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510 found
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  1. Knowledge & Logic: Towards a Science of Knowledge.Luis M. Augusto - manuscript
    Just started a new book. The aim is to establish a science of knowledge in the same way that we have a science of physics or a science of materials. This might appear as an overly ambitious, possibly arrogant, objective, but bear with me. On the day I am beginning to write it–June 7th, 2020–, I think I am in possession of a few things that will help me to achieve this objective. Again, bear with me. My aim is well (...)
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  2. Halfway Up To the Mathematical Infinity I: On the Ontological & Epistemic Sustainability of Georg Cantor’s Transfinite Design.Edward G. Belaga - manuscript
    Georg Cantor was the genuine discoverer of the Mathematical Infinity, and whatever he claimed, suggested, or even surmised should be taken seriously -- albeit not necessary at its face value. Because alongside his exquisite in beauty ordinal construction and his fundamental powerset description of the continuum, Cantor has also left to us his obsessive presumption that the universe of sets should be subjected to laws similar to those governing the set of natural numbers, including the universal principles of cardinal comparability (...)
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  3. Homo Deceptus: How Language Creates its Own Reality.Bruce Bokor - manuscript
    Homo deceptus is a book that brings together new ideas on language, consciousness and physics into a comprehensive theory that unifies science and philosophy in a different kind of Theory of Everything. The subject of how we are to make sense of the world is addressed in a structured and ordered manner, which starts with a recognition that scientific truths are constructed within a linguistic framework. The author argues that an epistemic foundation of natural language must be understood before laying (...)
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  4. Logics of Formal Inconsistency Enriched with Replacement: An Algebraic and Modal Account.Walter Carnielli, Marcelo E. Coniglio & David Fuenmayor - manuscript
    One of the most expected properties of a logical system is that it can be algebraizable, in the sense that an algebraic counterpart of the deductive machinery could be found. Since the inception of da Costa's paraconsistent calculi, an algebraic equivalent for such systems have been searched. It is known that these systems are non self-extensional (i.e., they do not satisfy the replacement property). More than this, they are not algebraizable in the sense of Blok-Pigozzi. The same negative results hold (...)
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  5. The Synthetic Concept of Truth and its Descendants.Boris Culina - manuscript
    The concept of truth has many aims but only one source. The article describes the primary concept of truth, here called the synthetic concept of truth, according to which truth is the objective result of the synthesis of us and nature in the process of rational cognition. It is shown how various aspects of the concept of truth -- logical, scientific, and mathematical aspect -- arise from the synthetic concept of truth. Also, it is shown how the paradoxes of truth (...)
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  6. Is Classical Mathematics Appropriate for Theory of Computation?Farzad Didehvar - manuscript
    Throughout this paper, we are trying to show how and why our Mathematical frame-work seems inappropriate to solve problems in Theory of Computation. More exactly, the concept of turning back in time in paradoxes causes inconsistency in modeling of the concept of Time in some semantic situations. As we see in the first chapter, by introducing a version of “Unexpected Hanging Paradox”,first we attempt to open a new explanation for some paradoxes. In the second step, by applying this paradox, it (...)
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  7. Proof Terms for Classical Derivations.Restall Greg - manuscript
    I give an account of proof terms for derivations in a sequent calculus for classical propositional logic. The term for a derivation δ of a sequent Σ≻Δ encodes how the premises Σ and conclusions Δ are related in δ. This encoding is many–to–one in the sense that different derivations can have the same proof term, since different derivations may be different ways of representing the same underlying connection between premises and conclusions. However, not all proof terms for a sequent Σ≻Δ (...)
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  8. A Comprehensive Theory of Induction and Abstraction, Part I.Cael L. Hasse - manuscript
    I present a solution to the epistemological or characterisation problem of induction. In part I, Bayesian Confirmation Theory (BCT) is discussed as a good contender for such a solution but with a fundamental explanatory gap (along with other well discussed problems); useful assigned probabilities like priors require substantive degrees of belief about the world. I assert that one does not have such substantive information about the world. Consequently, an explanation is needed for how one can be licensed to act as (...)
