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This document is a correction to a previous article titled "A note on functional relations in a certain class of implicative expansions of FDE related to Brady's 4-valued logic BN4." The correction addresses an error in the definition used in the proof of Proposition 3.2. The corrected definition states that A→B is equal to (A k3 B) ∨ (A→B), rather than (A k11 B) ∨ (A→B) as previously stated. The correction is reported by Gemma Robles and José M Méndez. [Extracted from the article]

A classical result by Słupecki states that a logic L is functionally complete for the 3-element set of truth-values THREE if, in addition to functionally including Łukasiewicz's 3-valued logic Ł3, what he names the ' |$T$| -function' is definable in L. By leaning upon this classical result, we prove a general theorem for defining binary expansions (i.e. expansions with a binary connective) of Kleene's strong logic that are functionally complete for THREE. [ABSTRACT FROM AUTHOR]

'Binary Routley-semantics' (bR-semantics) differs from Routley-Meyer semantics (RM-semantics) mainly in that the accessibility relation is binary instead of ternary. Intuitionistic bR-semantics is essentially defined when introducing the Routley operator (used for modelling negation) in Kripke models for positive intuitionistic logic. The aim of this article is to define the minimal logic in intuitionistic bR-semantics, HM, as well as a number of its extension. HM is minimal in intuitionistic bR-semantics in the same sense in which Sylvan and Plumwood's BM is minimal in RM-semantics with a set of designated points. [ABSTRACT FROM AUTHOR]

The aim of the article is to introduce a paraconsistent logic, G3Ł<, related to Gödel 3-valued logic G3. In order to adequately explain G3Ł<, the akin logics G3Ł(FD) and G3Ł1 are also investigated. A Henkin-style completeness proof is provided for each one of these logics by endowing them with dually equivalent under-determined and over-determined bivalent semantics of the type defined by Dunn. G3Ł(FD), G3Ł1 and G3Ł< are related to ‘quasi relevant’ logics such as R-Mingle or RM3, as well as to non-relevant logics such as Łukasiewicz Ł3 or some logics in the vicinity of intuitionistic logic. The logic G3Ł< belongs to the class of paraconsistent logics extending positive intuitionistic logic rather than positive classical logic. [ABSTRACT FROM AUTHOR]

Łukasiewicz 3-valued logic Ł3 is often understood as the set of all valid formulas according to Łukasiewicz 3-valued matrices MŁ3. Following Wojcicki, in addition, we shall consider two alternative interpretations of Ł3: ‘truth-preserving’ Ł3a and ‘well-determined’ Ł3b defined by two different consequence relations on the 3-valued matrices MŁ3. The aim of this article is to provide a Routley–Meyer ternary semantics for each one of these three versions of Łukasiewicz 3-valued logic: Ł3, Ł3a and Ł3b. [ABSTRACT FROM AUTHOR]

A very simple, yet efficient synthetic methodology, to obtain 3,4-diaryl-substituted pyrroles is described. The approach is based on the Knoevenagel condensation between arylacetonitriles and substituted aromatic aldehydes, followed by conjugate addition of cyanide to afford succinonitriles in excellent yields. The products thus obtained were subjected to DIBAL-H reduction, followed by cyclization under acidic conditions to produce the corresponding pyrroles in good overall yields. The utility of this protocol is exemplified by the synthesis of the marine alkaloids lamellarins O and Q. [ABSTRACT FROM AUTHOR]

The logic TM is the result of adding the mingle axiom, M to Ticket Entailment logic, T. In the present study, it is proved that TM has the variable-sharing property (vsp). Ternary relational semantics for TM is provided. Finally, an interesting extension of TM with the vsp is briefly discussed. [ABSTRACT FROM PUBLISHER]

In our paper "A general characterization of the variable-sharing property by means of logical matrices", a general class of so-called "Relevant logical matrices", RMLs, is defined. The aim of this paper is to define a class of simpler Relevant logical matrices RMLs' serving the same purpose that RMLs, to wit: any logic verified by an RML' has the variable-sharing property and related properties predicable of the logic of entailment E and of the logic of relevance R. [ABSTRACT FROM AUTHOR]

The aim of this paper is to provide a Routley-Meyer semantics for Ackermann's logics of "strenge Implikation" Π′ and Π″. Besides the Disjunctive Syllogism, this semantics validates the rules Necessitation and Assertion. Strong completeness theorems for Π′ and Π″ are proved. A brief discussion on Π′, Π″ and paraconsistency is included. [ABSTRACT FROM AUTHOR]