As used by professional logicians today, is the name of their chosen subject singular or plural, "logic" or "logics"? This is a special case of a more general question. For instance, an algebraist might write a book entitled "Algebra", which is about algebras. Though many mathematicians are not aware of it, logic today most decidedly has its plural aspect. Indeed, it always did. Classical logic, which mathematicians often tend to identify with the entirety of logic, was in place roughly by (...) the beginning of the twentieth century. Since then a wide range of so-called non-classical logics have been developed. But indeed, before the creation of classical logic, there were multiple versions of logic, some of them more-or-less formalized. The current growing interest in medieval and ancient European and Asian logics has brought much of this back to modern awareness. Perhaps a later volume in this series will look at the history from a contemporary viewpoint. But that is not our task here. This is the second volume in a series called Landscapes in Logic. The intention of the series is to present reports illustrating the interplay between contemporary work in logic and mainstream mathematics. Of course this is both vague and overly ambitious, and must result in heterogeneous collections. The first volume in the series, Contemporary Logic and Computing, appeared in 2020. The contents divided plausibly into topics from contemporary logic, and from contemporary computing. The present volume is more diverse, and includes articles about both classical and non-classical logics, sometimes from the semantic side and sometimes from the proof-theoretic side. Some articles are primarily technical, often algebraic, while others are more philosophical in nature. Many fit into multiple categories. This multiplicity should not be seen as a defect. The papers here do not just explore logics house by house, but say something about their general neighborhoods as well. (shrink)

Dans cet article, je présente une approche sémantique de l’analyse de la fonction de la métaphore du paysage dans la biologie de l’évolution. Le concept de paysage adaptatif a suscité une attention considérable dans la philosophie de la biologie récente. La plupart des auteurs ont considéré ce concept de l’une des deux manières suivantes: en tant qu’outil heuristique, comme partie intrinsèque de modèles mathématiques robustes, ou comme un ensemble définissable d’analogies sur lesquelles les modèles sont basés et testés. Chacune de (...) ces visions conduit à la conclusion que la valeur de la métaphore du paysage dépend seulement du succès des modèles que sous-tend la métaphore, en vue de représenter adéquatement la dynamique de l’évolution. J’essaie de montrer que cette conclusion, ainsi que les visions qui y conduisent, ne tiennent pas compte d’épisodes importants dans l’histoire de la métaphore du langage. Ces visions proviennent plutôt de thèses générales, en philosophie des sciences, quant au rôle des métaphores dans les théories scientifiques. L’analyse sémantique que je propose met en lumière le fait que la fonction première du concept de relief adaptatif, au cours de la synthèse évolutionniste, a été de servir de cadre général d’unification conceptuelle, qui a rendu possible la conciliation de phénomènes empiriques hétérogènes. De ce point de vue, la métaphore du paysage est un outil linguistique-théorique qui ne doit pas être abandonné (et qui ne l’est de fait pas) suite à la falsification des modèles construits et interprétés au moyen de la métaphore. (shrink)

According to Pigliucci and Kaplan, there is a revolution underway in how we understand fitness landscapes. Recent models suggest that a perennial problem in these landscapes—how to get from one peak across a fitness valley to another peak—is, in fact, non-existent. In this paper I assess the structure and the extent of Pigliucci and Kaplan’s proposed revolution and argue for two points. First, I provide an alternative interpretation of what underwrites this revolution, motivated by some recent (...) work on model-based science. Second, I show that the implications of this revolution need to carefully assessed depending on question being asked, for peak-shifting is not central to all evolutionary questions that fitness landscapes have been used to explore. (shrink)

