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Since Peirce defined the first operators for three-valued logic, it is usually assumed that he rejected the principle of bivalence. However, I argue that, because bivalence is a principle, the stra...

Classically, vagueness has been considered something bad. It leads to the Sorites paradox, borderline cases, and the (apparent) violation of the logical principle of bivalence. Nevertheless, there have always been scholars claiming that vagueness is also valuable. Many have pointed out that we could not communicate as successfully or efficiently as we do if we would not use vague language. Indeed, we often use vague terms when we could have used more precise ones instead. Many scholars (implicitly or explicitly) assume that we do so because their vagueness has a positive function. But how and in what sense can vagueness be said to have a function or value? This paper is an attempt to give an answer to this question. After clarifying the concepts of vagueness and value, it examines nine arguments for the value of vagueness, which have been discussed in the literature. The (negative) result of this examination is, however, that there is not much reason to believe that vagueness has a value or positive function at all because none of the arguments is conclusive. A tenth argument that has not been discussed so far seems most promising but rests on a solely strategic notion of function.

In the digital age, the crisis of journalism has been exacerbated by antagonistic actors infiltrating the journalistic system without adhering to its norms or logic. Journalism itself has been ill-prepared to respond to this challenge, but journalism theory and research have also had trouble in grasping these phenomena. It is thus the aim of this article to propose a theoretical perspective on a specific set of antagonists characterized by its paradoxical nature. It is ‘the excluded third, included’ as described by Serres, the parasite that is both part of the system and its antagonist. From the perspective of systems theory, the parasite is a subsystem that threatens the integrity of the primary system. Thus, the parasite is defined by the relations that describe its position, its behaviour towards the host system. Due to these peculiarities—this contradiction, this vagueness—it evades a classical bivalent logic. This may be one reason why the paradoxical nature of the antagonist from within, the ‘uninvited dinner guest,’ has not been described as such until now. The parasitic practices follow the logic of the hacker: He is the digital manifestation of Serres’ parasite. Accordingly, parasitic strategies can be described as news hacks whose attack vectors target a system’s weak points with the help of specific strategies. In doing so, they not only change the system output but also compromise its values and exploit its resources.

This essay studies the treatment of Hollywood cinema in the novels of Argentine writer Roberto Arlt, drawing on notions of simulation found in monographs written by sociologists Jose Maria Ramos Mejia and Jose Ingenieros. I argue that Arlt's understanding of the relationship between Hollywood cinema and literature is grounded in a bivalent logic of simulation. On the one hand, Arlt applauds the artistry of film actors and directors, and in his novels he compellingly simulates cinema's innovative techniques of visual representation. On the other, however, he condemns the ideological effects of Hollywood films on mass audiences who, as he sees it, are troublingly attempting to simulate the actions and behaviors of movie stars in order to influence others and get ahead in life. His novels are filled with detailed character studies of such individuals. After reviewing the early-twentieth-century sociological literature on simulation, this essay studies these two sides of Arlt's treatment of Hollywood cinema. It demonstrates that, while Arlt consistently condemns his characters' simulation of cinema, he ultimately must supplement this condemnation with an implicit understanding of artistic simulation that defends the novelist's capacity to simulate the new cinematic medium.

Roman Suszko said that “Obviously, any multiplication of logical values is a mad idea and, in fact, Łukasiewicz did not actualize it.” The aim of the present paper is to qualify this ‘obvious’ statement through a number of logical and philosophical writings by Professor Jan Woleński, all focusing on the nature of truth-values and their multiple uses in philosophy. It results in a reconstruction of such an abstract object, doing justice to what Suszko held a ‘mad’ project within a generalized logic of judgments. Four main issues raised by Woleński will be considered to test the insightfulness of such generalized truth-values, namely: the principle of bivalence, the logic of scepticism, the coherence theory of truth, and nothingness.

We start by presenting various ways to define and to talk about many-valued logic(s). We make the distinction between on the one hand the class of many-valued logics and on the other hand what we call “many-valuedness”: the meta-theory of many-valued logics and the related meta-theoretical framework that is useful for the study of any logical systems. We point out that universal logic, considered as a general theory of logical systems, can be seen as an extension of many-valuedness. After a short story of many-valuedness, stressing that it is present since the beginning of the history of logic in Ancient Greece, we discuss the distinction between dichotomy and polytomy and the possible reduction to bivalence. We then examine the relations between singularity and universality and the connection of many-valuedness with the universe of logical systems. In particular, we have a look at the interrelationship between modal logic, 3-valued logic and paraconsistent logic. We go on by dealing with philosophical aspects and discussing the applications of many-valuedness. We end with some personal recollections regarding Alexander Karpenko, from our first meeting in Ghent, Belgium in 1997, up to our last meeting in Saint Petersburg, Russia in 2016.

