Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucleus algebras unify these examples and further extend them to the non-commutative setting. We study their structure, establish a representation theorem for them in terms of twist structures and conuclei that results in a categorical adjunction, and explore situations where the representation is actually an isomorphism. In the latter case, the adjunction is elevated to a categorical (...) equivalence. By applying this representation to the original motivating special cases we bring to the surface their underlying similarities. (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.

A recent paper by Jakl, Jung and Pultr succeeded for the first time in establishing a very natural link between bilattice logic and the duality theory of d-frames and bitopological spaces. In this paper we further exploit, extend and investigate this link from an algebraic and a logical point of view. In particular, we introduce classes of algebras that extend bilattices, d-frames and N4-lattices to a setting in which the negation is not necessarily involutive, and we study corresponding logics. We (...) provide product representation theorems for these algebras, as well as completeness, algebraizability results for the corresponding logics. (shrink)

Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of (...) ZF, and can be expanded with a paraconsistent negation *, thus obtaining a paraconsistent model of ZF. The logic (PS3 ,*) coincides (up to language) with da Costa and D'Ottaviano logic J3, a 3-valued paraconsistent logic that have been proposed independently in the literature by several authors and with different motivations such as CluNs, LFI1 and MPT. We propose in this paper a family of algebraic models of ZFC based on LPT0, another linguistic variant of J3 introduced by us in 2016. The semantics of LPT0, as well as of its first-order version QLPT0, is given by twist structures defined over Boolean agebras. From this, it is possible to adapt the standard Boolean-valued models of (classical) ZFC to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. We argue that the implication operator of LPT0 is more suitable for a paraconsistent set theory than the implication of PS3, since it allows for genuinely inconsistent sets w such that [(w = w)] = 1/2 . This implication is not a 'reasonable implication' as defined by Löwe and Tarafder. This suggests that 'reasonable implication algebras' are just one way to define a paraconsistent set theory. Our twist-valued models are adapted to provide a class of twist-valued models for (PS3,*), thus generalizing Löwe and Tarafder result. It is shown that they are in fact models of ZFC (not only of ZF). (shrink)

We propose in this paper a family of algebraic models of ZFC based on the three-valued paraconsistent logic LPT0, a linguistic variant of da Costa and D’Ottaviano’s logic J3. The semantics is given by twist structures defined over complete Boolean agebras. The Boolean-valued models of ZFC are adapted to twist-valued models of an expansion of ZFC by adding a paraconsistent negation. This allows for inconsistent sets w satisfying ‘not (w = w)’, where ‘not’ stands for the paraconsistent negation. (...) Finally, our framework is adapted to provide a class of twist-valued models generalizing Löwe and Tarafder’s model based on logic (PS 3,∗), showing that they are paraconsistent models of ZFC. The present approach offers more options for investigating independence results in paraconsistent set theory. (shrink)

In sum, flashbacks and foreflashes are commonplace in narrative, and such rearrangements in the telling of a story seem to leave us not only with a story but with very much the same story.1 . . . Will no disparity between the order of telling and the order of occurrence destroy either the basic identity or the narrative status of any story? An exception seems ready at hand: suppose we simply run our film...backwards. The result, though indeed a story, seems (...) hardly to be the same story in any usual sense . . . Does cinematic narrative actually differ this sharply from narrative in a series of snapshots or in words? I think not. Our first impulse with any tale when the order of telling is clear is to take the order of occurrence to be the same as the order of telling; we then make any needed corrections in accord with temporal indications given in the narrative and with our antecedent knowledge both of what happened and of causal processes in general. But discrepancy between order of telling and order of occurrence cannot always be discovered instantaneously—or at all. If our series of snapshots is shown in reverse order at normal speed, we readily detect the reversal; for we know that a race begins at the starting gate, ends at the finish line, and so on. Even if the pictures do not show the starting gate or finish line or other identifiable parts of the track, we are not deceived, for we know that horses do not run backward. But when the film is run backward, such clues and considerations usually cannot be brought to bear soon enough, and we momentarily mistake the direction of the actions filmed. A little time is needed to make the correction. What seemed like a drastic difference between film and other forms of narrative amounts to nothing more than this lag. · 1. In an obvious and important sense. Of course, whether two version are properly said to be of the same story—or of the same world—depends upon which of many permissible interpretations of sameness is understood; but that need not trouble us here. Nelson Goodman is emeritus professor of philosophy at Harvard and the founder of both Project Zero and the Harvard Dance Center. His works include The Structure of Appearance; Fact, Fiction, and Forecast, and Ways of Worldmaking. His contributions to Critical Inquiry are "The Status of Style" , "Metaphor as Moonlighting" , and "The Telling and the Told". (shrink)