There is considerable correspondence between theories and models used in biology and the social sciences. One type of model that is in use in both biology and the social sciences is the fitness landscape model. The properties of the fitness landscape model have been applied rather freely in the social domain. This is partly due to the versatility of the model, but it is also due to the difficulties of transferring a model to another domain. We will demonstrate (...) that in order to transfer the biological fitness landscape model to the social science it needs to be substantially modified. We argue that the syntactic structure of the model can remain unaltered, whilst the semantic dimension requires considerable modification in order to fit the specific phenomena in the social sciences. We will first discuss the origin as well as the basic properties of the model. Subsequently, we will demonstrate the considerations and modifications pertaining to such a transfer by showing how and why we altered the model to analyse collective decision-making processes. We will demonstrate that the properties of the target domain allow for a transfer of the syntactic structure but don’t tolerate the semantic transfer. (shrink)

The concepts of adaptation and fitness have such an appeal that they have been used in other scientific domains, including the social sciences. One particular aspect of this theory transfer concerns the so-called fitness landscape models. At first sight, fitness landscapes visualize how an agent, of any kind, relates to its environment, how its position is conditional because of the mutual interaction with other agents, and the potential routes towards improved fitness. The allure of (...) class='Hi'>fitness landscapes is first and foremost that it represents a complex story about adaptation and fitness in one coherent image. Different accounts of fitness landscapes in different domains in the social sciences suggest that the properties and functions of fitness landscapes are attributed rather freely. These differences are testimony of the model’s versatility. At the same time, one will notice that the different approaches can also create ambiguity about the exact meaning and role of fitness landscapes in the social sciences. This article presents an extensive literature survey of the diverging interpretations and uses of fitness landscapes in the social sciences and discusses the implications in terms of how these models inform scientific inquiry. (shrink)

This article examines two questions about scientists’ search for knowledge. First, which search strategies generate discoveries effectively? Second, is it advantageous to diversify search strategies? We argue pace Weisberg and Muldoon, “Epistemic Landscapes and the Division of Cognitive Labor”, that, on the first question, a search strategy that deliberately seeks novel research approaches need not be optimal. On the second question, we argue they have not shown epistemic reasons exist for the division of cognitive labor, identifying the errors that (...) led to their conclusions. Furthermore, we generalize the epistemic landscape model, showing that one should be skeptical about the benefits of social learning in epistemically complex environments. (shrink)

I forgive the slight spin of sloganeering conveyed by the motto so frequently cited by proponents of a cosmos chock full of organisms: "Life will fed a way." Life is resilient and quite capable (especially in bacterial form) of living in the most damnably improbable places-from nearly boiling ponds in Yellowstone National Park to tiny pores in rocks as deep as two miles below the earth's surface. But even this degree of resilience must work within limits; if life ever evolved (...) on the Martian surface during its initial billion years with running water, the planet's later desiccation probably extinguished our solar system's second experiment in advanced carbon chemistry. (shrink)

Medical and Taoist sources written or compiled during the Han dynasty provide the first accounts, reflections, and theories on the self, on disease, and on the relationships between humans and the world in which they live. This chapter focuses on this particular period of time which, in fact, lays important foundations for Chinese society and culture. Relying mainly on medical and Taoist sources, it firstly sheds light on how the self was thought of and represented at this time and examines (...) how the links between human beings and their environment were conceived of. It then focuses on what, for humans and in the environment, were thought of as potential threats to health and how the image of an ideal landscape was thus constructed, that is, a landscape into which humans could fit perfectly and live healthy lives. Finally, we analyze how this ideal landscape was supposed to work to preserve good health in humans. (shrink)

Few metaphors in biology are more enduring than the idea of Adaptive Landscapes, originally proposed by Sewall Wright (1932) as a way to visually present to an audience of typically non- mathematically savvy biologists his ideas about the relative role of natural selection and genetic drift in the course of evolution. The metaphor, how- ever, was born troubled, not the least reason for which is the fact that Wright presented different diagrams in his original paper that simply can- not (...) refer to the same concept and are therefore hard to reconcile with each other (Pigliucci 2008). For instance, in some usages, the landscape’s non- fitness axes represent combinations of individual genotypes (which cannot sensibly be aligned on a linear axis, and accordingly were drawn by Wright as polyhedrons of increasing dimensionality). In other usages, however, the points on the diagram represent allele or genotypic frequencies, and so are actually populations, not individuals (and these can indeed be coherently represented along continuous axes). (shrink)