La asignación de valores veritativos que le asigna la lógica bivalente al condicional, en la definición tabular estándar, se basa en categorías de índole gnoseológica, incompatibles con el carácter formal y abstracto de las estructuras lógicas. La lógica pretende calificar con categorías gnoseológicas, estructuras formales no-gnoseológicas. Esta asignación evade el rigor de logicidad que demanda toda estructura formal y por lo tanto, carece de necesidad racional.

Aristotle argued that there are no true statements of the form . In his lectures on history of philosophy Hegel does not challenge this view and in his Science of Logic expresses admiration for Aristotle's rebuttal of Zeno of Elea's attempt to find such contradictions in his paradoxes of motion. Yet more than once in his logics Hegel insists that everything is contradictory. I approach this problem from two directions. First, Widerspruch often means, and is understood by Hegel to mean, ‘opposition’ rather than ‘contradiction’ in the strict logical sense. Thus Catullus's simultaneous love and hatred of Clodia is a contradiction, but not an Aristotelian, or formal logical, contradiction. I defuse Hegel's occasional suggestions of Aristotelian contradictions in motion and time. Second, I exploit Hegel's tacit rejection of Aristotle's official bivalence account of truth and falsity, in favour of the view that truth is approached by successive improvements in our inevitably imperfect attempts to attain it. In this respect Hegel's procedure is similar to that of Aristotle himself, who characteristically constructs his own view of metaphysics, physics, ethics, etc., from the imperfect, but not flatly false, opinions of his predecessors. ‘The truth is the whole’, that is, the whole sequence of our attempts to reach it.

This essay explores one of the first distinctively Sinitic reappropriations of Madhyamaka epistemology: Seng Zhao’s essay “Prajnā is Without Knowledge.” Seng Zhao’s work is here read as a deliberate collapse of the traditional Madhyamaka Two Truths into two simultaneous aspects of sagely wisdom, rather than a diachronic means-end relation, arriving at a crypto-Zhuangzian “trivialist” conclusion aimed at undermining epistemological bivalence at its roots. For Seng Zhao, because nothing can be established as true, nothing can be excluded as false. Here the understanding of Emptiness has become not the exclusion of all views, but the inclusion of all views. This is rooted in Seng Zhao’s view that, to use Jan Westerhoff’s terms, the denial of substance-svabhāva is always also implicitly the denial of essence-svabhāva. Seng Zhao move from Emptiness as exclusion to Emptiness as inclusion, and from denial of ontological substance to denial of mutually exclusive determinateness, sets the agenda for the distinctive developments of classical Chinese Buddhist philosophy to come.

An attempt was made to show how we can plausibly commit to mathematical realism. For the purpose of illustration, a defence of natural realism for arithmetic was developed that draws upon the American pragmatist’s, Hillary Putnam’s, early and later writings. Natural realism is the idea that truth is recognition-transcendent and knowable. It was suggested that the natural realist should embrace, globally, what N. Tennant has identified as M-realism (Tennant 1997, 160). M-realism is the idea that one rejects bivalence and assents to the recognition-transcendent requirement. It was argued that over-all—for all domains—the natural realist should be a M-realist, with the aim of clarifying the realist debate for arithmetic.

The problem of future contingents is examined here through the vantage point of another controversy, the one over which answer Aristotle should be credited with. Two answers are attributed to Aristotle. According to the first one, which is nowadays often referred to as the traditional answer, Aristotle argued that, to prevent determinism as the valid conclusion of the argument presented at the beginning of De interpretation 9, one has to deny the universal validity of the principle of bivalence; according to the other, Aristotle accepted the validity of the principle of bivalence, but averted the conclusion of determinism by introducing the notion of indefinite verum. Both answers are examined with a view to shedding some light on this chapter that has kindled so much discussion.