In sum, flashbacks and foreflashes are commonplace in narrative, and such rearrangements in the telling of a story seem to leave us not only with a story but with very much the same story.1... Will no disparity between the order of telling and the order of occurrence destroy either the basic identity or the narrative status of any story? An exception seems ready at hand: suppose we simply run our film...backwards. The result, though indeed a story, seems hardly to be (...) the same story in any usual sense... Does cinematic narrative actually differ this sharply from narrative in a series of snapshots or in words? I think not. Our first impulse with any tale when the order of telling is clear is to take the order of occurrence to be the same as the order of telling; we then make any needed corrections in accord with temporal indications given in the narrative and with our antecedent knowledge both of what happened and of causal processes in general. But discrepancy between order of telling and order of occurrence cannot always be discovered instantaneously—or at all. If our series of snapshots is shown in reverse order at normal speed, we readily detect the reversal; for we know that a race begins at the starting gate, ends at the finish line, and so on. Even if the pictures do not show the starting gate or finish line or other identifiable parts of the track, we are not deceived, for we know that horses do not run backward. But when the film is run backward, such clues and considerations usually cannot be brought to bear soon enough, and we momentarily mistake the direction of the actions filmed. A little time is needed to make the correction. What seemed like a drastic difference between film and other forms of narrative amounts to nothing more than this lag. · 1. In an obvious and important sense. Of course, whether two version are properly said to be of the same story—or of the same world—depends upon which of many permissible interpretations of sameness is understood; but that need not trouble us here. Nelson Goodman is emeritus professor of philosophy at Harvard and the founder of both Project Zero and the Harvard Dance Center. His works include The Structure of Appearance; Fact, Fiction, and Forecast, and Ways of Worldmaking. His contributions to Critical Inquiry are "The Status of Style", "Metaphor as Moonlighting", and "The Telling and the Told". (shrink)

The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of QmbC, (...) the simpler quantified LFI expanding classical logic, will be analyzed in detail. An axiomatic extension of QmbC called QLFI1o is also studied, which is equivalent to the quantified version of da Costa and D'Ottaviano 3-valued logic J3. The semantical structures for this logic turn out to be Tarkian structures based on twist structures. The expansion of QmbC and QLFI1o with a standard equality predicate is also considered. (shrink)

Contrary to what the name suggests, the recent work of Howard Margolis (1987) and Ronald Giere (1988) demonstrates that the “cognitive turn” in the philosophy of science is not simply the application of cognitive science to the study of science. For one thing, neither one is what Jerry Fodor (1981) has called a “methodological solipsist,” that is, someone who wants to account for thought processes without presupposing an account of the world of which those thoughts are about. Margolis, in fact, (...) comes perilously close to Fodor’s anti-cognitivist foe, J. J. Gibson (1979), whose “ecological” perspective requires that an organism’s thought processes be specified in terms of structures in the environment, “affordances,” capable of satisfying the organism’s desire to know. The Margolian focus on overcoming “barriers” to alternative “habits of mind,” as the psychic basis of Kuhn’s paradigm shifts, only serves to highlight this broadly “functional” side of thinking that typically has no place in cognitive science. (shrink)