One of the most characteristic features of Comparative Literature in terms of methodological practice is that of operating in “in between” spaces. Not only does this feature suggest the comparative approach as something which originates through movement, thus making it imperative for the researcher to deal with the notion of mobility, it also characterizes many of the concepts with which it operates. Considering the possibility, as well as the fertility, of practicing this methodology in the analysis and critique of contemporary (...) visual art, we understand that it fits the analysis of any enterprise regarding the in-betweens of visual and verbal texts. These fundamental aspects were elected for a comparative analysis of two visuals artists whose œuvres operate in in-between spaces between the visual and the verbal as much as between the self and the Other. José Leonilson (Brazil 1957-1993) and Louise Bourgeois (France/EUA 1911-2010) reveal, through a comparative analysis, creative and constitutive actions which elaborate a space we could best understand through the image of a seaside landscape where the line we try to draw to divide the saltwater from the sand never stands. But, in what manners could the constituted poetic space created by them be of significance for a broader spectrum than the literary interest? In our understanding, Leonilson’s and Bourgeois’s poetics operate through a silent hearing of the Other, might that be their loved ones, the stone or cloths. This conceptual notion, required for the creative action, thus establishes a particular notion of balance between them and the Other. It is this precise aspect that also operates the mobility of the notion of love through their œuvre, and through the election of personal emotional narratives as the thriving force for creation. And what could be more needed nowadays, here as elsewhere, than considering together with Leonilson’s and Bourgeois’ images that love shall be the perpetual moving space that at times nears, and later distances us from each other? (shrink)

This MPhil dissertation presents a novel account of teleological explanations in biology. I outline the “shorthand approach” to such explanations, on which they are taken to convey implicit evolutionary explanations. “Selected effects” accounts of teleological explanation dominate recent literature, but they struggle to accommodate teleological explanations of complex traits built through cumulative selection. I articulate the general notion of a landscape explanation, which, applied to biology, explains the evolution of complex features in a population by citing salient features of the (...) population’s fitness landscape. I show that such explanations lend themselves to a teleological shorthand. I close with remarks concerning when a teleological explanation of a trait is legitimate, and why teleological language strikes us as appropriate when we give evolutionary explanations. (shrink)

The adaptive landscape is one of the most widely used metaphors in evolutionary biology. It is created by plotting fitness against phenotypes or genotypes in a given environment. The shape of the landscape is crucial in predicting the outcome of evolution: whether evolution will result in populations reaching predictable end points, or whether multiple evolutionary outcomes are more likely. In a more applied sense, the landscape will determine whether organisms will evolve to lose ‘costly’ resistance to antibiotics, herbicides or (...) pesticides when the use of the control agent is stopped. Laboratory populations of microbes allow evolution to be observed in real time and, as such, provide key insights into the topology of adaptive landscapes. BioEssays 27:1167–1173, 2005. © 2005 Wiley Periodicals, Inc. (shrink)

The field of eSports is undergoing a process of developing and evolving with irresistible forces. The process witnesses the ever-refreshing and hybrid meanings and definitions of Sports and eSports in the digital era of technology empowerment and advancing artificial intelligence. This paper calls us to re-construct the meanings and sporting values of eSports, re-evaluate the eSports landscape, going beyond the debate ‘Are eSports Sports?’ and move to re-examine the contextual nature and values of Sports and eSports, as well as their (...) interweaving relationships in contemporary society. It is of significance to explore the way in which the intelligent embodiment of eSports and the virtualisation of traditional sports integrate with each other, offering the potential for fitness and physical exercises and practices in real and virtual spaces. Meanwhile, crucial digital ethics issues are emerging in the field of eSports, potentially challenging and alerting the eSports industry to take timely measurements to maintain the Sport’s integrity. (shrink)

