Results 51 to 60 of about 3,353 (149)

Fixed-point elimination in the intuitionistic propositional calculus

, 2016
It is a consequence of existing literature that least and greatest fixed-points of monotone polynomials on Heyting algebras-that is, the algebraic models of the Intuitionistic Propositional Calculus-always exist, even when these algebras are not complete
A Arnold, A Bauer, A Kock, Albert Visser, AM Pitts, D Kozen, F Dau, G D’Agostino, G D’Agostino, G Gentzen, G Kelly, JRB Cockett, L Alberucci, L Alberucci, N Bertrand, P Clairambault, S Frittella, S Ghilardi, S Ghilardi, SI Mardaev, SI Mardaev, W Ruitenburg   +21 more
core   +2 more sources

The Spectral Space of H‐Fuzzy Prime Ideals in Distributive Join‐Semilattices

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
The essential characteristics of H‐fuzzy prime ideals and H‐fuzzy maximal ideals within distributive join‐semilattices are introduced and examined in this work. We present a number of characterization theorems and prove findings related to the prime ideal theorem. We show that every H‐fuzzy prime ideal (or H‐fuzzy maximal ideal) has exactly two values:
Mohammed Amare Mohammed, Berehanu Bekele Belayneh, Zelalem Teshome Wale, Gezahagne Mulat Addis, John Venetis   +4 more
wiley   +1 more source

The Lattice‐Valued Turing Machines and the Lattice‐Valued Type 0 Grammars

Mathematical Problems in Engineering, Volume 2014, Issue 1, 2014., 2014
Purpose. The purpose of this paper is to study a class of the natural languages called the lattice‐valued phrase structure languages, which can be generated by the lattice‐valued type 0 grammars and recognized by the lattice‐valued Turing machines. Design/Methodology/Approach.
Juan Tang, Yong Fang, Jian-Gang Tang, Yang Xu   +3 more
wiley   +1 more source

Merging Intuitionistic and De Morgan Logics

Mathematics
We introduce De Morgan Heyting logic for Heyting algebras with De Morgan negation (DH-algebras). The variety DH of all DH-algebras is congruence distributive. The lattice of all subvarieties of DH is distributive.
Minghui Ma, Juntong Guo
doaj   +1 more source

Prawitz's completeness conjecture: A reassessment

Theoria, Volume 90, Issue 5, Page 492-514, October 2024.
Abstract In 1973, Dag Prawitz conjectured that the calculus of intuitionistic logic is complete with respect to his notion of validity of arguments. On the background of the recent disproof of this conjecture by Piecha, de Campos Sanz and Schroeder‐Heister, we discuss possible strategies of saving Prawitz's intentions.
Peter Schroeder‐Heister
wiley   +1 more source

Varieties of unary-determined distributive $\ell$-magmas and bunched implication algebras [PDF]

Logical Methods in Computer Science
A distributive lattice-ordered magma ($d\ell$-magma) $(A,\wedge,\vee,\cdot)$ is a distributive lattice with a binary operation $\cdot$ that preserves joins in both arguments, and when $\cdot$ is associative then $(A,\vee,\cdot)$ is an idempotent semiring.
Natanael Alpay, Peter Jipsen, Melissa Sugimoto   +2 more
doaj   +1 more source

Embeddings of Heyting Algebras

, 1996
Abstract In this paper we study embeddings ofHeyting algebras (Ha’s). Itis pointed out that such embeddings are naturally connected with Derived Rules and with propositional theories. We consider the Ha’s embeddable in the Ha of the Intuitionistic Propositional Calculus (IPC), i.e. the free Ha on N0 generators, those embeddable in the Ha
de Jongh, D., Visser, A.
openaire   +3 more sources

Isomorphism universal varieties of Heyting algebras [PDF]

Transactions of the American Mathematical Society, 1990
A variety V \mathbf {V} is group universal if every group G G is isomorphic to the automorphism group Aut ( A ) {\operatorname {Aut}}(A) of an algebra A ∈ V A \in \mathbf {V} ; if, in ...
Adams, M. E., Koubek, V., Sichler, J.
openaire   +1 more source

Topological Properties of Prime Filters and Minimal Prime Filters on a Paradistributive Latticoid

International Journal of Mathematics and Mathematical Sciences, Volume 2024, Issue 1, 2024.
In this paper, we study the concepts of prime filters and minimal prime filters on a paradistributive latticoid (PDL) and discuss various results. In addition, we prove that the annihilator filter S• is equal to the intersection of all prime filters not containing S.
Suryavardhani Ajjarapu, Ravikumar Bandaru, Ramakoteswara Rao Kotha, Rahul Shukla, Anwar Saleh Alwardi   +4 more
wiley   +1 more source

An Algebraic Proof of the Nishimura Theorem

Logics
An algebraic proof of the Nishimura theorem on one-generated Heyting algebras is presented.
Alex Citkin
doaj   +1 more source