Codd's Theorem, a fundamental result of database theory, asserts that relational algebra and calculus have the same expressive power on databases. We explore Theorem for databases over semirings establish two different versions this such databases: first version involves five basic operations algebra, while in second division operation is added to algebra. In both versions, difference relations given semantics using with monus, side limited form negation used. The reason considering these...

Abstract This paper studies which truth-values are most likely to be taken on finite models by arbitrary sentences of a many-valued predicate logic. The classical zero-one law (independently proved Fagin and Glebskiĭ et al.) states that every sentence in purely relational language is almost surely false or true, meaning the probability formula true randomly chosen structures cardinal n asymptotically $0$ $1$ as grows infinity. We obtain generalizations this result for any logic with values...

Starting from a decomposition result of monoidal t-norm-based logic (MTL)-chains as ordinal sums, we focus our attention on particular kind indecomposable semihoops, namely weakly cancellative semihoops. The weak cancellation property is proved to be the difference between and pseudocomplementation, so it gives new axiomatization product ΠMTL. By adding this property, some fuzzy logics (propositional first-order) are defined studied obtaining results about their (finite) strong standard...

The study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized this paper to the general non-involutive case, i.e. MTL-algebras. To end we describe radical MTL-algebras characterize perfect as those for which quotient by isomorphic two-element Boolean algebra, a special class MTL-algebras, 𝔹ℙ0, algebra. We prove that 𝔹ℙ0 variety generated all give some equational bases it. also introduce new way build adding negation fixpoint algebra set points whose fixpoint....

Journal Article On Product Logic with Truth-constants Get access Petr Savický, Savický Search for other works by this author on: Oxford Academic Google Scholar Roberto Cignoli, Cignoli Francesc Esteva, Esteva Lluís Godo, Godo Carles Noguera of and Computation, Volume 16, Issue 2, April 2006, Pages 205–225, https://doi.org/10.1093/logcom/exi075 Published: 01 2006

Abstract It is well known that MTL satisfies the finite embeddability property. Thus complete w. r. t. class of all MTL‐chains. In order to reach a deeper understanding structure this class, we consider extensions by adding generalized contraction since each MTL‐chain form contraction. Simultaneously, also excluded middle laws introduced in [9] and axiom weak cancellation defined [31]. The algebraic counterpart these logics studied characterizing subdirectly irreducible, semisimple, simple...

Abstract Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on study of their counterparts: residuated lattices. Recently, nonassociative generalization (which we call SL) has been studied by Galatos and Ono as logic lattice-ordered unital groupoids. This paper is an alternative Hilbert-style presentation for SL which almost MP -based . then used to obtain, in uniform way applicable most (both associative...

Abstract In this paper we carry out an algebraic investigation of the weak nilpotent minimum logic (WNM) and its t‐norm based axiomatic extensions. We consider counterpart WNM, variety WNM‐algebras (𝕎ℕ𝕄) prove that it is locally finite, so all subvarieties are generated by finite chains. give criteria to compare varieties families WNM‐chains, in particular standard or equivalently extensions study their completeness properties. also characterize generic i. e. those generate 𝕎ℕ𝕄,...

Abstract This paper considers Henkin’s proof of completeness classical first-order logic and extends its scope to the realm algebraizable logics in sense Blok Pigozzi. Given a propositional L (for which we only need assume that it has an algebraic semantics suitable disjunction) axiomatize two natural extensions L∀ m prove former is complete with respect all models over algebras from , while latter relatively finitely subdirectly irreducible algebras. While first result straightforward,...