Related papers: The logic with unsharp implication and negation
This paper deals with join-semilattices whose sections, i.e. principal filters, are pseudocomplemented lattices. The pseudocomplement of a\vee b in the section [b,1] is denoted by a\rightarrow b and can be considered as the connective…
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…
It is well-known that relatively pseudocomplemented lattices can serve as an algebraic semantics of intuitionistic logic. To extend the concept of relative pseudocomplementation to non-distributive lattices, the first author introduced…
Two kinds of the connective implication are introduced as term operations of a pseudocomplemented lattice. It is shown that they share a lot of properties with the intuitionistic implication based on Heyting algebras. In particular, if the…
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…
Sub-sub-intuitionistic logic is obtained from intuitionistic logic by weakening the implication and removing distributivity. It can alternatively be viewed as conditional weak positive logic. We provide semantics for sub-sub-intuitionistic…
Cumulative logics are studied in an abstract setting, i.e., without connectives, very much in the spirit of Makinson's early work. A powerful representation theorem characterizes those logics by choice functions that satisfy a weakening of…
We consider a 2-valued non-deterministic connective $\wedge \hskip-5.5pt \vee$ defined by the table resulting from the entry-wise union of the tables of conjunction and disjunction. Being half conjunction and half disjunction we named it…
We offer the proofs that complete our article introducing the propositional calculus called semi-intuitionistic logic with strong negation.
The Boolean logic of subsets, usually presented as `propositional logic,' is considered as being "classical" while intuitionistic logic and the many sublogics and off-shoots are "non-classical." But there is another mathematical logic, the…
In their seminal paper Birkhoff and von Neumann revealed the following dilemma: "... whereas for logicians the orthocomplementation properties of negation were the ones least able to withstand a critical analysis, the study of mechanics…
Bi-intuitionistic logic is the conservative extension of intuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
In this paper, a short survey about the concepts underlying general logics is given. In particular, a novel rigorous definition of a fuzzy negation as an operation acting on a lattice to render it into a fuzzy logic is presented. According…
We show the functional completeness for the connectives of the non-trivial negation inconsistent logic C by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that C contains a strong negation,…
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…
Using Vakarelov's theory of lattice logics with negation, we introduce the (co)quasiintuitionistic logic, and prove its soundness and completeness with respect to the class of (co)quasiintuitionistic algebras. Combining these algebras…
Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their…
In this work, we argue that ignorance can be inherently understood as a hyperintensional notion. When faced with two logically or necessarily equivalent propositions, an agent may be ignorant of one while not of the other. To capture…
Pomset logic introduced by Retor\'e is an extension of linear logic with a self-dual noncommutative connective. The logic is defined by means of proof-nets, rather than a sequent calculus. Later a deep inference system BV was developed with…