O-minimal structures have long been thought to occupy the base of a hierarchy of ordered structures, in analogy with the role that strongly minimal structures play with respect to stable theories. This is the first in an anticipated series of papers whose aim is the development of model theory for ordered structures of rank greater than one. A class of ordered structures to which a notion of finite rank can be assigned, the decomposable structures, is introduced here. These include all (...) ordered structures definable in o-minimal structures. The principal result in this paper, Theorem 5.1, asserts roughly that a decomposable structure [Formula: see text] can be partitioned into finitely many definable subsets such that on each set the restriction of < is a "twisted lexicographic" order. As a consequence, for all n and linear orders ≺ definable on a subset X ⊆ Mn in an o-minimal structure [Formula: see text], there is a definable partition of X such that the restriction of ≺ to each set in the partition is "lexicographic". (shrink)

This article examines the conceptualisation of materialities in feminist theory through two paradigmatic examples: (French) materialist feminism and new materialisms. What can be interpreted as an opposition between different paradigms can also be disrupted as long as we define what matters as a relation or a process rather than a substance or a lost paradise to which we should return. New materialisms indeed help to investigate aspects such as corporeality, human/non-human interaction and textures, but the role of feminist materialism is (...) invaluable in highlighting the social structures of power relations; more than ever, it makes a decisive contribution to the understanding of domination, such as the social relations and hierarchies implied in femosecularism conceptualised in this article. Ultimately, the tool of hybridised materialisms aims to articulate the theoretical perspective of materialist feminism with that of the new materialisms – in order to avoid the binarism between materiality and culture. (shrink)

This paper makes the assumption that organ transplantation is, under some conditions at least, a proper use of communal medical resources. Proceeding from this assumption, the author: (1) sketches the history of the problem; (2) briefly examines the prevalent models of communal structure and offers an alternate version; (3) discusses notions of justice and obligation derived from these different models; (4) applies these to the practice of harvesting organs for transplantation; and then (5) offers a different process for harvesting (...) organs from the newly dead.If community is viewed as united by a set of shred goals and common values among which the value of community itself is important, then certain reciprocal obligations among members obtain. I suggest that routine salvage of organs from the newly dead be instituted but that it be routine salvage with a twist: rather early in life all members of the community are given the opportunity to refuse but their refusal carries the reciprocal condition that they cannot later become the recipients of that which they refuse to others. (shrink)

Contemporary TV shows, characterized by their complex narrative form, are designed to reveal the simple. They enable characters and viewers alike to discover the ordinary by coupling the everyday to an underworld populated by criminals, demons, vampires, and other kinds of “lowlifes.” I will argue here that the structure of the Möbius strip, or Escher twist, draws a particular aesthetic appeal at the intersection of these worlds. I call these twists uncanny in the Cavellian sense that the underworld, (...) looking strangely familiar, has the capacity of making the ordinary look unfamiliar, inherently strange, and unstable. Rather than allowing us to judge the demonic or illegal, they disclose what is normally inaccessible to us precisely because it is so ordinary and simple, so familiar and in plain sight. I will support this idea of Escher-twisting from one world to another by analyzing examples from Twin Peaks (ABC 1990-2, Showtime 2017), The Sopranos (HBO 1999-2007), Awake (NBC 2012), and Ozark (Netflix 2017–2022). (shrink)

Structures of multisubunit RNA polymerases strongly differ from the many known structures of single subunit DNA and RNA polymerases. However, in functional complexes of these diverse enzymes, nucleic acids take a similar course through the active center. This finding allows superposition of diverse polymerases and reveals features that are functionally equivalent. The entering DNA duplex is bent by almost 90° with respect to the exiting template–product duplex. At the point of bending, a dramatic twist between subsequent DNA template bases (...) aligns the “coding“ base with the binding site for the incoming nucleoside triphosphate (NTP). The NTP enters through an opening that is found in all polymerases, and, in most cases, binds between an α‐helix and two catalytic metal ions. Subsequent phosphodiester bond formation adds a new base pair to the exiting template–product duplex, which is always bound from the minor groove side. All polymerases may undergo “induced fit” upon nucleic acid binding, but the underlying conformational changes differ. BioEssays 24:724–729, 2002. © 2002 Wiley Periodicals, Inc. (shrink)