Future Sixth generation (6G) wireless networks are anticipatedto offer entirecoverage, improved spectral, energyandcost-efficient communication.The 6G will enable a network collectivelyand offer seamless wireless connectionsbetween the devices. While the deployment of 5G is ongoing, mobile communication networks are still suffering many basic challenges such as high-energy consumption and operating costs. To address these issues, it is very important to consider and develop new technologies in next-generation mobile communication, namely 6G. Novel machine learning can potentially assist the 6G to obtain better communication. Bivalence Fuzzified Decision Stump Bootstrap Aggregating (BFDSBA) model is introduced for energy and cost efficient communication. The BFDSBA model considers the nodes i.e. devices in the forecasting process before the data communication in the 6G network. The Bootstrap Aggregative technique utilizes set of weak learners as Bivalence Fuzzified Decision Stump. For each device in the network, energy, signal strength, and bandwidth is measured. Based on the estimated resources, efficient devices are selected for the 6G network architectural design. This in turn helps to improvedata communication with lesser cost in6G networks. The result exposesimprovement of BFDSBA model than the conventional methods.

Metal-Organic Frameworks (MOFs) are highly porous materials composed of organic linkers connected by inorganic nodes. A unique subset of MOFs shows switchability, the ability to switch between at least two distinct structures differing significantly in porosity. These unique guest dependent pore opening and closing processes offer new opportunities in gas separation, selective recognition, sensing and energy storage. However, the factors affecting switchability are poorly understood. Network topology, micromechanics of building blocks and their hinges, but also particle size, defects, agglomeration, desolvation conditions etc. are convoluted into the responsiveness of the system. In essence all factors are a consequence of the materials history including synthesis procedure and desolvation but also all subsequent handling steps such as mechanical and adsorption stress leading to a complex interplay of factors which are difficult to express clearly by ordinary writing systems, chemical or mathematical symbols without loss of intuitive understanding. Here we propose a symbolic language for the rationalization of switchability emphasizing the history dependent responsivity of many dynamic frameworks and their stimuli induced 1st order phase transitions. Color representations of the guest and host offer an intuitive understanding of switchability phenomena even for non-experts. The system follows a bivalent logic inspired by Freges Begriffsschrift providing a fundamental logic structure for the rationalization of statements and representation of logic gates.

There is no interesting entailment either way between theism and various forms of realism. Taking its cue from Dummett’s characterisation of realism and his discussion of it with respect to theistic belief, this paper argues both that theism does not follow from realism, and that God cannot be appealed to in order to secure bivalence for an otherwise indeterminate subject matter. In both cases, significant appeal is made to the position that God is not a language user, which in turn is motivated by an account of understanding as aptitude possession. The resulting picture sits comfortably with the apophatism common within living religious traditions and with the view that the philosophy of religion ought to reorientate itself away from metaphysics towards more practical questions.

Various philosophers have long since been attracted to the doctrine that future contingent propositions systematically fail to be true—what is sometimes called the doctrine of the open future. However, open futurists have always struggled to articulate how their view interacts with standard principles of classical logic—most notably, with the Law of Excluded Middle (LEM). For consider the following two claims: (a) Trump will be impeached tomorrow; (b) Trump will not be impeached tomorrow. According to the kind of open futurist at issue, both of these claims may well fail to be true. According to many, however, the disjunction of these claims can be represented as p ∨ ~p—that is, as an instance of LEM. In this essay, however, I wish to defend the view that the disjunction these claims cannot be represented as an instance of p ∨ ~p. And this is for the following reason: the latter claim is not, in fact, the strict negation of the former. More particularly, there is an important semantic distinction between the strict negation of the first claim [~(Trump will be impeached tomorrow)] and the latter claim (Trump will not be impeached tomorrow). However, the viability of this approach has been denied by Thomason (Theoria 36:264–281, 1970), and more recently by MacFarlane (Assessment sensitivity: relative truth and its applications, Oxford University Press, Oxford, 2013) and Cariani and Santorio (Mind 127:129–165. doi: 10.1093/mind/fzw004, 2017), the latter of whom call the denial of the given semantic distinction “scopelessness”. According to these authors, that is, will is “scopeless” with respect to negation; whereas there is perhaps a syntactic distinction between ‘~Will p’ and ‘Will ~p’, there is no corresponding semantic distinction. And if this is so, the approach in question fails. In this paper, then, I criticize the claim that will is “scopeless” with respect to negation. I argue that will is a so-called “neg-raising” predicate—and that, in this light, we can see that the requisite scope distinctions aren’t missing, but are simply being masked. The result: a under-appreciated solution to the problem of future contingents that sees (a) and (b) as contraries, not contradictories.

