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  1. added 2020-06-27
    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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  2. added 2020-06-23
    Prior A. N.. Correspondence Theory of Truth. The Encyclopedia of Philosophy, Edited by Edwards Paul, The Macmillan Company & The Free Press, New York, and Collier-Macmillan Limited, London, 1967, Vol. 2, Pp. 223–232. [REVIEW]Benson Mates - 1970 - Journal of Symbolic Logic 35 (2):304.
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  3. added 2020-06-23
    John G. Kemeny. A New Approach to Semantics. The Journal of Symbolic Logic, Vol. 21 , Pp. 1–27, and Pp. 149–161. - Stephen Ullmann. The Principles of Semantics. Glasgow University Publications, No. 84. Second Edition. Basil Blackwell & Mott Ltd., Oxford, 1957; Philosophical Library, New York 1957; Title Pages, Prefaces and Table of Contents + 346 Pp. - Jens Erik Fenstad. Notes on Synonymy. Synthese, Vol. 14 , Pp. 35–77.L. Jonathan Cohen - 1970 - Journal of Symbolic Logic 35 (2):310-312.
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  4. added 2020-06-23
    Alan R. White. Coherence Theory of Truth. The Encyclopedia of Philosophy, Edited by Paul Edwards, The Macmillan Company & The Free Press, New York, and Collier-Macmillan Limited, London, 1967, Vol. 2, Pp. 130–133. [REVIEW]Benson Mates - 1970 - Journal of Symbolic Logic 35 (2):303.
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  5. added 2020-06-23
    Norman Kretzmann. Semantics, History Of. The Encyclopedia of Philosophy, Edited by Paul Edwards, The Macmillan Company & The Free Press, New York, and Collier-Macmillan Limited, London, 1967, Vol. 7, Pp. 358–406. [REVIEW]Benson Mates - 1970 - Journal of Symbolic Logic 35 (2):308.
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  6. added 2020-06-23
    Raymond D. Bradley. Geometry and Necessary Truth. The Philosophical Review, Vol. 73 , Pp. 59–75.Alonzo Church - 1969 - Journal of Symbolic Logic 34 (3):496-497.
  7. added 2020-06-23
    Ronald Prather. Computational Aids for Determining the Minimal Form of a Truth Function. Journal of the Association for Computing Machinery, Vol. 7 , Pp. 299–310. [REVIEW]Ann S. Ferebee - 1968 - Journal of Symbolic Logic 33 (4):630.
  8. added 2020-06-16
    Disquotation and Infinite Conjunctions.Lavinia Picollo & Thomas Schindler - 2017 - Erkenntnis (5):1-30.
    One of the main logical functions of the truth predicate is to enable us to express so-called ‘infinite conjunctions’. Several authors claim that the truth predicate can serve this function only if it is fully disquotational, which leads to triviality in classical logic. As a consequence, many have concluded that classical logic should be rejected. The purpose of this paper is threefold. First, we consider two accounts available in the literature of what it means to express infinite conjunctions with a (...)
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  9. added 2020-06-16
    Two's Company: The Humbug of Many Logical Values.Carlos Caleiro, Walter Carnielli, Marcelo Coniglio & João Marcos - 2005 - In J. Y. Beziau (ed.), Logica Universalis. Birkhäuser Verlag. pp. 169-189.
    The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logical values, true and false.” As a matter of fact, a result by W´ojcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued semantics can be reduced to a two-valued one. So, why should one even consider using logics with more (...)
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  10. added 2020-06-16
    E. M. Barth and R. T. P. Wiche. Problems, Functions and Semantic Roles. A Pragmatists’ Analysis of Montague's Theory of Sentence Meaning. Foundations of Communication. Walter de Gruyter, Berlin and New York1986, XVIII + 198 Pp. [REVIEW]Barbara Abbott - 1988 - Journal of Symbolic Logic 53 (1):317-318.
  11. added 2020-06-16
    George Pitcher. Introduction. Truth, Edited by George Pitcher, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1964, Pp. 1–15. [REVIEW]Jonathan Bennett - 1968 - Journal of Symbolic Logic 33 (1):147-148.
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  12. added 2020-06-16
    Michael Dummett. Truth. Edited by George Pitcher, Prentice-Hall, Inc., Englewood Cliffs, New Jersey, 1964, Pp. 93–111. , Pp. 141–162.). [REVIEW]Jonathan Bennett - 1968 - Journal of Symbolic Logic 33 (1):148.
