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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.

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.

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.

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.

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.

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.

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.

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.

In this article, I try to identify the right connexion between some metaphysical theses (eternalism and determinism) and some semantic theses (closed and open future). Having established that, I will then posit two principles (Metaphysical-Semantical Determination Principle and Semantical-Metaphysical Indetermination Principle), making them available to philosophical debates, such as the debate about future contingents and its variants. The principles in question summarize the contribution that the relations between those theses can offer when well established. We will eventually see that we cannot deduce those metaphysical theses from the semantic theses in question, although we can move from the metaphysical theses to the semantic theses., {"references":["Aristotle (1966). Categories and De Interpretatione. J. H. Ackrill (trans.), Oxford: Clarendon Press.","Armstrong, David Malet (1997). A World of States of Affairs. Cambridge: Cambridge University Press. https://doi.org/10.1017/CBO9780511583308","Balaguer, Mark (2016). «Anti–Metaphycalism, Necessity, and Temporal Ontology». Philosophy and Phenomenological Research 92: pp. 145–167. https://doi.org/10.1111/phpr.12129","Belnap, Nuel (1992). «Branching Space–Time». Synthese 92: pp. 385–434. https://doi.org/10.1007/BF00414289","Belnap, Nuel, e Green, Mitchell. (1994). «Indeterminism and the Thin Red Line». Philosophical Perspectives 8: pp. 365–388. https://doi.org/10.2307/2214178","Earman, John (1986). A Primer On Determinism. Dordrecht: Reidel. https://doi.org/10.1007/978-94-010-9072-8","Everett, Hugh (1957). «Relative State Formulation of Quantum Mechanics». Reviews of Modern Physics 29: pp. 454–462. https://doi.org/10.1103/RevModPhys.29.454","Fleck, Almeida (1997). O problema dos futuros contingentes. Porto Alegre: EDIPUCRS, pp. 12–13.","Haack, Susan (1998). Filosofia das Lógicas. Tradução de Cezar Augusto Mortari e Luiz Henrique Dutra. São Paulo: Editora UNESP, pp. 274–277.","Hugh, Rice (2015). «Fatalism». In: Stanford Encyclopedia of Philosophy, Acessado em: Março, 15 de 2017: http://plato.stanford.edu/archives/sum2015/entries/fatalism/.","Inwagen, Peter van (1975). «The incompatibility of Free Will and Determinism». Philosophical Studies 27: pp.185–199. https://doi.org/10.1007/BF01624156","Inwagen, Peter Van (1983). An Essay of Free Will. Oxford: Oxford University Press.","Łukasiewicz, Jan (1967). «Philosophical remarks on many–valued systems of propositional logic». In: S. McCall (ed.), Polish Logic, Oxford: Oxford University Press, pp. 40–65. Original de 1930.","Markosian, Ned (1995). «The open past». Philosophical Studies 79, no. 1: pp. 95–105. https://doi.org/10.1007/BF00989786","Mctaggart, J. Ellis (1908). «The Unreality of Time». Mind 18: pp. 457–484. https://doi.org/10.1093/mind/XVII.4.457","Ockham, William (1969). Predestination, God's Foreknowledge, and Future Contingents (trans: Marilyn McCord Adams and Norman Kretzmann), New York.","Putnam, Hilary (1967). «Time and Physical Geometry». Journal of Philosophy, 64, pp. 240–247. https://doi.org/10.2307/2024493","Rea, Michael e Finch, Alicia (2008). «Presentism and Ockham's Way Out». Oxford Studies in Philosophy of Religion, pp. 1–17.","Rea, Michael (2003). «Four–Dimensionalism». In: Michael Loux and Dean Zimmerman (ed.), The Oxford Handbook of Metaphysics. Oxford: Oxford University Press, pp. 246–280.","Rea, Michael (2006). «Presentism and Fatalism». Australasian Journal of Philosophy 84, no. 4: pp. 511–524. https://doi.org/10.1080/00048400601079003","Rosenkranz, Sven (2012). «In Defence of Ockhamism». Philosophia 40, no. 3, pp. 617–31. https://doi.org/10.1007/s11406-011-9337-2","Russell, Bertrand (1915). «On the Experience of Time». The Monist 25: pp. 212–33. https://doi.org/10.5840/monist191525217","Ryle, Gilbert (1953). Dilemmas. Cambridge, Cambridge University Press.","Schlick, Moritz (1954). «Die Kausalitaet in der gegenwartigen Physik». Naturwissenschaften 19: pp. 145–162. https://doi.org/10.1007/BF01516406","Sehon, Scott (2011). «A flawed conception of determinism in the Consequence Argument». Analysis 71, no. 1: pp. 30–38. https://doi.org/10.1093/analys/anq117","Sider, Theodore (2001). Four–Dimensionalism. An Ontology of Persistence and Time. Oxford: Clarendon Press. https://doi.org/10.1093/019924443X.001.0001","Smart, Jack (1963). Philosophy and Scientific Realism. London: Routledge & Kegan Paul.","Smart, Jack (2008). «The tenseless theory of time», in: Theodore Sider, John Hawthorne and Dean W. Zimmerman (eds.), Contemporary Debates in Metaphysics, pp. 226–238.","Vranas, Peter B. M (2005). «Do cry over spilt milk: Possibly you can change the past». Monist 88, no. 3: pp. 370–377. https://doi.org/10.5840/monist200588315."]}