In the paper, a value assignment for projection operators relating to a quantum system is equated with assignment of truth-values to the propositions associated with these operators. In consequence, the Kochen-Specker theorem (its localized variant, to be exact) can be treated as the statement that a logic of those projection operators does not obey the principle of bivalence. This implies that such a logic has a gappy (partial) semantics or many-valued semantics., This is a pre-print of an article published in Quantum Studies: Mathematics and Foundations. The final authenticated version is available online at: https://doi.org/10.1007/s40509-018-0173-y, Quantum Stud.: Math. Found. (2018)

Ludwik Borkowski’s vast knowledge of philosophy allowed him to put his logical studies in a philosophical context. As a logician, he continued the tradition of the Lvov-Warsaw school. He dealt with the basic issues of the widely understood logic as well as with those having strong philosophical implications (e.g. non-classical logics, the theory of truth, natural deduction, the theory of consequence). He also worked on the theory of definition and the intuitive interpretation of logical results. For Borkowski, logic was an autonomous science whose function is supposed to be ancillary towards the other sciences. Although he did not write any typical philosophical-logical works, investigating philosophical sources, inspirations and the implications of logical results was something he did throughout the whole period of his creative activity.

This paper is inspired by Marcin Tkaczyk’s works and discusses the problem of the necessity of the past (is the past determined?) and its role in the analysis of future contingents. The discussion centers on the statements (accepted by Tkaczyk, but slightly paraphrased)) firstly, that every past state of affairs is determined, and, secondly, that at least some some future states of affairs are contingent. The paper argues that because the first assertion is not justified, the antinomy of future contingents does not arise. The argument uses modal and metalogical devices.

The antinomy of future contingents is here understood as a trilemma whose horns are (a) the thesis of the closed past, (b) the thesis of the open future, and (c) the thesis that all events can be represented at any time. The latter thesis can take different forms, like the principle of bivalence or the thesis of divine foreknowledge. Different versions of (c) lead to different versions of the antinomy itself. The antinomy has been formalized. It has been proven that the theses (a), (b), and (c) make up an inconsistent set but are consistent with each other. Possible solutions have been considered. It has been argued that there are only two global solutions to the antinomy: radical determinism (fatalism) and retroactive causality. The latter solution has been recommended and developed.

Rough sets theory is used to handle uncertain and inconsistent information. While, Pawlak’s decision logic of rough sets is based on classical bivalence logic, this may cause a limitation for the various reasoning. In this study, we propose four-valued logics, as the deduction basis for the decision logic. To provide four-valued semantics to decision logic of rough set, we introduce a Ziarko’s variable precision rough set. As a deductive system, we adopt tableau calculi and define a consequence relation to construct deductive system based on four-valued semantics. Furthermore, weak-negation is introduced to compensate the deduction property of four-value logics. Finally, we discuss Henkin-type proof of the completeness theorem for the system.

A provocative view has it that word meanings are underdetermined and dynamic, frustrating traditional approaches to theorizing about meaning. Peter Ludlow’s Living Words provides some of the philosophical reasons and motivations for accepting one such view, develops some of its details, and explores some of its ramifications. We critically examine some of the arguments in Living Words, paying particular attention to some of Ludlow’s views about the meanings of predicates, preservation of bivalence and the T-schema, and methods of modulating meaning.

The author of the paper critically analyzes a quasi-theory of future contingents ( PFC ) given by Marcin Tkaczyk and proposes his own explication of its theses and terms. The author makes it by introducing operational definitions of temporal and modal concepts, distinguishing between the causal and functional determination, discussing the status of the principle of bivalence, and replacing Tkaczyk’s theses by their new formulations. As a result, the author states, among other things, that (contrary to Tkaczyk) there is no contradiction between the thesis about the opened future and the thesis about divine omniscience, because it requires the causal (but not functional as it is a case) determination between a true proposition and its determined fact. The author also shows that Tkaczyk’s examples of the retroactive causes are not an accurate solution of the antinomy because they are, at most, the examples of the factors which change the picture of the past but not the past itself.

