相关论文: Logics of involutive Stone algebras
We study the lattice of extensions of four-valued Belnap--Dunn logic, called super-Belnap logics by analogy with superintuitionistic logics. We describe the global structure of this lattice by splitting it into several subintervals, and…
Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…
Involutive Stone algebras (or {\bf S}--algebras) were introduced by R. Cignoli and M. Sagastume in connection to the theory of $n$-valued \L ukasiewicz--Moisil algebras. In this work we focus on the logic that preserves degrees of truth…
Quasi-set theory was proposed as a mathematical context to investigate collections of indistinguishable objects. After presenting an outline of this theory, we define an algebra that has most of the standard properties of an orthocomplete…
Perfect paradefinite algebras are De Morgan algebras expanded with an operation that allows for the full behavior of classical negation to be restored. They form a variety that is term-equivalent to the variety of involutive Stone algebras.…
In \cite{LC, LCMF}, it was introduced a logic (called \Six ) associated to a class of algebraic structures known as {\em involutive Stone algebras}. This class of algebras, denoted by \Sto , was considered by the first time in \cite{CS1} as…
We introduce and study single-conclusioned nested sequent calculi for a broad class of intuitionistic multi-modal logics known as "intuitionistic grammar logics (IGLs)." These logics serve as the intuitionistic counterparts of classical…
In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several structures of prominent importance for mathematical logic, e.g.…
Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is…
We present a novel unity of logic, viz., a single sequent calculus that embodies classical, intuitionistic and linear logics. Concretely, we define classical linear logic negative (CLL$^-$), a new logic that is classical and linear yet…
We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew…
Stone-type duality theorems, which relate algebraic and relational/topological models, are important tools in logic because -- in addition to elegant abstraction -- they strengthen soundness and completeness to a categorical equivalence,…
Fixed points are a recurring theme in computer science and are often constructed as limits of suitably seeded fixed point iterations. We present the algebra of iterative constructions (AIC) -- a purely algebraic approach to reasoning about…
Our main result is that any topological algebra based on a Boolean space is the extended Stone dual space of a certain associated Boolean algebra with additional operations. A particular case of this result is that the profinite completion…
This paper focuses on order-preserving logics defined from varieties of distributive lattices with negation, and in particular on the problem of whether these can be axiomatized by means of finite Hilbert calculi. On the side of negative…
We introduce a geometric model of shallow multiplicative exponential linear logic (MELL) using the Hilbert scheme. Building on previous work interpreting multiplicative linear logic proofs as systems of linear equations, we show that…
The main aim of this paper is to introduce the logics of evidence and truth LETK+ and LETF+ together with a sound, complete, and decidable six-valued deterministic semantics for them. These logics extend the logics LETK and LETF- with rules…
Inquisitive logic is a research program that extends the scope of logic to cover not only statements, but also questions. In the context of this program, a logic that plays a prominent role is inquisitive first-order logic, InqBQ, which…
Invariant Set Theory (IST) is a realistic, locally causal theory of fundamental physics which assumes a much stronger synergy between cosmology and quantum physics than exists in contemporary theory. In IST the (quasi-cyclic) universe $U$…
The increasing advancement of emerging device technologies that provide alternative basis logic sets necessitates the exploration of innovative logic design automation methodologies. Specifically, emerging computing architectures based on…