In this paper we intend to outline an introduction to Situation Theory as an approach to the liar paradoxes. This idea was first presented by the work of Barwise and Etchemendy (in their (1987)). First (section 1) we introduce the paradoxes in their most appealing and important versions. Second (section 2) we show that non-classical approaches on the problem usually get puzzled by the revenge problem on one side and loss of expressive power on the other side. Last (sections 3 and 4), we present Situation Theory and try to show how it is capable of solving the old paradoxes and blocking revenge. The price we pay on this view is universality, since it would allow a new revenge situated liar. We don’t intend to address the problem of universality here, but we try at least to motivate the reader to make sense of this theory.

Fregean theories of descriptions as terms have to deal with improper descriptions. To save bivalence various proposals have been made that involve assigning referents to improper descriptions. While bivalence is indeed saved, there is a price to be paid. Instantiations of the same general scheme, viz. the one and only individual that is F and G is G, are not only allowed but even required to have different truth values.

In matters of personal taste, faultless disagreement occurs between people who disagree over what is tasty, fun, etc., in those cases when each of these people seems equally far from the objective truth. Faultless disagreement is often taken as evidence that truth is relative. This article aims to help us avoid the truth-relativist conclusion. The article, however, does not argue directly against relativism; instead, the article defends non-relative truth constructively, aiming to explain faultless disagreement with the resources of semantic contextualism. To this end the article describes and advocates a contextualist solution inspired by supervaluationist truth-value gap approaches. The solution presented here, however, does not require truth value gaps; it preserves both logical bivalence and non-relative truth, even while it acknowledges and explains the possibility of faultless disagreement. The solution is motivated by the correlation between assertions’ being true and their being useful. This correlation, furthermore, is used not only to tell which assertions are true, but also to determine which linguistic intuitions are reliable.

In this paper I first take a critical look at Grube’s allegiance to the idea that bivalence should be rejected as it can serve the cause of religious toleration. I argue that bivalence is not what Grube says it is, and that rejection of bivalence comes at a very high price that we should not be willing to pay. Next I analyze Grube’s argument for religious toleration – an argument that does not involve the rejection of bivalence. I argue that the argument is unconvincing because there exists no relation between epistemic justification and toleration. (I also note problems with the notion of ‘justification’ as used by Grube.)

This paper responds to an essay by Dirk-Martin Grube published in this same journal issue. Special attention is drawn to issues such as tolerance, respect, and the recognition of otherness regarding religious beliefs. Grube interestingly suggests that the focus on religious truth should be replaced by a focus on justification. Some critical remarks on these suggestions are made.

In this paper, I provide a novel approach to the issue of religious diversity: I reject classical pluralist approaches to the issue, such as John Hick’s, and argue that their attempts to construe commonalities between the religions are contrived. The reason that they attempt to find commonalities at all costs is that they presuppose a bivalent notion of truth according to which that which is different is false. I suggest that, in order to get a robust theory on religious diversity off the ground, we should rely on the notion of justification rather than that of bivalent truth. Justification is pluralizable, dependent upon the (epistemic) circumstances, whereas bivalent truth is not. Armed with a pluralizable notion of justification, we can acknowledge that other religious beliefs are genuinely different without necessarily being false: They can be justified, given the (epistemic) circumstances a believer of a different religion is in. Perceiving religious differences in this way allows to liberate the int...