In this paper, we have analyzed a number of solutions to the antinomy between divine foreknowledge and human freedom. If we assume that God is temporal, then a sort of backwards causation of past divine beliefs by future human acts must be acknowledged. Since this solution runs into difficulties, we consider the prospects of the view according to which God is outside time. A timeless and omniscient God seems to imply a B-theory of time and, at least at first glance, seems to jeopardize human freedom. Therefore, we have examined what happens when a non-standard A-theory of time like Fragmentalism is assumed. We demonstrate that in this case the prospects of a timeless view of God are much better: both human freedom and divine knowledge of the results of human choices are preserved if this metaphysics of time is adopted. The costs of this solution are, however, very high. From the logical point of view, it rejects bivalence; from the metaphysical point of view, the world is regarded as fragmentary and incoherent. However, if one is ready to accept these costs, this solution is one of the most successful in the search for a solution to the centuries-old problem of the conciliation between divine foreknowledge and human freedom.

It is argued that truth value of a sentence containing free variables in a context of use (or the truth value of the proposition it expresses in a context of use), just as the reference of the free variables concerned, depends on the assumptions and posits given by the context. However, context may under-determine the reference of a free variable and the truth value of sentences in which it occurs. It is argued that in such cases a free variable has indeterminate reference and a sentence in which it occurs may have indeterminate truth value. On letting, say, x be such that $$x^2=4$$ , the sentence ‘Either $$x=2$$ or $$x=-2$$ ’ is true but the sentence ‘ $$x=2$$ ’ has an indeterminate truth value: it is determinate that the variable x refers to either 2 or $$-2$$ , but it is indeterminate which of the two it refers to, as a result ‘ $$x=2$$ ’ has a truth value but its truth value is indeterminate. The semantic indeterminacy is analysed in a ‘radically’ supervaluational (or plurivaluational) semantic framework closely analogous to the treatment of vagueness in McGee and McLaughlin (South J Philos 33:203–251, 1994, Linguist Philos 27:123–136, 2004) and Smith (Vagueness and degrees of truth, Oxford University Press, Oxford, 2008), which saves bivalence, the T-schema and the truth-functional analysis of the boolean connectives. It is shown that on such an analysis the modality ‘determinately’ is quite clearly not an epistemic modality, avoiding a potential objection raised by Williamson (Vagueness, Routledge, London, 1994) against such ‘radically’ supervaluational treatments of vagueness, and that determinate truth (rather than truth simpliciter) is the semantic value preserved in classically valid arguments. The analysis is contrasted with the epistemicist proposal of Breckenridge and Magidor (Philos Stud 158:377–400, 2012) which implies that (in the given context) ‘ $$x=2$$ ’ has a determinate but unknowable truth value.

The present note offers a proof for separating the truth-values of an arbitrary finitely many valued Łukasiewicz logic by making use of Gray codes.

Anti-exceptionalists about logic maintain that it is continuous with the empirical sciences. Taking anti-exceptionalism for granted, we argue that traditional approaches to explanation are inadequate in the case of logic. We argue that Andrea Woody's functional analysis of explanation is a better fit with logical practice and accounts better for the explanatory role of logical theories.

I examine Quine’s and Davidson’s arguments to the effect that classical logic is the one and only correct logic. This conclusion is drawn from their views on radical translation and interpretation, respectively. I focus on the latter, but I first address, independently, Quine’s argument to the effect that the ‘deviant’ logician, who departs from classical logic, is merely changing the subject. Regarding logical pluralism, the question is whether there is more than one correct logic. I argue that bivalence may be subject matter dependent, but that distribution and the law of excluded middle can probably not be dropped whilst maintaining the standard meanings of the connectives. In discussing the ramifications of the indeterminacy of interpretation, I ask whether it forces Davidsonian interpreters to adopt Dummett’s epistemic conception of truth vis-a-vis their interpretations. And, if so, does this cohere with their attributing a nonepistemic notion of truth to their interpretees? This would be a form of logical pluralism. In addition, I discuss Davidson’s arguments against conceptual schemes. Schemes incommensurable with our own could be construed as wholesale deviant logics, or so I argue. And, if so, their possibility would yield, in turn, the possibility of a radical logical pluralism. I also address Davidson’s application of Tarski’s definition of truth.