The present study is an attempt to relate the multicomponent response of the cytoskeleton (CSK), evaluated in twisted living adherent cells, to the heterogeneity of the cytoskeletal structure - evaluated both experimentally by means of 3D reconstructions, and theoretically considering the predictions given by two tensegrity models composed of (four and six) compressive elements and (respectively 12 and 24) tensile elements. Using magnetic twisting cytometry in which beads are attached to integrin receptors linked to the actin CSK of living (...) adherent epithelial cells, we specifically measured the elastic CSK response at quasi equilibrium state and partitioned this response in terms of cortical and cytosolic contributions with a two-component model (i.e., a series of two Voigt bodies). These two CSK components were found to be prestressed and exhibited a stress-hardening response which both characterize tensegrity behaviour with however significant differences: compared to the cytosolic component, the cortical cytoskeleton appears to be a faster responding component, being a less prestressed and easily deformable structure. The discrepancies in elastic behaviour between the cortical and cytosolic CSK components may be understood on the basis of prestress tensegrity model predictions, given that the length and number of constitutive actin elements are taken into account. (shrink)

Many metaphysicians often appeal to Hume’s dictum (HD), according to which there are no necessary connections between distinct entities (or states of entities), in order to resist theories that commit us to such connections. Some have argued that HD is an unsupported dogma of metaphysics. But theories that commit us to necessary connections between distinct goings-on can also be resisted by invoking a normative twist on HD, which I call the Humean Solvent (HS): “Do not connect distinct entities (or (...) states of entities) beyond necessity”. HS is a principle of structural parsimony – assuming that a theory is structurally more parsimonious than another when the latter is committed to a more connected ontology than the former is. Just as Ockham’s ‘razor’ encourages us to cut down superfluous ontological commitments, the Humean ‘solvent’ encourages us to dissolve dispensable metaphysical glue: we ought not to glue elements of our ontology beyond necessity. HS has both a qualitative and a quantitative dimension: qualitatively, it encourages us to avoid using metaphysical glues that are unnecessarily strong, the strongest of which being metaphysically necessary connections; quantitatively, it encourages us not to metaphysically glue things that need no gluing. Thus, given HS, other things being equal, what is worst is a theory that entails that everything is metaphysically necessarily connected to anything else and what is best is a theory that leaves all things loose and separable. In this paper, I will first compare HD and HS as grounds for paradigmatic Humean doctrines in contemporary metaphysics, then I will argue that structural parsimony is neither a variety of ontological nor of ideological parsimony; finally, I will offer an argument for HS. (shrink)

The recognition of extracellular molecules by cell surface receptors is the principal mechanism used by cells to sense their environment. Consequently, signals transduced as a result of these interactions make a major contribution to the regulation of cellular phenotype. Historically, particular emphasis has been placed on elucidating the intracellular consequences of growth factor and cytokine binding to cells. In addition to these interactions, however, cells are usually in intimate contact with a further source of complex structural and functional information, namely (...) immobilised extracellular matrix and/or cell surface adhesion proteins. A key question in recent years has been whether cells use the myriad of adhesion protein‐receptor interactions purely for structural and migratory function, or whether these interactions also make a more varied contribution to cell phenotype. Here we review dynamic aspects of the function of one major class of adhesion receptor, the integrins. In particular, we focus on the evidence for shape changes in integrin molecules, the mechanisms responsible for regulating ligand binding, and the signals transduced following integrin occupancy. (shrink)

In US history, much human rights policy developed in four waves during the twentieth century. These waves were triggered by similar circumstances, but all proved short-lived as structural constraints such as limited US power over other countries’ domestic actions, competing US policy priorities, a US hesitance to join multilateral institutions, and the continued domestic political weakness of human rights advocates led to setbacks. As Barack Obama took office, his campaign comments and the past patterns led to widespread expectations that he (...) would introduce new human rights initiatives. His policies, though, would continue to face the structural constraints and would be affected by the Bush administration’s legacy. It was predictable that many of Obama’s initiatives would be only partially implemented and only partially successful. As expected, Obama’s first years have seen mixed results, but the Obama administration has advanced US human rights policies sufficiently in half-dozen key areas to say that a fifth wave of human rights policy development is underway. (shrink)