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  13. added 2020-06-16
    Nicholas Rescher. Quasi-Truth-Functional Systems of Prepositional Logic. The Journal of Symbolic Logic, Vol. 27 , Pp. 1–10.Gene F. Rose - 1964 - Journal of Symbolic Logic 29 (1):50-51.
  14. added 2020-06-14
    Axiomatization of Crisp Gödel Modal Logic.Ricardo Oscar Rodriguez & Amanda Vidal - forthcoming - Studia Logica:1-29.
    In this paper we consider the modal logic with both \ and \ arising from Kripke models with a crisp accessibility and whose propositions are valued over the standard Gödel algebra \. We provide an axiomatic system extending the one from Caicedo and Rodriguez :37–55, 2015) for models with a valued accessibility with Dunn axiom from positive modal logics, and show it is strongly complete with respect to the intended semantics. The axiomatizations of the most usual frame restrictions are given (...)
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  15. added 2020-06-14
    Classical Logic and the Strict Tolerant Hierarchy.Chris Scambler - 2020 - Journal of Philosophical Logic 49 (2):351-370.
    In their recent article “A Hierarchy of Classical and Paraconsistent Logics”, Eduardo Barrio, Federico Pailos and Damien Szmuc present novel and striking results about meta-inferential validity in various three valued logics. In the process, they have thrown open the door to a hitherto unrecognized domain of non-classical logics with surprising intrinsic properties, as well as subtle and interesting relations to various familiar logics, including classical logic. One such result is that, for each natural number n, there is a logic which (...)
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  16. added 2020-06-14
    Unsettling Preferential Semantics.Audun Stolpe - 2020 - Journal of Philosophical Logic 49 (2):371-399.
    This paper is concerned with removing the identity schema from the axiomatic basis of deontic conditionals. This is in order to allow a stipulated ideal to be contrary or opposite in nature to the fact it is predicated upon. It is desirable, or so it is argued, to retain the order-theoretic orientation of preferential semantics towards the analysis of deontic conditionals, more specifically of maximality semantics in the tradition from Bengt Hansson. So understood, the problem involves abstracting away the settledness (...)
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  17. added 2020-06-14
    Free Choice Impossibility Results.Simon Goldstein - 2020 - Journal of Philosophical Logic 49 (2):249-282.
    Free Choice is the principle that possibly p or q implies and is implied by possibly p and possibly q. A variety of recent attempts to validate Free Choice rely on a nonclassical semantics for disjunction, where the meaning of p or q is not a set of possible worlds. This paper begins with a battery of impossibility results, showing that some kind of nonclassical semantics for disjunction is required in order to validate Free Choice. The paper then provides a (...)
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  18. added 2020-06-14
    Axiomatizing the Logic of Imagination.Alessandro Giordani - 2019 - Studia Logica 107 (4):639-657.
    In a recent paper Berto introduces a semantic system for a logic of imagination, intended as positive conceivability, and aboutness of imaginative acts. This system crucially adopts elements of both the semantics of conditionals and the semantics of analytical implications in order to account for the central logical traits of the notion of truth in an act of imagination based on an explicit input. The main problem left unsolved is to put forward a complete set of axioms for the proposed (...)
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  19. added 2020-06-14
    Categories of Models of R-Mingle.Wesley Fussner & Nick Galatos - 2019 - Annals of Pure and Applied Logic 170 (10):1188-1242.
    We give a new Esakia-style duality for the category of Sugihara monoids based on the Davey-Werner natural duality for lattices with involution, and use this duality to greatly simplify a construction due to Galatos-Raftery of Sugihara monoids from certain enrichments of their negative cones. Our method of obtaining this simplification is to transport the functors of the Galatos-Raftery construction across our duality, obtaining a vastly more transparent presentation on duals. Because our duality extends Dunn's relational semantics for the logic R-mingle (...)
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  20. added 2020-06-05
    Interpreting the Compositional Truth Predicate in Models of Arithmetic.Cezary Cieslinski - manuscript
    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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  21. added 2020-06-05
    Belnap-Dunn Semantics for Natural Implicative Expansions of Kleene's Strong Three-Valued Matrix II. Only One Designated Value.Gemma Robles, Francisco Salto & José M. Méndez - 2019 - Journal of Applied Non-Classical Logics 29 (3):307-325.