In this chapter the integrative property of narrative comprehension is explored, consisting in connecting the paradigmatic and syntagmatic axes of logic and language. Narrative thought is situated in the world of psycho-logic more than logic, a world in which paradigmatic and syntagmatic axes are partially confused and the boundaries are fuzzy. In it, people don not often use logic to solve their problems, but rather, the rules of thumb, and apply a completely different logic of a nonbivalent nature. Many examples of fuzzy concepts are shown such as that of disfrasismo or post-formal logic, and of course stories. In them there is space and movement for processes and categories that are discontinuous but also continuous, paradigmatic and syntagmatic at the same time, because they must represent infinite states of the world. Taleb’s criticism against narrative is discussed and by means of this discussion it is the nature of both everyday narrative reasoning and more refined and elaborated narrative logic is emphasized. This analysis shows how narrative comprehension is a powerful, adaptable and creative means of giving meaning to the other’s speech.

Este artigo aborda a profunda reorganização do campo político-identitário no Brasil, que vinha sendo avançada gradualmente através de redes sociais, mas que ganhou força e projeção repentinas com a vitória de Jair Bolsonaro nas eleições presidenciais de 2018. Partindo de uma perspectiva cibernética inspirada em Gregory Bateson, explora alguns dos dilemas emergentes que a digitalização da política tem colocado para a dupla problemática da identidade e representação na antropologia, a partir de três ângulos: representação populista e formação do “corpo digital do rei”; bivalência reconhecimento-redistribuição; e formação fractal de identidades por meio de mídias digitais.

The method of synthetic tableaux is a cut-based tableau system with synthesizing rules introducing complex formulas. In this paper, we present the method of synthetic tableaux for Classical First-Order Logic, and we propose a strategy of extending the system to first-order theories axiomatized by universal axioms. The strategy was inspired by the works of Negri and von Plato. We illustrate the strategy with two examples: synthetic tableaux systems for identity and for partial order.

International audience; In this paper, we provide a rigorous characterization of consensus solvability in synchronous directed dynamic networks controlled by an arbitrary message adversary using point-set topology: We extend the approach introduced by Alpern and Schneider in 1985 by introducing two novel topologies on the space of infinite executions: the process-view topology, induced by a distance function that relies on the local view of a given process in an execution, and the minimum topology, which is induced by a distance function that focuses on the local view of the process that is the last to distinguish two executions. We establish some simple but powerful topological results, which not only lead to a topological explanation of bivalence arguments, but also provide necessary and sufficient topological conditions on the admissible graph sequences of a message adversary for solving consensus. In particular, we characterize consensus solvability in terms of connectivity of the set of admissible graph sequences. For non-compact message adversaries, which are not limit-closed in the sense that there is a convergent sequence of graph sequences whose limit is not permitted, this requires the exclusion of all "fair" and "unfair" limit sequences that coincide with the forever bivalent runs constructed in bivalence proofs. For both compact and non-compact message adversaries, we also provide tailored characterizations of consensus solvability, i.e., tight conditions for impossibility and existence of algorithms, based on the broadcastability of the connected components of the set of admissible graph sequences.

It is disputed what norm, if any, governs assertion. We address this question by looking at assertions of future contingents: statements about the future that are neither metaphysically necessary nor metaphysically impossible. Many philosophers think that future contingents are not truth apt, which together with a Truth Norm or a Knowledge Norm of assertion implies that assertions of these future contingents are systematically infelicitous.In this article, we argue that our practice of asserting future contingents is incompatible with the view that they are not truth apt. We consider a range of norms of assertion and argue that the best explanation of the data is provided by the view that assertion is governed by the Knowledge Norm.

This paper deals with the changeover from decision tree (bivalent logic) approach to fuzzy logic approach to highway traffic control, particularly to variable speed limits display. The usage of existing knowledge from decision tree control is one of the most suitable methods for identication of new fuzzy model. However, such method introduces several difficulties. These difficulties are described and possible measures are proposed. Several fuzzy logic algorithms were developed and tested by a microsimulation model. The results are presented and the finest algorithm is recommended for testing on the Prague City Ring Road in real conditions. This paper provides a guidance for researchers and practitioners dealing with similar problem formulation.

The contribution of this paper lies with providing a systematically specified and intuitive interpretation pattern and delineating a class of relational structures (frames) and models providing a natural interpretation of logical operators on an underlying propositional calculus of Positive Lattice Logic (the logic of bounded lattices) and subsequently proving a generic completeness theorem for the related class of logics, sometimes collectively referred to as (non-distributive) Generalized Galois Logics (GGL’s).

In this paper we introduce complete game semantics for Product, Godel, BL and SBL logics (game semantics for Łukasiewicz logic are well-known). For each of these logics we introduce a variant of the Renyi-Ulam game whose states are equipped in a natural way with an algebraic structure. Moreover we prove that each logic is complete with respect to the algebras of the states for the corresponding game.