The concepts of adaptive/fitness landscapes and adaptive peaks are a central part of much of contemporary evolutionary biology; the concepts are introduced in introductory texts, developed in more detail in graduate-level treatments, and are used extensively in papers published in the major journals in the field. The appeal of visualizing the process of evolution in terms of the movement of populations on such landscapes is very strong; as one becomes familiar with the metaphor, one often develops the (...) feeling that it is possible to gain deep insights into evolution by thinking about the movement of populations on landscapes consisting of adaptive valleys and peaks. But, since Wright first introduced the metaphor in 1932, the metaphor has been the subject of persistent confusion, from equivocation over just what the features of the landscape are meant to represent to how we ought to expect the landscapes to look. Recent advances—conceptual, empirical, and computational—have pointed towards the inadequacy and indeed incoherence of the landscapes as usually pictured. I argue that attempts to reform the metaphor are misguided; it is time to give up the pictorial metaphor of the landscape entirely and rely instead on the results of formal modeling, however difficult such results are to understand in ‘intuitive’ terms. (shrink)

This commentary considers the role of Socratic questioning in Alien Landscapes? I discuss the three roles that Glover sees Socratic questioning playing in psychiatry: 1. Questioning to clarify problems, 2. Questioning to treat symptoms, 3. Questioning to reconstruct lives. Although I am broadly sympathetic to the idea that philosophical conversations can help us conceptualise, and deal with, mental distress, I raise two concerns. First, is there any way of providing courses of transformative Socratic questioning cheaply? Second, how close is (...) the connection between helping individuals to develop systems of belief and value that fit epistemic norms and helping them to live flourishing lives? (shrink)

Covid-19 brought back memories of past pandemics. In society, a pandemic imaginary was installed, framing an imaginary landscape, alongside a rationalized pandemic intellect to which the media contributed a lot. We live immersed in tele technologies, adding present to the past and past to the present. At a time when home confinement became the rule, this was even more highlighted. In this screen technological Era, social practices were even more subject to the five great sociotechnical effects that condition information and (...) the way it articulates memory and the present: ubiquity, instantaneity, acceleration, mobilization and presentism. This article intends to demonstrate the presence of the imaginary of past pandemics in the present (Applying Einstein's Theory of General Relativity), the way in which we appropriate these memories to create solutions and the way in which we mix the present with the solutions that came from the past. (shrink)

Despite the fact that they are in most respects environmentally benign, electricity-generating wind turbines frequently encounter a great deal of resistance. Much of this resistance is aesthetic in character; wind turbines somehow do not "fit" in the landscape. On one (classical) view, landscapes are beautiful to the extent that they are "scenic," well-balanced compositions. But wind turbines introduce a discordant note, they are out of "scale." On another (ecological) view, landscapes are beautiful if their various elements form a (...) stable and integrated organic whole. But wind turbines are difficult to integrate into the biotic community; at least in certain respects, they are like "weeds." Moreover, there is a reason why the 100-meter, three bladed wind turbines now favored by the industry cannot very well be accommodated to any landscape view. They are, as Albert Borgmann would put it, characteristic of contemporary technology, distanced "devices" for the production of a commodity rather than "things" with which one can engage. It follows that the only way in which the aesthetic resistance to wind turbines can be overcome is to make them more "thing-like." One such "thing-like" turbine is discussed. (shrink)

Despite the fact that they are in most respects environmentally benign, electricity-generating wind turbines frequently encounter a great deal of resistance. Much of this resistance is aesthetic in character; wind turbines somehow do not "fit" in the landscape. On one view, landscapes are beautiful to the extent that they are "scenic," well-balanced compositions. But wind turbines introduce a discordant note, they are out of "scale." On another view, landscapes are beautiful if their various elements form a stable and (...) integrated organic whole. But wind turbines are difficult to integrate into the biotic community; at least in certain respects, they are like "weeds." Moreover, there is a reason why the 100-meter, three bladed wind turbines now favored by the industry cannot very well be accommodated to any landscape view. They are, as Albert Borgmann would put it, characteristic of contemporary technology, distanced "devices" for the production of a commodity rather than "things" with which one can engage. It follows that the only way in which the aesthetic resistance to wind turbines can be overcome is to make them more "thing-like." One such "thing-like" turbine is discussed. (shrink)

