Modularity, atomicity and states in Archimedean lattice effect algebras.
Modules over a quantale and models for the operator in linear logic
Modus ponens on Boolean algebras revisited.
In a Boolean Algebra B, an inequality f(x,x --> y)) ≤ y satisfying the condition f(1,1)=1, is considered for defining operations a --> b among the elements of B. These operations are called Conditionals'' for f. In this paper, we obtain all the boolean Conditionals and Internal Conditionals, and some of their properties as, for example, monotonicity are briefly discussed.
Modyfications of Csákány's Theorem
Varieties whose algebras have no idempotent element were characterized by B. Csákány by the property that no proper subalgebra of an algebra of such a variety is a congruence class. We simplify this result for permutable varieties and we give a local version of the theorem for varieties with nullary operations.
Molecules and linerly ordered ideals of MV-algebras.
We show that an ideal I of an MV-algebra A is linearly ordered if and only if every non-zero element of I is a molecule. The set of molecules of A is contained in Inf(A) ∪ B2(A) where B2(A) is the set of all elements x ∈ A such that 2x is idempotent. It is shown that I ≠ {0} is weakly essential if and only if B⊥ ⊂ B(A). Connections are shown among the classes of ideals that have various combinations of the properties of being implicative, essential, weakly essential, maximal or prime.
Monadic basic algebras
The concept of monadic MV-algebra was recently introduced by A. Di Nola and R. Grigolia as an algebraic formalization of the many-valued predicate calculus described formerly by J. D. Rutledge [9]. This was also genaralized by J. Rachůnek and F. Švrček for commutative residuated -monoids since MV-algebras form a particular case of this structure. Basic algebras serve as a tool for the investigations of much more wide class of non-classical logics (including MV-algebras, orthomodular lattices and...
Monadic epimorphisms and applications
Monadic involutive pseudo-BCK algebras.
Monadic -valued Łukasiewicz-Moisil algebras
Here we initiate an investigation into the class of monadic -valued Łukasiewicz-Moisil algebras (or -algebras), namely -valued Łukasiewicz-Moisil algebras endowed with a unary operation. These algebras constitute a generalization of monadic -valued Łukasiewicz-Moisil algebras. In this article, the congruences on these algebras are determined and subdirectly irreducible algebras are characterized. From this last result it is proved that is a discriminator variety and as a consequence, the...
Monadic quasi-modal distributive nearlattices
We prove that there is a one to one correspondence between monadic finite quasi-modal operators on a distributive nearlattice and quantifiers on the distributive lattice of its finitely generated filters, extending the results given in ``Calomino I., Celani S., González L. J.: Quasi-modal operators on distributive nearlattices, Rev. Unión Mat. Argent. 61 (2020), 339--352".
Monads in basic equivalences
Monads of indiscernibles
Monomorphisms of inductive number systems
Monotone (co)inductive types and positive fixed-point types
Monotone (co)inductive types and positive fixed-point types
We study five extensions of the polymorphically typed lambda-calculus (system F) by type constructs intended to model fixed-points of monotone operators. Building on work by Geuvers concerning the relation between term rewrite systems for least pre-fixed-points and greatest post-fixed-points of positive type schemes (i.e., non-nested positive inductive and coinductive types) and so-called retract types, we show that there are reduction-preserving embeddings even between systems of monotone (co)inductive...
Monotone modal operators on bounded integral residuated lattices
Bounded integral residuated lattices form a large class of algebras containing some classes of commutative and noncommutative algebras behind many-valued and fuzzy logics. In the paper, monotone modal operators (special cases of closure operators) are introduced and studied.
Monotone sequent calculus and resolution
We study relations between propositional Monotone Sequent Calculus (MLK --- also known as Geometric Logic) and Resolution with respect to the complexity of proofs, namely to the concept of the polynomial simulation of proofs. We consider Resolution on sets of monochromatic clauses. We prove that there exists a polynomial simulation of proofs in MLK by intuitionistic proofs. We show a polynomial simulation between proofs from axioms in MLK and corresponding proofs of contradiction (refutations) in...
Monotonic mappings on ordered sets, a class of inequalities with finite differences and fixed points.
Monotonic valuations and valuations of triads of higher types
Monotonic valuations of -triads and evaluations of ideals
We develop problems of monotonic valuations of triads. A theorem on monotonic valuations of triads of the type is presented. We study, using the notion of the monotonic valuation, representations of ideals by monotone and subadditive mappings. We prove, for example, that there exists, for each ideal of the type on a set , a monotone and subadditive set-mapping on with values in non-negative rational numbers such that . Some analogical results are proved for ideals of the types and...