Paraconsistent logics are the formal systems in which absurdities do not trivialise the logic. In this paper, we give Hintikka-style game theoretical semantics for a variety of paraconsistent and non-classical logics. For this purpose, we consider Priest’s Logic of Paradox, Dunn’s First-Degree Entailment, Routleys’ Relevant Logics, McCall’s Connexive Logic and Belnap’s four-valued logic. We also present a game theoretical characterisation of a translation between Logic of Paradox/Kleene’s K3 and S5. We underline how non-classical logics require different verification games and prove the correctness theorems of their respective game theoretical semantics. This allows us to observe that paraconsistent logics break the classical bidirectional connection between winning strategies and truth values.

There is a familiar debate between Russell and Strawson concerning bivalence and ‘the present King of France’. According to the Strawsonian view, ‘The present King of France is bald’ is neither true nor false, whereas, on the Russellian view, that proposition is simply false. In this paper, I develop what I take to be a crucial (and unnoticed) connection between this debate and a different domain where bivalence has been at stake: future contingents. On the familiar ‘Aristotelian’ view, future contingent propositions are neither true nor false. However, I argue that, just as there is a Russellian alternative to the Strawsonian view concerning ‘the present King of France’, according to which the relevant class of propositions all turn out false, so there is a Russellian alternative to the Aristotelian view, according to which future contingents all turn out false, not neither true nor false. The result: contrary to millennia of philosophical tradition, we can be open futurists without denying bivalence.

Pavelka-style completeness, a property relating degrees of provability and truth, was previously studied mainly in the context of logics with continuous connectives. It is known that in some other logics one can use infinitary deduction rule(s) to retain this form of completeness. The present paper offers a systematic study of this idea for fuzzy logics which expand MTL and are given by a fixed standard algebra. We explore the structure of the class of all 'reasonable' expansions of any such logic by rational truth constants and, for several prominent cases, provide axiomatizations of particular expansions enjoying the Pavelka-style completeness.

We provide a methodology to introduce proof search oriented calculi for a large class of many-valued logics, and a sufficient condition for their Co-NP completeness. Our results apply to many well known logics including Godel, Łukasiewicz and Product Logic, as well as Hajek's Basic Fuzzy Logic.

The present article studies the connection of scientific reasoning with fuzzy logic. Induction and deduction are the two main types of human reasoning. Although deduction is the basis of the scientific method, almost all the scientific progress (with pure mathematics being probably the unique exception) has its roots to inductive reasoning. Fuzzy logic gives to the disdainful by the classical/bivalent logic induction its proper place and importance as a fundamental component of the scientific reasoning. The error of induction is transferred to deductive reasoning through its premises. Consequently, although deduction is always a valid process, it is not an infallible method. Thus, there is a need of quantifying the degree of truth not only of the inductive, but also of the deductive arguments. In the former case, probability and statistics and of course fuzzy logic in cases of imprecision are the tools available for this purpose. In the latter case, the Bayesian probabilities play a dominant role. As many specialists argue nowadays, the whole science could be viewed as a Bayesian process. A timely example, concerning the validity of the viruses’ tests, is presented, illustrating the importance of the Bayesian processes for scientific reasoning.

This chapter distinguishes respecting religious Otherness as Otherness from exclusivism and religious pluralism: The exclusivist fails to respect the religious Other, pluralists (e.g., John Hick) fail to respect the Otherness of the religious Other (rather, they regard it to be sameness in disguise). The kind of interreligious dialogue implied in respecting religious Otherness differs from the kind implied in exclusivism and pluralism: The exclusivist does not engage in a serious dialogue since she possesses the truth and the religious Other does not, the pluralist is interested only in the commonalities with the religious Other. Different from that, respecting religious Otherness as Otherness implies a “robust interreligious dialogue” in which believers mirror their own religion in light of the other religion and learn from each other.In order to get such a dialogue off the ground, we should abandon the principle of bivalence in the religious realm. Rather than considering religious beliefs which differ from our own to be false, we should acknowledge that the person holding them could be justified to do so (although we continue disagreeing with her). Abandoning bivalent truth in favour of the concept of justification is the heart of the “justified religious difference approach” recommended in this chapter. It makes a robust interreligious dialogue, differing from the kind of dialogues implied in exclusivism and pluralism, possible.