In 1988, David Hull presented an evolutionary account of science. This was a direct analogy to evolutionary accounts of biological adaptation, and part of a generalized view of Darwinian selection accounts that he based upon the Universal Darwinism of Richard Dawkins. Criticisms of this view were made by, among others, Kim Sterelny, which led to it gaining only limited acceptance. Some of these criticisms are, I will argue, no longer valid in the light of developments in the formal modeling of (...) evolution, in particular that of Sergey Gavrilets’ work on adaptive landscapes. If we can usefully recast the Hullian view of science as being driven by selection in terms of Gavrilets’ and Kaufmann’s view of there being “giant components” of high-fitness networks through any realistic adaptive landscape, we may now find it useful to ask what the adaptive pressures on science are, and to extend the metaphor into a full analogy. This is in effect to reconcile the Fisherianism of the Dawkins–Hull approach to selection and replicators, with a Wrightean drift account of social constructionist views of science, preserving, it is to be hoped, the valuable aspects of both. (shrink)

Allen Carlson's aesthetics of nature contends that a deepening in the scientific knowledge of natural objects and environments is required to achieve an appropriate aesthetic appreciation of them. This 'scientific cognitivism' is often presented as supporting the emergence and development of environmental awareness as well as a theory consistent with the requirements of environmentalism that have been set out by Carlson himself. But Carlson's view about the aesthetic appreciation of contemporary agricultural landscapes gives more relevance to their functional (...) class='Hi'>fitness for human purposes than to scientific cognitivism. It will be shown here how this different treatment weakens the link between Carlson's work and his requirements of environmentalism. (shrink)

I consider recent uses of the notion of neutrality in evolutionary biology and ecology, questioning their relevance to the kind of explanation recently labeled ‘topological explanation’. Focusing on fitness landscapes and genotype-phenotype maps, I explore the explanatory uses of neutral subspaces, as modeled in two perspectives: hyperdimensional fitness landscapes and RNA sequence-structure maps. I argue that topological properties of such spaces account for features of evolutionary systems: respectively, capacity for adaptive evolution toward global optima and mutational (...) robustness of genotypes. Thus many models appealing to “neutral” manifolds provide topological alternatives to hypothetical mechanisms. (shrink)

What makes it the case that an utterance constitutes an illocutionary act of a given kind? This is the central question of speech-act theory. Answers to it—i.e., theories of speech acts—have proliferated. Our main goal in this chapter is to clarify the logical space into which these different theories fit. -/- We begin, in Section 1, by dividing theories of speech acts into five families, each distinguished from the others by its account of the key ingredients in illocutionary acts. Are (...) speech acts fundamentally a matter of convention or intention? Or should we instead think of them in terms of the psychological states they express, in terms of the effects that it is their function to produce, or in terms of the norms that govern them? In Section 2, we take up the highly influential idea that speech acts can be understood in terms of their effects on a conversation’s context or “score”. Part of why this idea has been so useful is that it allows speech-act theorists from the five families to engage at a level of abstraction that elides their foundational disagreements. In Section 3, we investigate some of the motivations for the traditional distinction between propositional content and illocutionary force, and some of the ways in which this distinction has been undermined by recent work. In Section 4, we survey some of the ways in which speech-act theory has been applied to issues outside semantics and pragmatics, narrowly construed. (shrink)

