منابع مشابه
An implication in orthologic
We involve a certain propositional logic based on an ortholattice. We characterize the implication reduct of such a logic and show that its algebraic counterpart is the so-called orthosemilattice. Properties of congruences and congruence kernels of these algebras are described.
متن کاملFocusing in Orthologic
We propose new sequent calculus systems for orthologic (also known as minimal quantum logic) which satisfy the cut elimination property. The first one is a very simple system relying on the involutive status of negation. The second one incorporates the notion of focusing (coming from linear logic) to add constraints on proofs and thus to facilitate proof search. We demonstrate how to take benef...
متن کاملOrthologic Tetrahedra with Intersecting Edges
Two tetrahedra are called orthologic if the lines through vertices of one and perpendicular to corresponding faces of the other are intersecting. This is equivalent to the orthogonality of non-corresponding edges. We prove that the additional assumption of intersecting non-corresponding edges (“orthosecting tetrahedra”) implies that the six intersection points lie on a sphere. To a given tetrah...
متن کاملOn Different Proof-Search Strategies for Orthologic
In this paper, we consider three different search strategies for a cut-free sequent system formalizing orthologic, and estimate the respective search spaces. Applying backward search, there are classes of formulae for which both the minimal proof length and the search space are exponential. In a combined forward and backward approach, all proofs are polynomial, but the potential search space re...
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ژورنال
عنوان ژورنال: The Mathematical Gazette
سال: 1909
ISSN: 0025-5572
DOI: 10.2307/3602160