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  9. Some Open Questions About Degrees of Paradoxes.Ming Hsiung - manuscript
    We can classify the (truth-theoretic) paradoxes according to their degrees of paradoxicality. Roughly speaking, two paradoxes have the same degrees of paradoxicality, if they lead to a contradiction under the same conditions, and one paradox has a (non-strictly) lower degree of paradoxicality than another, if whenever the former leads to a contradiction under a condition, the latter does so under the very condition. This paper aims at setting forth the theoretical framework of the theory of paradoxicality degree, and putting forward (...)
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  10. What Achilles Did and the Tortoise Wouldn't.Catherine Legg - manuscript
    This paper offers an expressivist account of logical form, arguing that in order to fully understand it one must examine what valid arguments make us do (or: what Achilles does and the Tortoise doesn’t, in Carroll’s famed fable). It introduces Charles Peirce’s distinction between symbols, indices and icons as three different kinds of signification whereby the sign picks out its object by learned convention, by unmediated indication, and by resemblance respectively. It is then argued that logical form is represented by (...)
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  11. Valuations.Jean-Louis Lenard - manuscript
    Is logic empirical? Is logic to be found in the world? Or is logic rather a convention, a product of conventions, part of the many rules that regulate the language game? Answers fall in either camp. We like the linguistic answer. In this paper, we want to analyze how a linguistic community would tackle the problem of developing a logic and show how the linguistic conventions adopted by the community determine the properties of the local logic. Then show how to (...)
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  12. Meaning, Presuppositions, Truth-Relevance, Gödel's Sentence and the Liar Paradox.X. Y. Newberry - manuscript
    Section 1 reviews Strawson’s logic of presuppositions. Strawson’s justification is critiqued and a new justification proposed. Section 2 extends the logic of presuppositions to cases when the subject class is necessarily empty, such as (x)((Px & ~Px) → Qx) . The strong similarity of the resulting logic with Richard Diaz’s truth-relevant logic is pointed out. Section 3 further extends the logic of presuppositions to sentences with many variables, and a certain valuation is proposed. It is noted that, given this valuation, (...)
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  13. Prolog Detects Pathological Self Reference in the Gödel Sentence.P. Olcott - manuscript
    This sentence G ↔ ¬(F ⊢ G) and its negation G ↔ ~(F ⊢ ¬G) are shown to meet the conventional definition of incompleteness: Incomplete(T) ↔ ∃φ ((T ⊬ φ) ∧ (T ⊬ ¬φ)). They meet conventional definition of incompleteness because neither the sentence nor its negation is provable in F (or any other formal system).
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  14. Defining Gödel Incompleteness Away.P. Olcott - manuscript
    We can simply define Gödel 1931 Incompleteness away by redefining the meaning of the standard definition of Incompleteness: A theory T is incomplete if and only if there is some sentence φ such that (T ⊬ φ) and (T ⊬ ¬φ). This definition construes the existence of self-contradictory expressions in a formal system as proof that this formal system is incomplete because self-contradictory expressions are neither provable nor disprovable in this formal system. Since self-contradictory expressions are neither provable nor disprovable (...)
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  15. Proof That Wittgenstein is Correct About Gödel.P. Olcott - manuscript
    The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic property of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide valid the deductive inference. Conclusions of sound arguments are derived from truth preserving finite string transformations applied to true premises.
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  16. Deductively Sound Formal Proofs.P. Olcott - manuscript
    Could the intersection of [formal proofs of mathematical logic] and [sound deductive inference] specify formal systems having [deductively sound formal proofs of mathematical logic]? All that we have to do to provide [deductively sound formal proofs of mathematical logic] is select the subset of conventional [formal proofs of mathematical logic] having true premises and now we have [deductively sound formal proofs of mathematical logic].
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  17. Refuting Tarski and Gödel with a Sound Deductive Formalism.P. Olcott - manuscript
    The conventional notion of a formal system is adapted to conform to the sound deductive inference model operating on finite strings. Finite strings stipulated to have the semantic value of Boolean true provide the sound deductive premises. Truth preserving finite string transformation rules provide the valid deductive inference. Sound deductive conclusions are the result of these finite string transformation rules.