According to evolutionary theory, emotions are psychological mechanisms that have evolved to enhance fitness in specific situations by motivating appropriate (adaptive) behavior. Taking this perspective, a previous study examined the relationship between mood and preference for natural environments. It reported that participants’ anxiety level was associated with a preference for landscapes offering what Appleton called "refuge," while participants’ anger and cheerfulness were both associated with a preference for landscapes offering what Appleton called "prospect." We attempted to replicate (...) these results and to improve on the study by experimentally manipulating mood. Using a between-subjects design, 80 participants were instructed to self-induce one of four moods: anger, sadness, anxiety, or joy. After the mood induction, they viewed fourteen landscape photographs and recorded the seven most preferred. It was hypothesized that subjects experiencing anger or joy would prefer landscapes rich in "prospect" features, whereas participants experiencing sadness or anxiety would prefer landscapes rich in "refuge" features. In contrast to the previous study, the predictions were not supported: artificially induced moods may not provide ecological validity as a test of the "mood as motivator" model; alternatively, the first study may have reported an alpha error. To see whether the model has practical value, we recommend a study of landscape preference using participants with clinically significant levels of mood dysphoria. (shrink)

Yih, Uusberg, Qian, and Gross (2019) proposed an appraisal approach to help conceptualize five different states that researchers have used as neutral control conditions. This approach has the potential to enrich our understanding of these states and how they function. Here, we discuss four points to keep in mind while implementing this approach with the hope that these ideas will further assist researchers in understanding how neutrality might fit within the affective landscape.

Atran & Norenzayan's (A&N's) analysis fits with other perspectives on evoked culture: Cultural beliefs might emerge simply from the fact that people share a common cognitive architecture. But no perspective on culture can be complete without incorporating the unstoppable role of communication. The evolutionary landscape of culture will be most completely mapped by theories that describe specifically how communication translates evolved cognitive canals into cultural beliefs.

The text treats the theme of cruelty starting from how it appears in the everyday dominant ideology. If we want to feel the pulse of our modern ideological landscape, we cannot ignore the fact that it has recently been severely shaken by the Russian aggression against Ukraine. The war in Ukraine has repeatedly been called cruel, and cruelty in general is today unanimously seen as something reprehensible and repulsive. But the same is true of torture, which, although in principle prosecuted, (...) is carried out in secret. And if every war is cruel, what does the statement “the war in Ukraine is cruel” mean? In what contexts does it fit? The text explores this question on several levels, beginning with modern understandings of war and cruelty, moving to the broader historical context in which the statement is made, and finally asking whether it means that we still have one foot in the 20th century in some sense. Following Badiou’s work _The Century_, which emphasises the role of the passion of the real, war (which is intended to end all wars), and cruelty in the twentieth century, this statement also means that the twentieth century is not (yet) over in a sense, and that this century may be settling accounts with itself (again) with the war in Ukraine. (shrink)

A considerable number of areas of bioscience, including gene and drug discovery, metabolic engineering for the biotechnological improvement of organisms, and the processes of natural and directed evolution, are best viewed in terms of a ‘landscape’ representing a large search space of possible solutions or experiments populated by a considerably smaller number of actual solutions that then emerge. This is what makes these problems ‘hard’, but as such these are to be seen as combinatorial optimisation problems that are best attacked (...) by heuristic methods known from that field. Such landscapes, which may also represent or include multiple objectives, are effectively modelled in silico, with modern active learning algorithms such as those based on Darwinian evolution providing guidance, using existing knowledge, as to what is the ‘best’ experiment to do next. An awareness, and the application, of these methods can thereby enhance the scientific discovery process considerably. This analysis fits comfortably with an emerging epistemology that sees scientific reasoning, the search for solutions, and scientific discovery as Bayesian processes. (shrink)