What would your life be like if you committed to something larger than yourself? Find out in the newest book from global transformation thought leader Lynne Twist. How does one person make a difference in the world? People constantly seek to discover meaning in their lives, but as humans take on the challenges facing us in this decade and beyond, we're searching for it now more than ever. Living a Committed Life demonstrates the power of dedication that goes beyond (...) the self and teaches how to live a committed life that enables you to draw on resources and capacities from your most authentic self. In five parts, Lynne Twist shows how to make and keep commitments, engage in individual and collective action, and discover ways to connect and collaborate to make a difference. By sharing stories and perspectives from her life, Twist reveals her unique experience as a thought leader and activist in multiple causes, from ending world hunger and protecting the Amazon rainforest to empowering women's leadership. The book presents the guiding principles that have enabled her own success and that turn inspiration into action for everyone. (shrink)

This paper is about the dilemma raised against musical ontology by Roger Scruton, in his The Aesthetics of Music: either musical ontology is about certain mind-independent “things” and so music is left out of the picture, or it is about an “intentional object” and so its puzzles are susceptible of an arbitrary answer. I argue the dilemma is merely apparent and deny that musical works can be identified with sound structures, whether or not conceived as abstract entities. The general idea (...) is this: both Platonism and nominalism about musical works are a kind of fetishism: musical works are not “things”, in Danto’s sense of “mere real things”; they rather involve complex relationships between objects, events, and different kinds of functional properties. For this, I draw on Levinson and Howell’s notion of indication, combined with Searle’s approach to institutional reality... with a little twist of my own. (shrink)

Although research integrity practices in institutional settings is not a new area of study, because of its foundational importance in university settings it remains a topic worthy of study. In addition, rarely are all members of the university community included as participants in studies focused upon research integrity and ethics. Thus, to add to the existent literature, the authors investigated research integrity practices in a medium-sized Midwestern polytechnic university setting, including 467 participants from across all divisions of the university community. (...) This mixed data survey study was comprised of six sections; presented is information for two sections—sample demographics and research integrity. The demographics appear reflective of those of the larger survey, as well as the university setting of study. In the research integrity section there were two parts—one qualitative and one quantitative. Implications with regard to research integrity and ethics in the institutional setting of study are presented. (shrink)

Although research integrity practices in institutional settings is not a new area of study, because of its foundational importance in university settings it remains a topic worthy of study. In addition, rarely are all members of the university community included as participants in studies focused upon research integrity and ethics. Thus, to add to the existent literature, the authors investigated research integrity practices in a medium-sized Midwestern polytechnic university setting, including 467 participants from across all divisions of the university community. (...) This mixed data survey study was comprised of six sections; presented is information for two sections—sample demographics and research integrity. The demographics appear reflective of those of the larger survey, as well as the university setting of study. In the research integrity section there were two parts—one qualitative and one quantitative. Implications with regard to research integrity and ethics in the institutional setting of study are presented. (shrink)

The well-known algebraic semantics and topological semantics for intuitionistic logic (Int) is here extended to Wansing's bi-intuitionistic logic (2Int). The logic 2Int is also characterised by a quasi-twist structure semantics, which leads to an alternative topological characterisation of 2Int. Later, notions of Fregean negation and of unilateralisation are proposed. The logic 2Int is extended with a ‘Fregean negation’ connective ∼, obtaining 2Int∼, and it is showed that the logic N4⋆ (an extension of Nelson's paraconsistent logic) results to be (...) the unilateralisation of 2Int∼ via ∼. The logic 2Int∼ is also characterised by a Kripke-style semantics, a twist structure semantics and a topological semantics. (shrink)