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  18. Minimal Type Theory (MTT).Pete Olcott - manuscript
    Minimal Type Theory (MTT) is based on type theory in that it is agnostic about Predicate Logic level and expressly disallows the evaluation of incompatible types. It is called Minimal because it has the fewest possible number of fundamental types, and has all of its syntax expressed entirely as the connections in a directed acyclic graph.
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  19. Defining a Decidability Decider.Pete Olcott - manuscript
    By extending the notion of a Well Formed Formula to include syntactically formalized rules for rejecting semantically incorrect expressions we recognize and reject expressions that have the semantic error of Pathological self-reference(Olcott 2004). The foundation of this system requires the notion of a BaseFact that anchors the semantic notions of True and False. When-so-ever a formal proof from BaseFacts of language L to a closed WFF X or ~X of language L does not exist X is decided to be semantically (...)
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  20. Contradiction From the Fixed Point Lemma.T. Parent - manuscript
    Assuming that Q (Robinson arithmetic) is consistent and Church's Thesis is true, the Fixed Point Lemma enables the derivation of a contradiction, in a manner akin to the v-Curry paradox. The derivation could be blocked by excluding certain formulae from the scope of the Lemma, but this would effectively concede that the unrestricted Lemma is false. The resolution of the paradox thus remains an open question.
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  21. A New Modal Liar.T. Parent - manuscript
    Montague's modal liar is thought to show that 'necessarily' cannot be treated as a predicate of sentences. However, if 'necessarily' is treated as an operator on propositions (as is standard), we can also generate paradox (and without Montague's contentious use of the necessitation rule). The reasoning of the new modal liar is not immediately obvious--however, assuming that accessibility is reflexive, one can derive a contradiction from the proposition: This very proposition is not necessary. Thus the key advantage of the operator (...)
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  22. Paradox with Just Self-Reference.T. Parent - manuscript
    If a semantically open language has no constraints on self-reference, one can prove an absurdity. The argument utilizes co-referring names 'a0' and 'a1', and the definition of a functional expression 'The reflection of x = y'. The definition enables a type of self-reference without deploying any semantic terminology--yet given that a0= a1, the definition implies the that 'a0' = 'a1', which is absurd. In truth, however, 'the reflection of x = y' expresses an ill-defined function. And since there is a (...)
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  23. The Theory of Relations, Complex Terms, and a Connection Between Λ and Ε Calculi.Edward N. Zalta - manuscript
    This paper introduces a new method of interpreting complex relation terms in a second-order quantified modal language. We develop a completely general second-order modal language with two kinds of complex terms: one kind for denoting individuals and one kind for denoting n-place relations. Several issues arise in connection with previous, algebraic methods for interpreting the relation terms. The new method of interpreting these terms described here addresses those issues while establishing an interesting connection between λ and ε calculi. The resulting (...)
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  24. Tales Tall and True: John Woods on Truth in Fiction. [REVIEW]Andrew Aberdein - forthcoming - Philosophia.
    A review of John Woods, Truth in Fiction: Rethinking its Logic. Cham: Springer, 2018.
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  25. The Significance of Evidence-Based Reasoning for Mathematics, Mathematics Education, Philosophy and the Natural Sciences.Bhupinder Singh Anand - forthcoming
    In this multi-disciplinary investigation we show how an evidence-based perspective of quantification---in terms of algorithmic verifiability and algorithmic computability---admits evidence-based definitions of well-definedness and effective computability, which yield two unarguably constructive interpretations of the first-order Peano Arithmetic PA---over the structure N of the natural numbers---that are complementary, not contradictory. The first yields the weak, standard, interpretation of PA over N, which is well-defined with respect to assignments of algorithmically verifiable Tarskian truth values to the formulas of PA under the interpretation. (...)
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  26. Logical Pluralism Without the Normativity.Christopher Blake-Turner & Gillian Russell - forthcoming - Synthese:1-19.
    Logical pluralism is the view that there is more than one logic. Logical normativism is the view that logic is normative. These positions have often been assumed to go hand-in-hand, but we show that one can be a logical pluralist without being a logical normativist. We begin by arguing directly against logical normativism. Then we reformulate one popular version of pluralism—due to Beall and Restall—to avoid a normativist commitment. We give three non-normativist pluralist views, the most promising of which depends (...)
