Related papers: Tense logic based on finite orthomodular posets

Similarly as classical propositional calculus is based algebraically on Boolean algebras, the logic of quantum mechanics was based on orthomodular lattices by G. Birkhoff and J. von Neumann and K. Husimi. However, this logic does not…

Not all logical systems can be captured using algebras. We see this in classical logic (formalized by Boolean algebras) and many-valued logics (like Lukasiewicz logic with MV-algebras). Even quantum mechanics, initially formalized with…

Orthomodular posets form an algebraic formalization of the logic of quantum mechanics. The question is how to introduce the connective implication in such a logic. We show that this is possible when the orthomodular poset in question is of…

When an algebraic logic based on a poset instead of a lattice is investigated then there is a natural problem how to introduce the connective implication to be everywhere defined and satisfying (left) adjointness with the connective…

The concept of operator left residuation has been introduced by the authors in a previous paper. Modifications of so-called quantum structures, in particular orthomodular posets, like pseudo-orthomodular, pseudo-Boolean and Boolean posets…

We start from two closure operators defined on the elements of a special kind of partially ordered sets, called causal nets. Causal nets are used to model histories of concurrent processes, recording occurrences of local states and of…

As algebraic semantics of the logic of quantum mechanics there are usually used orthomodular posets, i.e. bounded posets with a complementation which is an antitone involution and where the join of orthogonal elements exists and the…

We consider orthomodular posets endowed with a symmetric difference. We call them ODPs. Expressed in the quantum logic language, we consider quantum logics with an XOR-type connective. We study three classes of "almost Boolean" ODPs, two of…

Generalized orthomodular posets were introduced recently by D. Fazio, A. Ledda and the first author of the present paper in order to establish a useful tool for studying the logic of quantum mechanics. They investigated structural…

Tense logic was introduced by Arthur Prior in the late 1950s as a result of his interest in the relationship between tense and modality. Prior's idea was to add four primitive modal-like unary connectives to the base language today widely…

For effect algebras, the so-called tense operators were already introduced by Chajda and Paseka. They presented also a canonical construction of them using the notion of a time frame. Tense operators express the quantifiers "it is always…

Effect algebras were introduced in order to describe the structure of effects, i.e. events in quantum mechanics. They are partial algebras describing the logic behind the corresponding events. It is natural to ask how to introduce the…

In this paper we enrich the orthomodular structure by adding a modal operator, following a physical motivation. A logical system is developed, obtaining algebraic completeness and completeness with respect to a Kripke-style semantic founded…

It is well-known that in the logic of quantum mechanics disjunctions and conjunctions can be represented by joins and meets, respectively, in an orthomodular lattice provided their entries commute. This was the reason why J. Pykacz…

We give the quantum subset construction of orthomodular lattice-valued finite automata, then we show the equivalence between orthomodular lattice-valued finite automata, orthomodular lattice-valued deterministic finite automata and…

We consider intuitionistic variants of linear temporal logic with `next', `until' and `release' based on expanding posets: partial orders equipped with an order-preserving transition function. This class of structures gives rise to a logic…

We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a…

In order to enrich dynamic semantic theories with a `pragmatic' capacity, we combine dynamic and nonmonotonic (preferential) logics in a modal logic setting. We extend a fragment of Van Benthem and De Rijke's dynamic modal logic with…

This paper surveys some recent developments towards a dynamic quantum logic and outlines its explicite construction -- some analogies and contrasts with other logics of dynamics are indicated. Abstract: The development of ``(static)…

Quantum logic aims to capture essential quantum mechanical structure in order-theoretic terms. The Achilles' heel of quantum logic is the absence of a canonical description of composite systems, given descriptions of their components. We…