A hemi-implicative lattice is an algebra \((A,\wedge,\vee,\rightarrow,1)\) of type (2, 2, 2, 0) such that \((A,\wedge,\vee,1)\) is a lattice with top and for every \(a,b\in A\), \(a\rightarrow a = 1\) and \(a\wedge (a\rightarrow b) \le b\). A new variety of hemi-implicative lattices, here named sub-Hilbert lattices, containing both the variety generated by the \(\{\wedge,\vee,\rightarrow,1\}\) -reducts of subresiduated lattices and that of Hilbert lattices as proper subvarieties is defined. It is shown that any sub-Hilbert lattice is determined (up to isomorphism) by (...) a triple (_L_, _D_, _S_) which satisfies the following conditions: _L_ is a bounded distributive lattice, _D_ is a sublattice of _L_ containing 0, 1 such that for each \(a, b \in L\) there is an element \(c \in D\) with the property that for all \(d \in D\), \(a \wedge d \le b\) if and only if \(d \le c\) (we write \(a \rightarrow _D b\) for the element _c_), and _S_ is a non void subset of _L_ such that _S_ is closed under \(\rightarrow _D\) and _S_, with its inherited order, is itself a lattice. Finally, the congruences of sub-Hilbert lattices are studied. (shrink)

Society Semantics, introduced by W. Carnielli and M. Lima-Marques, is a method for obtaining new logics from the combination of agents of a given logic. The goal of this paper is to present several generalizations of this method, as well as to show some applications to many-valued logics. After a reformulation of Society Semantics in a wider setting, we develop in detail two examples of application of the new formalism, characterizing a hierarchy of paraconsistent logics called Pn and a hierarchy (...) of paracomplete logics In. We also propose three further generalizations, obtaining Society Semantics for several many-valued logics, including a hierarchy of logics called In Pk which are both paraconsistent and paracomplete. (shrink)

In this work we define, in a general way, an algebraic semantics for the logics of the hierarchy InPk. This semantics is defined by means of an alternative construction, with respect to the usual algebraic semantics, and it is known in the literature as Twist-structures semantics. Besides that, we modify such construction, defining the so-called ω-Twist-structures here. This adaptation allows us to prove adequacy theorems for every logic of the hierarchy InPk.

This article studies preservation of certain algebraic properties of propositional logics when combined by fibring. The logics analyzed here are classified in protoalgebraic, equivalential and algebraizable. By introducing new categories of algebrizable logics and of deductivizable quasi-varieties, it is stated an isomorphism between these categories. This constitutes an alternative to a similar result found in the literature.

The acquisition and evolution of speech production, discourse and communication can be negatively impacted by brain malformations. We describe, for the first time, a case of developmental dynamic dysphasia (DDD) in a right-handed adolescent boy (subject D) with cortical malformations involving language-eloquent regions (inferior frontal gyrus) in both the left and the right hemispheres. Language evaluation revealed a markedly reduced verbal output affecting phonemic and semantic fluency, phrase and sentence generation and verbal communication in everyday life. Auditory comprehension, repetition, naming, (...) reading and spelling were relatively preserved, but executive function was impaired. Multimodal neuroimaging showed a malformed cerebral cortex with atypical configuration and placement of white matter tracts bilaterally and abnormal callosal fibers. Dichotic listening showed right hemisphere dominance for language and functional magnetic resonance imaging (fMRI) additionally revealed dissociated hemispheric language representation with right frontal activation for phonology and bilateral dominance for semantic processing. Moreover, subject D also had congenital mirror movements (CMM), defined as involuntary movements of one side of the body that mirror intentional movements of the other side. Transcranial magnetic stimulation and fMRI during voluntary unimanual (left and right) hand movements showed bilateral motor cortex recruitment and tractography revealed a lack of decussation of bilateral corticospinal tracts. Genetic testing aimed to detect mutations that disrupt the development of commissural tracts correlating with CMM (e.g., Germline DCC mutations) was negative. Overall, our findings suggest that DDD in subject D resulted from the underdevelopment of the left inferior frontal gyrus with limited capacity for plastic reorganization by its homologous counterpart in the right hemisphere. Corpus callosum anomalies probably contributed to hinder interhemispheric connectivity necessary to compensate language and communication deficits after left frontal involvement. (shrink)