Related papers: A Weakly Intuitionistic Quantum Logic
In arXiv: math.LO/0011208 we proposed the {\sl intuitionistic or disjunctive representation of quantum logic}, i.e., a representation of the property lattice of physical systems as a complete Heyting algebra of logical propositions on these…
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)…
This paper consists of a short version of the derivation of the intuitionistic quantum logic L_QM (which was originally introduced by Caspers, Heunen, Landsman and Spitters). The elaboration consists of extending this logic to a classical…
In their seminal paper Birkhoff and von Neumann revealed the following dilemma: "... whereas for logicians the orthocomplementation properties of negation were the ones least able to withstand a critical analysis, the study of mechanics…
We have proposed in several recent papers a critical view of some parts of quantum mechanics (QM) that is methodologically unusual because it rests on analysing the language of QM by using some elementary but fundamental tools of…
We propose a semantic representation of the standard quantum logic QL within a classical, normal modal logic, and this via a lattice-embedding of orthomodular lattices into Boolean algebras with one modal operator. Thus our classical logic…
This paper presents a novel explanation of the cause of quantum probabilities and the Born rule based on the intuitionistic interpretation of quantum mechanics where propositions obey constructive (intuitionistic) logic. The use of…
We review recent work that employs the framework of logical inference to establish a bridge between data gathered through experiments and their objective description in terms of human-made concepts. It is shown that logical inference…
Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic…
In this paper, we use a new method to prove cut-elimination of weak intuitionistic tense logic. This method focuses on splitting the contraction rule and cut rules. Further general theories and applications of this method shall be developed…
Use is made of a relativistic kinematic modulation effect to compliment imagery from Stochastic Electrodynamics to provide intuitive paradigms for Quantum Mechanics. Based on these paradigms, resolutions for epistemological problems vexing…
We show that intuitionistic logic is deductively equivalent to Connexive Heyting Logic (CHL), hereby introduced as an example of a strong connexive logic with intuitive semantics. We use the reverse algebraisation paradigm: CHL is presented…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
An introduction is given to an algebraic formulation and generalisation of the consistent histories approach to quantum theory. The main technical tool in this theory is an orthoalgebra of history propositions that serves as a generalised…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
Verifying the functional correctness of programs with both classical and quantum constructs is a challenging task. The presence of probabilistic behaviour entailed by quantum measurements and unbounded while loops complicate the…
Scholars have wondered for a long time whether quantum mechanics (QM) subtends a quantum concept of truth which originates quantum logic (QL) and is radically different from the classical (Tarskian) concept of truth. We show in this paper…
This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic…
Doubts are raised concerning the usual interpretation of the alleged failure, by quantum mechanics, of the distributive law of classical logic. The difficulty raised by incompatible sets of observables is overcome within an epistemic…
We explore various semantic understandings of dual intuitionistic logic by exploring the relationship between co-Heyting algebras and topological spaces. First, we discuss the relevant ideas in the setting of Heyting algebras and…