Results 1 to 10 of about 122 (115)
Connecting the free energy principle with quantum cognition [PDF]
Frontiers in Neurorobotics, 2022 It appears that the free energy minimization principle conflicts with quantum cognition since the former adheres to a restricted view based on experience while the latter allows deviations from such a restricted view.
Yukio-Pegio Gunji +2 more
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Rough Approximation Operators on a Complete Orthomodular Lattice
Axioms, 2021 This paper studies rough approximation via join and meet on a complete orthomodular lattice. Different from Boolean algebra, the distributive law of join over meet does not hold in orthomodular lattices. Some properties of rough approximation rely on the
Songsong Dai
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Interplay Between Vertical and Horizontal Schemes of Computation: From Bayesian Inference to Quantum Logic via Gluing Boolean Algebras [PDF]
EntropyArtificial intelligence is typically formulated as an information-processing system composed of artificial neurons, where computation is understood as recursive operations connecting inputs and outputs.
Yukio-Pegio Gunji +7 more
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Residuation in orthomodular lattices
Topological Algebra and its Applications, 2017 We show that every idempotent weakly divisible residuated lattice satisfying the double negation law can be transformed into an orthomodular lattice. The converse holds if adjointness is replaced by conditional adjointness.
Chajda Ivan, Länger Helmut
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Weakly Orthomodular and Dually Weakly Orthomodular Lattices [PDF]
Order, 2018 The authors study the varieties of lattices with a unary operation~\('\) satisfying one or two or the following equations: \begin{align*} x= & (x\land y) \lor (x\land (x\land y)')\\ x= & (x\lor y) \land (x\lor (x\lor y)')\,. \end{align*} In ortholattices, any of these equations is equivalent to orthomodularity.
Helmut Langer +2 more
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Relatively orthomodular lattices
Discrete Mathematics, 2001 \textit{M.~F.~Janowitz} [``A note on generalized orthomodular lattices'', J. Nat. Sci. Math. 8, 89-94 (1968; Zbl 0169.02104)] defined a generalized orthomodular lattice (GOML) as a lattice with 0 and with an orthogonality relation (similar to that considered in orthomodular lattices (OMLs)).
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On Quantum-MV algebras - Part II: Orthomodular Lattices, Softlattices and Widelattices [PDF]
Transactions on Fuzzy Sets and Systems, 2022 Orthomodular lattices generalize the Boolean algebras; they have arisen in the study of quantum logic. Quantum-MV algebras were introduced as non-lattice theoretic generalizations of MV algebras and as non-idempotent generalizations of ...
Afrodita Iorgulescu
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Orthogonality and complementation in the lattice of subspaces of a finite vector space [PDF]
Mathematica Bohemica, 2022 We investigate the lattice $ L( V)$ of subspaces of an $m$-dimensional vector space $ V$ over a finite field ${\rm GF}(q)$ with a prime power $q=p^n$ together with the unary operation of orthogonality.
Ivan Chajda, Helmut Länger
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Residuated Structures and Orthomodular Lattices [PDF]
Studia Logica, 2021 AbstractThe variety of (pointed) residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., $$\ell $$ ℓ -groups, Heyting algebras, MV-algebras, or De Morgan monoids.
fazio, davide +2 more
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Subalgebras of Orthomodular Lattices [PDF]
Order, 2010 Sachs showed that a Boolean algebra is determined by its lattice of subalgebras. We establish the corresponding result for orthomodular lattices. We show that an orthomodular lattice L is determined by its lattice of subalgebras Sub(L), as well as by its poset of Boolean subalgebras BSub(L).
John Harding, Mirko Navara
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