Nucleosomes are the basic elements of chromatin structure. Polyamines, such as spermine and spermidine, are small ubiquitous molecules absolutely required for cell growth. Photoaffinity polyamines bind to specific locations in nucleosomes and can change the helical twist of DNA in nucleosomes. Acetylation of polyamines reduces their affinity for DNA and nucleosomes, thus the helical twist of DNA in nucleosomes could be regulated by cells through acetylation. I suggest that histone and polyamine acetylation act synergistically to modulate chromatin (...) structure. On naked DNA, the photoaffinity spermine bound preferentially to a specific ‘TATA’ sequence element, suggesting that polyamines may be involved in the unusual chromatin structure in this region. Further work is needed to test whether the specificities shown by photoaffinity polyamines are also shown by cellular polyamines; such experiments are now feasible. (shrink)

The results of the Progress in International Reading Literacy Study (PIRLS 2001) were published in 2003. In addition to data about the reading achievements of 10?year?olds in 35 countries, PIRLS 2001 also collected questionnaire information from children, their teachers, headteachers and parents. The results showed not just how well students can perform in various reading tasks, but also the relationship between reading abilities and other characteristics, including the characteristics of their homes and schools, the students' attitudes to reading, reading enjoyment, (...) self?confidence, engagement and perceptions of their reading abilities. Surprisingly enough, children in England were reported as having poor attitudes to reading, compared to children in many other countries, despite high achievement on the reading tests. This paper raises some concerns about the interpretation of results from the study, suggesting a more complex picture than that presented in the summary index published in 2003. Our secondary analysis of the attitude and achievement data from PIRLS shows that pupils with low ability levels have misunderstood the questions which tested their attitudes towards reading. The authors point out that caution is needed when making cross?country comparisons to avoid naïve approaches to interpretation. (shrink)

Earlier algebraic semantics for Belnapian modal logics were defined in terms of twist-structures over modal algebras. In this paper we introduce the class of BK -lattices, show that this class coincides with the abstract closure of the class of twist-structures, and it forms a variety. We prove that the lattice of subvarieties of the variety of BK -lattices is dually isomorphic to the lattice of extensions of Belnapian modal logic BK . Finally, we describe invariants determining a (...) class='Hi'>twist-structure over a modal algebra. (shrink)

Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap structures are given. Specifically, (...) a formal study of swap structures for LFIs is developed, by adapting concepts of universal algebra to multialgebras in a suitable way. A decomposition theorem similar to Birkhoff’s representation theorem is obtained for each class of swap structures. Moreover, when applied to the 3-valued algebraizable logics J3 and Ciore, their classes of algebraic models are retrieved, and the swap structures semantics become twist structures semantics. This fact, together with the existence of a functor from the category of Boolean algebras to the category of swap structures for each LFI, suggests that swap structures can be seen as non-deterministic twist structures. This opens new avenues for dealing with non-algebraizable logics by the more general methodology of multialgebraic semantics. (shrink)

This work treats the problem of axiomatizing the truth and falsity consequence relations, $ \vDash _t $ and $ \vDash _f $, determined via truth and falsity orderings on the trilattice SIXTEEN₃. The approach is based on a representation of SIXTEEN₃ as a twist-structure over the two-element Boolean algebra.

In 2016, Béziau introduces a restricted notion of paraconsistency, the so-called genuine paraconsistency. A logic is genuine paraconsistent if it rejects the laws $\varphi,\neg \varphi \vdash \psi$ and $\vdash \neg (\varphi \wedge \neg \varphi)$. In that paper, the author analyzes, among the three-valued logics, which of them satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above-mentioned are $\vdash \varphi, \neg \varphi$ and $\neg (\varphi \vee \neg \varphi) \vdash$. We call genuine paracomplete logics those rejecting (...) the mentioned properties. We present here an analysis of the three-valued genuine paracomplete logics. A very natural twist structures semantics for these logics is also found in a systematic way. This semantics produces automatically a simple and elegant Hilbert-style characterization for all these logics. Finally, we introduce the logic LGP which is genuine paracomplete is not genuine paraconsistent, not even paraconsistent and cannot be characterized by a single finite logical matrix. (shrink)