In this work, we combine features from Justification Logics and Logics of Plausibility-Based Beliefs to build a logic for Multi-Agent Systems where each agent can explicitly state his justification for believing in a given sentence. Our logic is a normal modal logic based on the standard Kripke semantics, where we provide a semantic definition for the evidence terms and define the notion of plausible evidence for an agent, based on plausibility relations in the model. As we deal with beliefs, justifications can be faulty and unreliable. In our logic, agents can disagree not only over whether a sentence is true or false, but also on whether some evidence is a valid justification for a sentence or not. After defining our logic and its semantics, we provide a strongly complete axiomatic system for it, show that it has the finite model property, analyze the complexity of its Model-Checking Problem and show that its Satisfiability Problem has the same complexity as the one from basic modal logics. Thus, this logic seems to be a good first step for the development of a dynamic logic that can model the processes of argumentation and debate in Multi-Agent Systems.

In this essay I respond to three of the most forceful objections to the open view of the future. It is argued that a) open view advocates must deny bivalence; b) the open view offers no theodicy advantages over classical theism; and c) the open view can’t assure believers that God can work all things to the better (Rom. 8:28). I argue that the first objection is premised on an inadequate assessment of future tensed propositions, the second is rooted in an inadequate assessment of free will, and the third is grounded in an inadequate assessment of God’s intelligence.

This work presents an overview of four different approaches to the problem of future contingency and determinism in temporal logics. All of them are bivalent, viz. they share the assumption that propositions concerning future contingent facts have a determinate truth-value (true or false). We introduce Ockhamism, Peirceanism, Actualism and T × W semantics, the four most relevant bivalent alternatives in this area, and compare them from the point of view of their expressiveness and their underlying metaphysics of time.

In this paper we study the relationships between a family of ALC-like fuzzy description logics (FDLs) defined over left-continuous t-norms and some many-valued multi-modal logics (MMLs). We analyze these relationships in both directions, that is, how to merge FDLs into MMLs and vice-versa. The analysis starts from the relationships between the languages to reach systematically the deeper level of reasoning tasks. At this level we are able to truly investigate both formalisms from each other point of view. Finally, the results concerning translations between reasoning tasks are applied in order to get decidability and complexity bounds., F. Esteva and À. García-Cerdaña acknowledge support from the Spanish MICINN project RASO TIN2015-71799-C2-1-P (MINECO/FEDER). À. García-Cerdaña also acknowledges support from the Spanish MICINN project Lógica algebraica y lógicas no clásicas ( MTM 2011-25747 ), and the grant 2014SGR-788 from the Generalitat de Catalunya . Esteva also acknowledges support via grant 2014SGR-118 from the Generalitat de Catalunya .

This paper considers logics which are formally dual to intuitionistic logic in order to investigate a co-constructive logic for proofs and refutations. This is philosophically motivated by a set of problems regarding the nature of constructive truth, and its relation to falsity. It is well known both that intuitionism can not deal constructively with negative information, and that defining falsity by means of intuitionistic negation leads, under widely-held assumptions, to a justification of bivalence. For example, we do not want to equate falsity with the non-existence of a proof since this would render a statement such as “pi is transcendental” false prior to 1882. In addition, the intuitionist account of negation as shorthand for the derivation of absurdity is inadequate, particularly outside of purely mathematical contexts. To deal with these issues, I investigate the dual of intuitionistic logic, co-intuitionistic logic, as a logic of refutation, alongside intuitionistic logic of proofs. Direct proof and refutation are dual to each other, and are constructive, whilst there also exist syntactic, weak, negations within both logics. In this respect, the logic of refutation is weakly paraconsistent in the sense that it allows for statements for which, neither they, nor their negation, are refuted. I provide a proof theory for the co-constructive logic, a formal dualizing map between the logics, and a Kripke-style semantics. This is given an intuitive philosophical rendering in a re-interpretation of Kolmogorov's logic of problems.

We apply the Triangular Fuzzy Assessment Model (TFAM) for analogical reasoning skills assessment. The TFAM is a new original model based on the Centre of Gravity (COG) defuzzification technique, which we have properly adapted and used in earlier papers as an assessment method of several human activities. The main idea of the TFAM is the replacement of the rectangles appearing in the graph of the COG technique by isosceles triangles sharing common parts. In this way, we can treat better the ambiguous cases of scores being at the boundaries between two successive linguistic characterizations (grades) of the level of the individuals’ performance. An application is also presented illustrating our results in practice, where the TFAM is compared with two traditional assessment methods (calculation of the means and of the GPA index) based on principles of the bivalent logic (yes-no).