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  27. AISC 2018 - Extended Abstract Pavia - December 2018.Fabrizio Calzavarini & Antonio Lieto - forthcoming - In Cristiano Chesi (ed.), AISC Proceedings, Pavia. 27100 Pavia, Province of Pavia, Italy: pp. 20-23.
    Extended abstract presented at the AISC 2018 Conference, 15th International Conference of the Italian Association of Cognitive Science, Pavia.
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  28. An Expressivist Analysis of the Indicative Conditional with a Restrictor Semantics.John Cantwell - forthcoming - Review of Symbolic Logic:1-44.
    A globally expressivist analysis of the indicative conditional based on the Ramsey Test is presented. The analysis is a form of ‘global’ expressivism in that it supplies acceptance and rejection conditions for all the sentence forming connectives of propositional logic and so allows the conditional to embed in arbitrarily complex sentences. The expressivist framework is semantically characterized in a restrictor semantics due to Vann McGee, and is completely axiomatized in a logic dubbed ICL. The expressivist framework extends the AGM framework (...)
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  29. Interpreting the Compositional Truth Predicate in Models of Arithmetic.Cezary Cieśliński - forthcoming - Archive for Mathematical Logic:1-22.
    We present a construction of a truth class (an interpretation of a compositional truth predicate) in an arbitrary countable recursively saturated model of first-order arithmetic. The construction is fully classical in that it employs nothing more than the classical techniques of formal proof theory.
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  30. First-Order Swap Structures Semantics for Some Logics of Formal Inconsistency.Marcelo E. Coniglio - forthcoming - Journal of Logic and Computation.
    The logics of formal inconsistency (LFIs, for short) are paraconsistent logics (that is, logics containing contradictory but non-trivial theories) having a consistency connective which allows to recover the ex falso quodlibet principle in a controlled way. The aim of this paper is considering a novel semantical approach to first-order LFIs based on Tarskian structures defined over swap structures, a special class of multialgebras. The proposed semantical framework generalizes previous aproaches to quantified LFIs presented in the literature. The case of QmbC, (...)
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  31. Tarski’s Convention T: Condition Beta.John Corcoran - forthcoming - South American Journal of Logic 1 (1).
    Tarski’s Convention T—presenting his notion of adequate definition of truth (sic)—contains two conditions: alpha and beta. Alpha requires that all instances of a certain T Schema be provable. Beta requires in effect the provability of ‘every truth is a sentence’. Beta formally recognizes the fact, repeatedly emphasized by Tarski, that sentences (devoid of free variable occurrences)—as opposed to pre-sentences (having free occurrences of variables)—exhaust the range of significance of is true. In Tarski’s preferred usage, it is part of the meaning (...)
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  32. The Power of Naive Truth.Hartry Field - forthcoming - Review of Symbolic Logic:1-34.
    Nonclassical theories of truth that take truth to be transparent have some obvious advantages over any classical theory of truth. But several authors have recently argued that there’s also a big disadvantage of nonclassical theories as compared to their “external” classical counterparts: proof-theoretic strength. While conceding the relevance of this, the paper argues that there is a natural way to beef up extant internal theories so as to remove their proof-theoretic disadvantage. It is suggested that the resulting internal theories are (...)
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  33. Agentive Free Choice.Melissa Fusco - forthcoming - Journal of Philosophical Logic:1-31.
    The Free Choice effect---whereby <>(p or q) seems to entail both <>p and <>q---has traditionally been characterized as a phenomenon affecting the deontic modal "may". This paper presents an extension of the semantic account of free choice defended in Fusco (2015) to the agentive modal "can", the "can" which, intuitively, describes an agent's powers. -/- I begin by sketching a model of inexact ability, which grounds a modal approach to agency (Belnap & Perloff 1998; Belnap, Perloff, and Xu 2001) in (...)
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  34. Deep Fried Logic.Shay Allen Logan - forthcoming - Erkenntnis:1-30.
    There is a natural story about what logic is that sees it as tied up with two operations: a ‘throw things into a bag’ operation and a ‘closure’ operation. In a pair of recent papers, Jc Beall has fleshed out the account of logic this leaves us with in more detail. Using Beall’s exposition as a guide, this paper points out some problems with taking the second operation to be closure in the usual sense. After pointing out these problems, I (...)