    This paper is a sequel to ‘Belnap-Dunn semantics for natural implicative expansions of Kleene's strong three-valued matrix with two designated values’, where a ‘bivalent’ Belnap-Dunn semantics is provided for all the expansions referred to in its title. The aim of the present paper is to carry out a parallel investigation for all natural implicative expansions of Kleene's strong 3-valued matrix now with only one designated value.
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  22. added 2020-06-05
    Logic for Exact Entailment.Kit Fine & Mark Jago - 2019 - Review of Symbolic Logic 12 (3):536-556.
    An exact truthmaker for A is a state which, as well as guaranteeing A’s truth, is wholly relevant to it. States with parts irrelevant to whether A is true do not count as exact truthmakers for A. Giving semantics in this way produces a very unusual consequence relation, on which conjunctions do not entail their conjuncts. This feature makes the resulting logic highly unusual. In this paper, we set out formal semantics for exact truthmaking and characterise the resulting notion of (...)
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  23. added 2020-06-05
    Varieties of Rigidity.Tuukka Tanninen - 2019 - Logica Universalis 13 (2):219-240.
    In this paper certain aspects of rigidity are studied through Hintikka’s work in modal semantics. The paper surveys Hintikka’s extraordinary struggles with rigidity from the late 50’s to this millennium. I argue that Hintikka’s many ambivalent remarks concerning rigidity become more comprehensible if, first, three different variants of rigidity are distinguished and, second, Hintikka’s largely implicit doctrine of semantic neo-Kantianism is made explicit.
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  24. added 2020-06-02
    The Explanation of Logical Theorems and Reductive Truthmakers.Yannic Kappes - forthcoming - Philosophical Studies:1-18.
    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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  25. added 2020-06-01
    Agentive Free Choice.Melissa Fusco - forthcoming - Journal of Philosophical Logic.
    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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  26. added 2020-06-01
    A Game Theoretical Semantics for a Logic of Formal Inconsistency.Can Başkent & Pedro Henrique Carrasqueira - forthcoming - Logic Journal of the IGPL.
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  27. added 2020-06-01
    Herzberger’s Limit Rule with Labelled Sequent Calculus.Andreas Fjellstad - forthcoming - Studia Logica:1-41.
    Inspired by recent work on proof theory for modal logic, this paper develops a cut-free labelled sequent calculus obtained by imitating Herzberger’s limit rule for revision sequences as a clause in a possible world semantics. With the help of two completeness theorems, one between the labelled sequent calculus and the corresponding possible world semantics, and one between the axiomatic theory of truth PosFS and a neighbourhood semantics, together with the proof of the equivalence between the two semantics, we show that (...)
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  28. added 2020-06-01
    A Note on the Cut-Elimination Proof in “Truth Without Contraction”.Andreas Fjellstad - 2020 - Review of Symbolic Logic:1-5.
    This note shows that the permutation instructions presented by Zardini for eliminating cuts on universally quantified formulas in the sequent calculus for the noncontractive theory of truth IKT ω are inadequate. To that purpose the note presents a derivation in the sequent calculus for IKT ω ending with an application of cut on a universally quantified formula which the permutation instructions cannot deal with. The counterexample is of the kind that leaves open the question whether cut can be shown to (...)
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  29. added 2020-06-01
    Alethic Reference.Lavinia Picollo - 2020 - Journal of Philosophical Logic 49 (3):417-438.
    I put forward precise and appealing notions of reference, self-reference, and well-foundedness for sentences of the language of first-order Peano arithmetic extended with a truth predicate. These notions are intended to play a central role in the study of the reference patterns that underlie expressions leading to semantic paradox and, thus, in the construction of philosophically well-motivated semantic theories of truth.
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  30. added 2020-06-01
    Rabern’s Semantics for Metaphysical and Epistemic Modalities and the Nesting Problem.Fabian Heimann - 2020 - Journal of Philosophical Logic 49 (3):497-507.
    In a recent paper, Brian Rabern suggests a semantics for languages with two kinds of modality, standard Kripkean metaphysical modality as well as epistemic modality. This semantics presents an alternative to two-dimensionalism, which was developed in the last decades. Both Rabern’s semantics and two-dimensionalism are subject to a puzzle that Chalmers and Rabern, 210–224 2014) call the nesting problem. I will investigate how Rabern’s semantics answers this puzzle.
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  31. added 2020-06-01
    Indicative Conditionals and Graded Information.Ivano Ciardelli - 2020 - Journal of Philosophical Logic 49 (3):509-549.
