Dalla Chiara et al. (Foundations of Physics 39(6):559–572, 2009), where we have introduced the notion of ShiAharonov quantum computational structure. In this paper we propose an algebraic abstraction from the Hilbertspace quantum computational structures, by introducing the notion o…Read more

33The algebraic structure of an approximately universal system of quantum computational gatesFoundations of Physics 39 (6): 559572. 2009.

32On Certain Quasivarieties of QuasiMV AlgebrasStudia Logica 98 (12): 149174. 2011.QuasiMV algebras are generalisations of MV algebras arising in quantum computational logic. Although a reasonably complete description of the lattice of subvarieties of quasiMV algebras has already been provided, the problem of extending this description to the setting of quasivarieties has so far remained open. Given its apparent logical repercussions, we tackle the issue in the present paper. We especially focus on quasivarieties whose generators either are subalgebras of the standard square…Read more

29The Lattice of Subvarieties of $${\sqrt{\prime}}$$ quasiMV AlgebrasStudia Logica 95 (12): 3761. 2010.In the present paper we continue the investigation of the lattice of subvarieties of the variety of ${\sqrt{\prime}}$ quasiMV algebras, already started in [6]. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a longstanding open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra D r is not finitely based, and we provide an infinite equational basis for the same variety

16A New View of Effects in a Hilbert SpaceStudia Logica 104 (6): 11451177. 2016.We investigate certain BrouwerZadeh lattices that serve as abstract counterparts of lattices of effects in Hilbert spaces under the spectral ordering. These algebras, called PBZ*lattices, can also be seen as generalisations of orthomodular lattices and are remarkable for the collapse of three notions of “sharpness” that are distinct in general BrouwerZadeh lattices. We investigate the structure theory of PBZ*lattices and their reducts; in particular, we prove some embedding results for PBZ*…Read more

14Algebraic Analysis of Demodalised Analytic ImplicationJournal of Philosophical Logic 48 (6): 957979. 2019.The logic DAI of demodalised analytic implication has been introduced by J.M. Dunn as a variation on a timehonoured logical system by C.I. Lewis’ student W.T. Parry. The main tenet underlying this logic is that no implication can be valid unless its consequent is “analytically contained” in its antecedent. DAI has been investigated both prooftheoretically and modeltheoretically, but no study so far has focussed on DAI from the viewpoint of abstract algebraic logic. We provide several differen…Read more

13StoneType Representations and Dualities for Varieties of BisemilatticesStudia Logica 106 (2): 417448. 2018.In this article we will focus our attention on the variety of distributive bisemilattices and some linguistic expansions thereof: bounded, De Morgan, and involutive bisemilattices. After extending Balbes’ representation theorem to bounded, De Morgan, and involutive bisemilattices, we make use of Hartonas–Dunn duality and introduce the categories of 2spaces and 2spaces\. The categories of 2spaces and 2spaces\ will play with respect to the categories of distributive bisemilattices and De Morgan bi…Read more

12Completion and amalgamation of bounded distributive quasi latticesLogic Journal of the IGPL 19 (1): 110120. 2011.In this note we present a completion for the variety of bounded distributive quasi lattices, and, inspired by a wellknown idea of L.L. Maksimova [14], we apply this result in proving the amalgamation property for such a class of algebras

11The Lattice of Subvarieties of √′ quasiMV AlgebrasStudia Logica 95 (12). 2010.In the present paper we continue the investigation of the lattice of subvarieties of the variety of √′ P quasiMV algebras, already started in [6]. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a longstanding open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra D r is not finitely based, and we provide an infinite equational basis for the same variety

6Quasisubtractive varieties: Open filters, congruences and the commutatorLogic Journal of the IGPL 22 (6): 844871. 2014.

6On the structure theory of Łukasiewicz near semiringsLogic Journal of the IGPL 26 (1): 1428. 2018.

On some properties of quasiMV algebras and $\sqrt{^{\prime }}$ quasiMV algebrasReports on Mathematical Logic 3163. 2009.We investigate some properties of two varieties of algebras arising from quantum computation  quasiMV algebras and $\sqrt{^{\prime }}$ quasiMV algebras  first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et al. 200+} and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasiMV reducts and subreducts of $\sqrt{^{\prime }}$ quasiMV algebras; we give a representation of semisimple…Read more