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  35. An Informational Interpretation of Weak Relevant Logic and Relevant Property Theory.Edwin Mares - forthcoming - Synthese:1-23.
    This paper extends the theory of situated inference from Mares to treat two weak relevant logics, B and DJ. These logics are interesting because they can be used as bases for consistent naïve theories, such as naïve set theory. The concepts of a situation and of information that are employed by the theory of situated inference are used to justify various aspects of these logics and to give an interpretation of the notion of set that is represented in the naïve (...)
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  36. Compositionality, Computability, and Complexity.Peter Pagin - forthcoming - Review of Symbolic Logic:1-52.
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  37. Secunda Operatio Respicit Ipsum Esse Rei: An Evaluation of Jacques Maritain, Étienne Gilson, and Ralph McInerny on the Relation of Esse to the Intellect’s Two Operations.Elliot Polsky - forthcoming - Nova et Vetera.
    In a few texts, Thomas Aquinas says that the first operation of the intellect pertains to (respicit) “the quiddity of a thing” whereas the second operation pertains to “the to be itself of a thing” (esse). But Aquinas also says that quiddities are to the intellect as color is to the power of sight. Statements such as these seem to have led Jacques Maritain and Étienne Gilson to see esse as the proper object of the intellect’s second operation. Against this (...)
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  38. “In as Many Ways as Something is Predicated ... In That Many Ways is Something Signified to Be”: The Logic Behind Thomas Aquinas’s Predication Thesis, Esse Substantiale, and Esse in Rerum Natura.Elliot Polsky - forthcoming - Proceedings of the American Catholic Philosophical Association.
    Thomistic commentators agree that Thomas Aquinas at least nominally allows for 'to be' (esse) to signify not only an act contrasted with essence in creatures, but also the essence itself of those creatures. Nevertheless, it is almost unheard of for any author to interpret Thomas's use of the word 'esse' as referring to essence. Against this tendency, this paper argues that Thomas's In V Metaphysics argument that every predication signifies esse provides an important instance of Thomas using esse to signify (...)
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  39. Chisholm's Modal Paradox(Es) and Counterpart Theory 50 Years On.Murali Ramachandran - forthcoming - Logic and Logical Philosophy:1.
    Lewis’s [1968] counterpart theory (LCT for short), motivated by his modal realism, made its appearance within a year of Chisholm’s modal paradox [1967]. We are not modal realists, but we argue that a satisfactory resolution to the paradox calls for a counterpart-theoretic (CT-)semantics. We make our case by showing that the Chandler–Salmon strategy of denying the S4 axiom [◊◊ψ →◊ψ] is inadequate to resolve the paradox – we take on Salmon’s attempts to defend that strategy against objects from Lewis and (...)
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  40. Logic Isn’T Normative.Gillian Russell - forthcoming - Inquiry: An Interdisciplinary Journal of Philosophy 1:1-18.
    Some writers object to logical pluralism on the grounds that logic is normative. The rough idea is that the relation of logical consequence has consequences for what we ought to think and h...
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  41. Against Logical Generalism.Nicole Wyatt & Gillman Payette - forthcoming - Synthese:1-18.
    The orthodox view of logic takes for granted the central importance of logical principles. Logic, and thus logical reasoning, is to be understood as a system of rules or principles with universal application. Let us call this orthodox view logical generalism. In this paper we argue that logical generalism, whether monist or pluralist, is wrong. We then outline an account of logical consequence in the absence of general logical principles, which we call logical particularism.
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  42. Tennant’s Conjecture for Self-Referential Paradoxes and its Classical Counterexample.Seungrak Choi - 2021 - Korean Journal of Logic 1 (24):1-30.
    In his paper, “On paradox without self-reference”, Neil Tennant proposed the conjecture for self-referential paradoxes that any derivation formalizing self-referential paradoxes only generates a looping reduction sequence. According to him, the derivation of the Liar paradox in natural deduction initiates a looping reduction sequence and the derivation of the Yablo's paradox generates a spiral reduction. The present paper proposes the counterexample to Tennant's conjecture for self-referential paradoxes. We shall show that there is a derivation of the Liar paradox which generates (...)
