Search
Search Results
-
Representability of Kleene Posets and Kleene Lattices
A Kleene lattice is a distributive lattice equipped with an antitone involution and satisfying the so-called normality condition. These lattices were...
-
A Cartography of LFIs and Truth
The goal of this paper is to offer an initial taxonomy of the LFIs (logics of formal inconsistency) and that can be non-trivially extended with a...
-
Nelson Conuclei and Nuclei: The Twist Construction Beyond Involutivity
Recent work by Busaniche, Galatos and Marcos introduced a very general twist construction, based on the notion of conucleus , which subsumes most...
-
An Algebraic Glimpse at Bunched Implications and Separation Logic
We overview the logic of Bunched Implications (BI) and Separation Logic (SL) from a perspective inspired by Hiroakira Ono’s algebraic approach to...
-
Naïve Truth and the Evidential Conditional
This paper develops the idea that valid arguments are equivalent to true conditionals by combining Kripke’s theory of truth with the evidential...
-
Intuitionistic Modal Algebras
Recent research on algebraic models of quasi-Nelson logic has brought new attention to a number of classes of algebras which result from enriching...
-
Aspects of Categorical Recursion Theory
We present a survey of some developments in the general area of category-theoretic approaches to the theory of computation, with a focus on topics...
-
Płonka Sums and Regular Varieties
As we have hinted in the previous chapter, the algebraic construction of Płonka sums yields a convenient representation for algebras defined by means...
-
Quantum Logic for Observation of Physical Quantities
Dynamic quantum logic (DQL) is studied to represent the proposition of dynamism in quantum information theory as traditional quantum logic cannot...
-
Group Representation for Even and Odd Involutive Commutative Residuated Chains
For odd and for even involutive, commutative residuated chains a representation theorem is presented in this paper by means of direct systems of...
-
Twist Structures and Nelson Conuclei
Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common...
-
Operation and Predicativity: Lorenzen’s Approach to Arithmetic
In this article we give an overview, from a philosophical point of view, of Lorenzen’s construction of the natural and the real numbers. Particular...
-
Algebraic Analysis of Demodalised Analytic Implication
The logic DAI of demodalised analytic implication has been introduced by J.M. Dunn (and independently investigated by R.D. Epstein) as a variation on...
-
On Paraconsistent Weak Kleene Logic: Axiomatisation and Algebraic Analysis
Paraconsistent Weak Kleene logic (PWK) is the 3-valued logic with two designated values defined through the weak Kleene tables. This paper is a first...
-
Kleene Algebras and Logic: Boolean and Rough Set Representations, 3-Valued, Rough Set and Perp Semantics
A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets, and...
-
Meaning-Preserving Translations of Non-classical Logics into Classical Logic: Between Pluralism and Monism
In order to prove the validity of logical rules, one has to assume these rules in the metalogic. However, rule-circular ‘justifications’ are...
-
Well-Quasi Orders and Hierarchy Theory
We discuss some applications of WQOs to several fields were hierarchies and reducibilities are the principal classification tools, notably to...
-
A Duality for Involutive Bisemilattices
We establish a duality between the category of involutive bisemilattices and the category of semilattice inverse systems of Stone spaces, using Stone...
-
Graded Consequence in Decision-Making: A Few Applications
In this chapter, we shall present some aspects of decision-making based on the basic idea of the theory of graded consequence. In the first case, we...
-
Introducing Boolean Semilattices
We present and discuss a variety of Boolean algebras with operators that is closely related to the variety generated by all complex algebras of...