Journal ArticleDOI
Proof Theory of Paraconsistent Quantum Logic
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TLDR
Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved.Abstract:
Paraconsistent quantum logic, a hybrid of minimal quantum logic and paraconsistent four-valued logic, is introduced as Gentzen-type sequent calculi, and the cut-elimination theorems for these calculi are proved. This logic is shown to be decidable through the use of these calculi. A first-order extension of this logic is also shown to be decidable. The relationship between minimal quantum logic and paraconsistent four-valued logic is clarified, and a survey of existing Gentzen-type sequent calculi for these logics and their close relatives is addressed.read more
Citations
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Journal ArticleDOI
Gentzen-Type Sequent Calculi for Extended Belnap–Dunn Logics with Classical Negation: A General Framework
TL;DR: Theorems for syntactically and semantically embedding these calculi into a Gentzen-type sequent calculus LK for classical logic are proved and the cut-elimination, decidability, and completeness theorems are obtained.
Proceedings ArticleDOI
First-Order Nelsonian Paraconsistent Quantum Logic
TL;DR: The duality and cut-elimination theorems for NL are proved and Decidability, some constructive properties, some constructible falsity properties, and Craig interpolation property are shown for NL.
Journal ArticleDOI
Extending paraconsistent quantum logic: a single‐antecedent/succedent system approach
Journal ArticleDOI
Modal and Intuitionistic Variants of Extended Belnap–Dunn Logic with Classical Negation
TL;DR: In this article, Gentzen-type sequent calculi BDm and BDi for a modal extension and an intuitionistic modification, respectively, of De and Omori's extended Belnap-Dunn logic BD+ with classical negation were introduced.
Journal ArticleDOI
Lattice Logic, Bilattice Logic and Paraconsistent Quantum Logic: a Unified Framework Based on Monosequent Systems
TL;DR: A completeness theorem with respect to a lattice-valued semantics holds for a monosequent system for lattice logic, and a completeness thesis is proved for paraconsistent quantum logic and bilattice logic.
References
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Journal ArticleDOI
The Logic of Quantum Mechanics
TL;DR: In this article, it was shown that even a complete mathematical description of a physical system S does not in general enable one to predict with certainty the result of an experiment on S, and in particular one can never predict both the position and the momentum of S, (Heisenberg's Uncertainty Principle) and most pairs of observations are incompatible, and cannot be made on S simultaneously.
Book ChapterDOI
A Useful Four-Valued Logic
TL;DR: It is argued that a sophisticated question-answering machine that has the capability of making inferences from its data base should employ a certain four-valued logic, the motivating consideration being that minor inconsistencies in its data should not be allowed to lead to irrelevant conclusions.
Book ChapterDOI
The Logic of Quantum Mechanics
TL;DR: In this article, it was shown that even a complete mathematical description of a physical system S does not in general enable one to predict with certainty the result of an experiment on S, and that in particular one can never predict both the position and the momentum of S, (Heisenberg's Uncertainty Principle).
Book
Entailment : the logic of relevance and necessity
TL;DR: The Description for this book, Entailment: The Logic of Relevance and Necessity, will be forthcoming.
Journal ArticleDOI
Intuitive semantics for first-degree entailments and ‘coupled trees’
TL;DR: In this paper, the authors propose a tableau-based approach to show that an argument A may entail B because of some feature of A alone, irrespective of B, and vice versa.