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  43. The Explanation of Logical Theorems and Reductive Truthmakers.Yannic Kappes - 2021 - Philosophical Studies 178 (4):1267-1284.
    This paper first identifies several plausible desiderata on satisfactory explanations of logical theorems, shows that ordinary grounding explanations cannot satisfy them and argues that there is reason to believe that no alternative grounding explanations of logical theorems can be given. It then develops an alternative explanation of logical theorems based on Yablo’s idea of reductive truthmaking. The resulting proposal invokes instances of reductive truthmaking that bear an interesting structural similarity to the notion of zero-ground, in virtue of which it is (...)
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  44. Non-distributive Relatives of ETL and NFL.Daniil Kozhemiachenko - 2021 - Studia Logica 109 (1):137-165.
    In this paper we devise non-distributive relatives of Exactly true logic by Pietz and Riveccio and its dual Non-falsity logic by Shramko, Zaitsev and Belikov. We consider two pre-orders which are algebraic counterparts of the ETL’s and NFL’s entailment relations on the de Morgan lattice 4. We generalise these pre-orders and determine which distributive properties that hold on 4 are not forced by either of the pre-orders. We then construct relatives of ETL and NFL but lack such distributive properties. For (...)
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  45. Normalisation for Bilateral Classical Logic with Some Philosophical Remarks.Nils Kürbis - 2021 - Journal of Applied Logics 2 (8):531-556.
    Bilateralists hold that the meanings of the connectives are determined by rules of inference for their use in deductive reasoning with asserted and denied formulas. This paper presents two bilateral connectives comparable to Prior's tonk, for which, unlike for tonk, there are reduction steps for the removal of maximal formulas arising from introducing and eliminating formulas with those connectives as main operators. Adding either of them to bilateral classical logic results in an incoherent system. One way around this problem is (...)
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  46. Kripke Semantics for Intuitionistic Łukasiewicz Logic.A. Lewis-Smith, P. Oliva & E. Robinson - 2021 - Studia Logica 109 (2):313-339.
    This paper proposes a generalization of the Kripke semantics of intuitionistic logic IL appropriate for intuitionistic Łukasiewicz logic IŁL — a logic in the intersection between IL and (classical) Łukasiewicz logic. This generalised Kripke semantics is based on the poset sum construction, used in Bova and Montagna (Theoret Comput Sci 410(12):1143–1158, 2009) to show the decidability (and PSPACE completeness) of the quasiequational theory of commutative, integral and bounded GBL algebras. The main idea is that w \Vdash \sigma—which for IL is (...)
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  47. Truthmakers and Normative Conflicts.Albert Anglberger & Johannes Korbmacher - 2020 - Studia Logica 108 (1):49-83.
    By building on work by Kit Fine, we develop a sound and complete truthmaker semantics for Lou Goble’s conflict tolerant deontic logic BDL.
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  48. Toward a General Theory of Knowledge.Luis M. Augusto - 2020 - Journal of Knowledge Structures and Systems 1 (1):63-97.
    For millennia, knowledge has eluded a precise definition. The industrialization of knowledge (IoK) and the associated proliferation of the so-called knowledge communities in the last few decades caused this state of affairs to deteriorate, namely by creating a trio composed of data, knowledge, and information (DIK) that is not unlike the aporia of the trinity in philosophy. This calls for a general theory of knowledge (ToK) that can work as a foundation for a science of knowledge (SoK) and additionally distinguishes (...)
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  49. A Game Theoretical Semantics for a Logic of Formal Inconsistency.Can Başkent & Pedro Henrique Carrasqueira - 2020 - Logic Journal of the IGPL 28 (5):936-952.
    This paper introduces a game theoretical semantics for a particular logic of formal inconsistency called mbC.
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  50. A Note on FDE “All the Way Up”.Jc Beall & Caleb Camrud - 2020 - Notre Dame Journal of Formal Logic 61 (2):283-296.
    A very natural and philosophically important subclassical logic is FDE. This account of logical consequence can be seen as going beyond the standard two-valued account to a four-valued account. A natural question arises: What account of logical consequence arises from considering further combinations of such values? A partial answer was given by Priest in 2014; Shramko and Wansing had also given a partial result some years earlier, although in a different context. In this note we generalize Priest’s result to show (...)
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