Quantum Logic associated to Finite Dimensional Intervals of Modular ortholattices
نویسندگان
چکیده
In this work we study an abstract formulation of a problem posed by J.M. Dunn, T.J. Hagge et al. about the inclusion of varieties generated by the modular ortholattice of subspaces of C. We shall prove that, this abstract formulation is equivalent to the direct irreducibility for atomic complete modular ortholattices.
منابع مشابه
The two parameter quantum groups $U_{r,s}(mathfrak{g})$ associated to generalized Kac-Moody algebra and their equitable presentation
We construct a family of two parameter quantum grou-\ps $U_{r,s}(mathfrak{g})$ associated with a generalized Kac-Moody algebra corresponding to symmetrizable admissible Borcherds Cartan matrix. We also construct the $textbf{A}$-form $U_{textbf{A}}$ and the classical limit of $U_{r,s}(mathfrak{g})$. Furthermore, we display the equitable presentation for a subalgebra $U_{r...
متن کاملThe Deduction Theorem for Quantum Logic - Some Negative Results
We prove that no logic (i.e.consequence operation) determined by any class of orthomodular lattices admits the deduction theorem (Theorem 2.7). We extend those results to some broader class of logics determined by ortholattices (Corollary 2.6).
متن کاملOn the Lattice of Orthomodular Logics
The upper part of the lattice of orthomodular logics is described. In [1] and [2] Bruns and Kalmbach have described the lower part of the lattice of varieties of orthomodular lattices. They proved that any variety of orthomodular lattices essentially larger than variety generated by a contains at least one of lattices b, c, d, e. (By a, b, c, d, e, f , g we denote the lattice depicted in respec...
متن کاملStrong Versus Weak Quantum Consequence Operations
This paper is a study of similarities and di erences between strong and weak quantum consequence operations determined by a given class of ortholattices. We prove that the only strong orthologics which admits the deduction theorem (the only strong orthologics with algebraic semantics, the only equivalential strong orthologics, respectively) is the classical logic. In the papers concerning quant...
متن کاملAutomated Discovery of Single Axioms for Ortholattices
We present short single axioms for ortholattices, orthomodular lattices, and modular ortholattices, all in terms of the Sheffer stroke. The ortholattice axiom is the shortest possible. We also give multiequation bases in terms of the Sheffer stroke and in terms of join, meet, and complementation. Proofs are omitted but are available in an associated technical report and on the Web. We used comp...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Symb. Log.
دوره 81 شماره
صفحات -
تاریخ انتشار 2016