Related papers: A New Connective in Natural Deduction, and its App…
The usual reading of logical implication "A implies B" as "if A then B" fails in intuitionistic logic: there are formulas A and B such that "A implies B" is not provable, even though B is provable whenever A is provable. Intuitionistic…
A prototypical example of categorial grammars are those based on Lambek calculus, i.e. noncommutative intuitionistic linear logic. However, it has been noted that purely noncommutative operations are often not sufficient for modeling even…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been…
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)…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…
In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…
Fundamental logic was introduced by Wesley Holliday (2023) to unify intuitionistic logic and quantum logic from a proof-theoretic perspective, capturing the logic determined solely by the introduction and elimination rules of connectives…
Logic programs with ordered disjunction (LPODs) combine ideas underlying Qualitative Choice Logic (Brewka et al. KR 2002) and answer set programming. Logic programming under answer set semantics is extended with a new connective called…
This paper establishes the normalisation of natural deduction or lambda calculus formulation of Intuitionistic Non Commutative Logic --- which involves both commutative and non commutative connectives. This calculus first introduced by de…
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…
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by…
The notion of a non-deterministic logical matrix (where connectives are interpreted as multi-functions) extends the traditional semantics for propositional logics based on logical matrices (where connectives are interpreted as functions).…
Propositional G\"odel logic extends intuitionistic logic with the non-constructive principle of linearity $A\rightarrow B\ \lor\ B\rightarrow A$. We introduce a Curry-Howard correspondence for this logic and show that a particularly simple…
We report first steps towards elucidating the relationship between contextuality, measurement-based quantum computation (MBQC) and the non-classical logic of a topos associated with the computation. We show that, in a class of MBQC,…
We initiate the study of parallel quantum programming by defining the operational and denotational semantics of parallel quantum programs. The technical contributions of this paper include: (1) find a series of useful proof rules for…
We present quantitative separation logic ($\mathsf{QSL}$). In contrast to classical separation logic, $\mathsf{QSL}$ employs quantities which evaluate to real numbers instead of predicates which evaluate to Boolean values. The connectives…
Based on the ideas of quantum theory of open systems (QTOS) we propose the consistent approach to study probabilistic many-valued propositional logic of intelligent devices that are composed from separate but interconnected logical units.…
The nondistributivity of compound quantum mechanical propositions leads to a theorem that rules out the possibility of microscopic deterministic hidden variables, the Logical No-Go Theorem. We observe that there appear in fact two distinct…