    I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: “if p then q” is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the p-worlds. However, information states are not modeled as simple sets of worlds, but by means of a Lewisian system of (...)
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  32. added 2020-06-01
    Graham Priest on Dialetheism and Paraconsistency.Can Başkent & Thomas Macaulay Ferguson (eds.) - 2019 - Springer Verlag.
  33. added 2020-06-01
    Two Proofs of the Algebraic Completeness Theorem for Multilattice Logic.Oleg Grigoriev & Yaroslav Petrukhin - 2019 - Journal of Applied Non-Classical Logics 29 (4):358-381.
    Shramko [. Truth, falsehood, information and beyond: The American plan generalized. In K. Bimbo, J. Michael Dunn on information based logics, outstanding contributions to logic...
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  34. added 2020-06-01
    A Yabloesque Paradox in Epistemic Game Theory.Can Başkent - 2018 - Synthese 195 (1):441-464.
    The Brandenburger–Keisler paradox is a self-referential paradox in epistemic game theory which can be viewed as a two-person version of Russell’s Paradox. Yablo’s Paradox, according to its author, is a non-self referential paradox, which created a significant impact. This paper gives a Yabloesque, non-self-referential paradox for infinitary players within the context of epistemic game theory. The new paradox advances both the Brandenburger–Keisler and Yablo results. Additionally, the paper constructs a paraconsistent model satisfying the paradoxical statement.
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  35. added 2020-06-01
    Game Theoretical Semantics for Some Non-Classical Logics.Can Başkent - 2016 - Journal of Applied Non-Classical Logics 26 (3):208-239.
    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 (...)
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  36. added 2020-05-31
    Confused Terms in Ordinary Language.Greg Frost-Arnold & James R. Beebe - 2020 - Journal of Logic, Language and Information 29 (2):197-219.
    Confused terms appear to signify more than one entity. Carnap maintained that any putative name that is associated with more than one object in a relevant universe of discourse fails to be a genuine name. Although many philosophers have agreed with Carnap, they have not always agreed among themselves about the truth-values of atomic sentences containing such terms. Some hold that such atomic sentences are always false, and others claim they are always truth-valueless. Field maintained that confused terms can still (...)
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  37. added 2020-05-26
    Fractional Semantics for Classical Logic.Mario Piazza & Gabriele Pulcini - forthcoming - Review of Symbolic Logic:1-19.
    This article presents a new semantics for classical propositional logic. We begin by maximally extending the space of sequent proofs so as to admit proofs for any logical formula; then, we extract the new semantics by focusing on the axiomatic structure of proofs. In particular, the interpretation of a formula is given by the ratio between the number of identity axioms out of the total number of axioms occurring in any of its proofs. The outcome is an informational refinement of (...)
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  38. added 2020-05-26
    Paracomplete Logics Which Are Dual to the Paraconsistent Logics L3A and L3B.Alejandro Hernández-Tello, Verónica Borja-Macı́as & Marcelo E. Coniglio - 2020 - LANMR 2019: Proceedings of the 12th Latin American Workshop on Logic/Languages, Algorithms and New Methods of Reasoning.
    In 2016 Beziau, introduce a more restricted concept of paraconsistency, namely the genuine paraconsistency. He calls genuine paraconsistent logic those logic rejecting φ, ¬φ |- ψ and |- ¬(φ ∧ ¬φ). In that paper the author analyzes, among the three-valued logics, which of these logics satisfy this property. If we consider multiple-conclusion consequence relations, the dual properties of those above mentioned are: |- φ, ¬φ, and ¬(ψ ∨ ¬ψ) |- . We call genuine paracomplete logics those rejecting the mentioned properties. (...)
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  39. added 2020-05-26
    A Formal Framework for Future Contingents.Tero Tulenheimo - 2020 - Filosofiska Notiser 7 (1):79-136.
    In this article, I present a formal semantic framework that renders explicit how to reconcile the condition that a proposition about a contingent future event is true at a moment t0 with the idea that at t0, this proposition is ‘truth-maker indeterminate’: a state of affairs making it true will obtain later on, though no such state of affairs obtains at t0. The semantics I formulate employs ‘open temporal models’. They represent the passage of time by a specific component termed (...)
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  40. added 2020-05-26
    The Truth of Future Contingents: An Analysis of Truth-Maker Indeterminacy.Tero Tulenheimo - 2020 - Filosofiska Notiser 7 (1):53-77.