A fitness landscape presents the relationship between individual and its reproductive success in evolutionary computation (EC). However, discrete and approximate landscape in an original search space may not support enough and accurate information for EC search, especially in interactive EC (IEC). The fitness landscape of human subjective evaluation in IEC is very difficult and impossible to model, even with a hypothesis of what its definition might be. In this paper, we propose a method to establish a human model in projected high dimensional search space by kernel classification for enhancing IEC search. Because bivalent logic is a simplest perceptual paradigm, the human model is established by considering this paradigm principle. In feature space, we design a linear classifier as a human model to obtain user preference knowledge, which cannot be supported linearly in original discrete search space. The human model is established by this method for predicting potential perceptual knowledge of human. With the human model, we design an evolution control method to enhance IEC search. From experimental evaluation results with a pseudo-IEC user, our proposed model and method can enhance IEC search significantly.

This dialogue between Achilles and the Tortoise – in the spirit of those of Carroll and Hofstadter – argues against the idea, identified with the “traditional” interpretation of Aristotle’s “sea battle argument”, that future contingents are an exception to the Principle of Bivalence. It presents examples of correct everyday predictions, without which one would not be able to decide and to act; however, doing this is incompatible with the belief that the content of these predictions lacks a truth-value. The cost of using a non-classical logic to cope with that may be too high for Stagirite’s defenders, and they would still need to explain why our ordinary predictions seem to have a binary truth-value. In the end, the paper suggests that the problem of future contingents – and of free will – is not a logical problem at all, but rather a limit on what an agent can believe before taking a decision. Keywords: future contingents, bivalence, beliefs.

This paper proposes a computational framework to reason with conflicting and gradual evidence. The framework is a synthesis of Dung’s seminal work in argumentation semantics with multi-valued logic. Abstract grounded semantics is used to identify the conditions under which a conclusion can be accepted, while multi-valued logic operators are used to quantify the degree of truth of such conditions. We propose a truth-compositional recursive computation based on the notion of irrelevant arguments, and we discuss examples using the major multi-valued logics: Godel’s, Zadeh’s and Łukasiewicz's logic.

We extend the framework of Inductive Logic to Second Order languages and introduce Wilmers' Principle, a rational principle for probability functions on Second Order languages. We derive a representation theorem for functions satisfying this principle and investigate its relationship to the first order principles of Regularity and Super Regularity.

Fuzzy logic due to its nature of characterizing each case with multiple values offers is a rich field of resources covering the assessment of situations characterized by a degree of fuzziness and/or uncertainty. In this paper, we present two different fuzzy assessment models: The Centre of Gravity (COG) model and Trapezoidal Fuzzy Assessment Model (TRFAM). The last one is a new model covering the ambiguous cases being at the boundaries between two successive assessment intervals. An application (students' assessment) is also presented, through which the above methods are compared to each other and also with two traditional assessment methods based on principles of bivalent logic (the calculation of means and of the GPA index). Some useful conclusions are drawn about the characteristics of the above fuzzy assessment models.

Fuzzy logic due to its nature of characterizing each case with multiple values offers a rich field of resources covering the assessment of situations characterized by a degree of vagueness and/or uncertainty. In this paper, we apply a new trapezoidal fuzzy assessment model (TRFAM) for measuring students’ mathematical modeling (MM) skills. TRFAM is actually a variation of the commonly used in fuzzy logic centre of gravity (COG) defuzzification technique, which we have properly adapted and utilized in earlier papers as an assessment model. Our COG and TRFAM models focus on students’ quality performance by assigning greater coefficients to the higher scores. A classroom experiment is also presented, illustrating our results in practice. Through this experiment the above two models are compared to each other and also with two traditional assessment methods based on principles of bivalent logic (the calculation of means and of the GPA index) and some useful conclusions are drawn.

One well known approach to the soritical paradoxes is epistemicism, the view that propositions involving vague notions have definite truth values, though it is impossible in principle to know what they are. Recently, Paul Horwich has extended this approach to the liar paradox, arguing that the liar proposition has a truth value, though it is impossible to know which one it is. The main virtue of the epistemicist approach is that it need not reject classical logic, and in particular the unrestricted acceptance of the principle of bivalence and law of excluded middle. Regardless of its success in solving the soritical paradoxes, the epistemicist approach faces a number of independent objections when it is applied to the liar paradox. I argue that the approach does not offer a satisfying, stable response to the paradoxes—not in general, and not for a minimalist about truth like Horwich.

We present a unifying semantic and proof-theoretical framework for investigating depth-bounded approximations to Boolean Logic in which the number of nested applications of a single structural rule, representing the classical Principle of Bivalence (classical cut), is bounded above by a fixed natural number. These approximations provide a hierarchy of tractable logical systems that indefinitely converge to classical propositional logic. The operational rules are shared by all approximation systems and are justified by an “informational semantics” whereby the meaning of a logical operator is specified solely in terms of the information that is actually possessed by an agent.