The primary impediment to formulating a general theory for adaptive evolution has been the unknown distribution of fitness effects for new beneficial mutations. By applying extreme value theory, Gillespie circumvented this issue in his mutational landscape model for the adaptation of DNA sequences, and Orr recently extended Gillespie's model, generating testable predictions regarding the course of adaptive evolution. Here we provide the first empirical examination of this model, using a single-stranded DNA bacteriophage related to phiX174, and find that our (...) data are consistent with Orr's predictions, provided that the model is adjusted to incorporate mutation bias. Orr's work suggests that there may be generalities in adaptive molecular evolution that transcend the biological details of a system, but we show that for the model to be useful as a predictive or inferential tool, some adjustments for the biology of the system will be necessary. (shrink)

This chapter presents the two faces of Britain; on the one hand, there is the idyllic representation of it as “an astounding collection of busy cities, towns rife with history, quaint villages, looming castle, cathedrals, mansions and abbeys,” and on the other there is the darker and more realistic view of it as “a cosmopolitan mix of Third and First Worlds, chauffeurs and beggars, the stubbornly traditional and the proudly avant garde.” It also explains how, despite the fact that the (...) national iconography used to present Britain does not fit with actuality, it still persists as a representation of its landscape. (shrink)

This research article focuses on the use of the water metaphor in column 16 of the Hodayot. Previous scholarship has often concentrated on the garden metaphor in this section, particularly on its intertextual links with the book of Isaiah. By drawing on contemporary metaphor theory, in particular blending theory, I show how the author of the Hodayot creates poetry through a multiple blended network of garden and water metaphors, and how aspects of the linguistic form of the poem, in particular (...) the phrase מבוע מים חיים‘well of living waters’, can be read as an expression of this blend. The aim of this study is to contribute (1) to the study of the Hodayot and its poetic practices, against older dismissals of the poetic quality of the Hodayot, and (2) to our understanding of semantic constellations and the conceptual world of ancient Judaism. Contribution: This article fits within the scope of HTS’s theme ‘Historical Thought and Source Interpretation’ as it contributes to our insights into ancient Jewish thought through the interpretation of a religious source text using metaphor theory. (shrink)

This is a thorough treatment of first-order modal logic. The book covers such issues as quantification, equality (including a treatment of Frege's morning star/evening star puzzle), the notion of existence, non-rigid constants and function symbols, predicate abstraction, the distinction between nonexistence and nondesignation, and definite descriptions, borrowing from both Fregean and Russellian paradigms.

Bilattices, due to M. Ginsberg, are a family of truth value spaces that allow elegantly for missing or conflicting information. The simplest example is Belnap’s four-valued logic, based on classical two-valued logic. Among other examples are those based on finite many-valued logics, and on probabilistic valued logic. A fixed point semantics is developed for logic programming, allowing any bilattice as the space of truth values. The mathematics is little more complex than in the classical two-valued setting, but the result provides (...) a natural semantics for distributed logic programs, including those involving confidence factors. The classical two-valued and the Kripke/Kleene three-valued semantics become special cases, since the logics involved are natural sublogics of Belnap’s logic, the logic given by the simplest bilattice. (shrink)

A new semantics is presented for the logic of proofs (LP), [1, 2], based on the intuition that it is a logic of explicit knowledge. This semantics is used to give new proofs of several basic results concerning LP. In particular, the realization of S4 into LP is established in a way that carefully examines and explicates the role of the + operator. Finally connections are made with the conventional approach, via soundness and completeness results.

Kleene’s strong three-valued logic extends naturally to a four-valued logic proposed by Belnap. We introduce a guard connective into Belnap’s logic and consider a few of its properties. Then we show that by using it four-valued analogs of Kleene’s weak three-valued logic, and the asymmetric logic of Lisp are also available. We propose an extension of these ideas to the family of distributive bilattices. Finally we show that for bilinear bilattices the extensions do not produce any new equivalences.

Two families of many-valued modal logics are investigated. Semantically, one family is characterized using Kripke models that allow formulas to take values in a finite many-valued logic, at each possible world. The second family generalizes this to allow the accessibility relation between worlds also to be many-valued. Gentzen sequent calculi are given for both versions, and soundness and completeness are established.