    I argue that the semantics of sentences expressing future contingent propositions is best viewed as being based on a clear distinction between a time at which a proposition is true and a time at which a state of affairs that makes it true gets actualized. That a prediction is true here and now means that its truth-maker gets actualized later. This is not to say that if a contingent proposition p concerning the future is true at t, it acquires the (...)
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  41. added 2020-05-25
    Deontology of Compound Actions.Janusz Czelakowski - 2020 - Studia Logica 108 (1):5-47.
    This paper, being a companion to the book [2] elaborates the deontology of sequential and compound actions based on relational models and formal constructs borrowed from formal linguistics. The semantic constructions presented in this paper emulate to some extent the content of [3] but are more involved. Although the present work should be regarded as a sequel of [3] it is self-contained and may be read independently. The issue of permission and obligation of actions is presented in the form of (...)
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  42. added 2020-05-25
    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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  43. added 2020-05-20
    Probability Modals and Infinite Domains.Adam Marushak - forthcoming - Journal of Philosophical Logic:1-15.
    Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely thought to (...)
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  44. added 2020-05-20
    Definable Operators on Stable Set Lattices.Robert Goldblatt - forthcoming - Studia Logica:1-18.
    A fundamental result from Boolean modal logic states that a first-order definable class of Kripke frames defines a logic that is validated by all of its canonical frames. We generalise this to the level of non-distributive logics that have a relational semantics provided by structures based on polarities. Such structures have associated complete lattices of stable subsets, and these have been used to construct canonical extensions of lattice-based algebras. We study classes of structures that are closed under ultraproducts and whose (...)
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  45. added 2020-05-20
    Non-distributive Relatives of ETL and NFL.Daniil Kozhemiachenko - forthcoming - Studia Logica:1-29.
    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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  46. added 2020-05-19
    Extended Contact Algebras and Internal Connectedness.Tatyana Ivanova - 2020 - Studia Logica 108 (2):239-254.
    The notion of contact algebra is one of the main tools in the region-based theory of space. It is an extension of Boolean algebra with an additional relation C, called contact. Standard models of contact algebras are topological and are the contact algebras of regular closed sets in a given topological space. In such a contact algebra we add the predicate of internal connectedness with the following meaning—a regular closed set is internally connected if and only if its interior is (...)
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  47. added 2020-05-19
    Completeness Theorems for Σ–Additive Probabilistic Semantics.Nebojša Ikodinović, Zoran Ognjanović, Aleksandar Perović & Miodrag Rašković - 2020 - Annals of Pure and Applied Logic 171 (4):102755.
  48. added 2020-05-18
    Is Logic Out of This World?Michael J. Raven - forthcoming - Journal of Philosophy.
    Is logic out of this world? This elusive question reveals a tension in our thinking about the basis of logic: both worldly and unworldly answers get something right and yet they conflict. My aim is to clarify the question and explore a conciliatory answer. I focus on a characterization of unworldliness in terms of ground. This allows for a distinction between proximal and distal unworldliness. That in turn reconfigures our approach to the question. It may now be taken as asking (...)
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  49. added 2020-05-16
    Intuitionistic Non-normal Modal Logics: A General Framework.Tiziano Dalmonte, Charles Grellois & Nicola Olivetti - forthcoming - Journal of Philosophical Logic:1-50.
    We define a family of intuitionistic non-normal modal logics; they can be seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only Necessity or Possibility. We then consider the more important case of bimodal logics, which contain both modal operators. In this case we define several interactions between Necessity and Possibility of increasing strength, although weaker than duality. We thereby obtain a lattice of 24 distinct bimodal logics. For all logics we provide both a Hilbert (...)
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  50. added 2020-05-12
    Truth and Feasible Reducibility.Ali Enayat, Mateusz Łełyk & Bartosz Wcisło - 2020 - Journal of Symbolic Logic 85 (1):367-421.
    Let ${\cal T}$ be any of the three canonical truth theories CT^− (compositional truth without extra induction), FS^− (Friedman–Sheard truth without extra induction), or KF^− (Kripke–Feferman truth without extra induction), where the base theory of ${\cal T}$ is PA. We establish the following theorem, which implies that ${\cal T}$ has no more than polynomial speed-up over PA. Theorem.${\cal T}$is feasibly reducible to PA, in the sense that there is a polynomial time computable function f such that for every ${\cal T}$-proof (...)
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