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Substructural Logics: A Primer

Dordrecht, Netherland: Springer (2002)

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  1. (Meta)inferential levels of entailment beyond the Tarskian paradigm.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2019 - Synthese 198 (S22):5265-5289.
    In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences—and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical systems, and propose an (...)
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  • Variations on intra-theoretical logical pluralism: internal versus external consequence.Bogdan Dicher - 2020 - Philosophical Studies 177 (3):667-686.
    Intra-theoretical logical pluralism is a form of meaning-invariant pluralism about logic, articulated recently by Hjortland :355–373, 2013). This version of pluralism relies on it being possible to define several distinct notions of provability relative to the same logical calculus. The present paper picks up and explores this theme: How can a single logical calculus express several different consequence relations? The main hypothesis articulated here is that the divide between the internal and external consequence relations in Gentzen systems generates a form (...)
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  • Hopeful Monsters: A Note on Multiple Conclusions.Bogdan Dicher - 2020 - Erkenntnis 85 (1):77-98.
    Arguments, the story goes, have one or more premises and only one conclusion. A contentious generalisation allows arguments with several disjunctively connected conclusions. Contentious as this generalisation may be, I will argue nevertheless that it is justified. My main claim is that multiple conclusions are epiphenomena of the logical connectives: some connectives determine, in a certain sense, multiple-conclusion derivations. Therefore, such derivations are completely natural and can safely be used in proof-theoretic semantics.
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  • Logics for modelling collective attitudes.Daniele Porello - 2018 - Fundamenta Informaticae 158 (1-3):239-27.
    We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal modalities (...)
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  • Tolerant reasoning: nontransitive or nonmonotonic?Pablo Cobreros, Paul Egré, Dave Ripley & Robert van Rooij - 2017 - Synthese 199 (Suppl 3):681-705.
    The principle of tolerance characteristic of vague predicates is sometimes presented as a soft rule, namely as a default which we can use in ordinary reasoning, but which requires care in order to avoid paradoxes. We focus on two ways in which the tolerance principle can be modeled in that spirit, using special consequence relations. The first approach relates tolerant reasoning to nontransitive reasoning; the second relates tolerant reasoning to nonmonotonic reasoning. We compare the two approaches and examine three specific (...)
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  • Contraction, Infinitary Quantifiers, and Omega Paradoxes.Bruno Da Ré & Lucas Rosenblatt - 2018 - Journal of Philosophical Logic 47 (4):611-629.
    Our main goal is to investigate whether the infinitary rules for the quantifiers endorsed by Elia Zardini in a recent paper are plausible. First, we will argue that they are problematic in several ways, especially due to their infinitary features. Secondly, we will show that even if these worries are somehow dealt with, there is another serious issue with them. They produce a truth-theoretic paradox that does not involve the structural rules of contraction.
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  • LP, K3, and FDE as Substructural Logics.Lionel Shapiro - 2017 - In Arazim Pavel & Lávička Tomáš (eds.), The Logica Yearbook 2016. College Publications.
    Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.
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  • The Logics of Strict-Tolerant Logic.Eduardo Barrio, Lucas Rosenblatt & Diego Tajer - 2015 - Journal of Philosophical Logic 44 (5):551-571.
    Adding a transparent truth predicate to a language completely governed by classical logic is not possible. The trouble, as is well-known, comes from paradoxes such as the Liar and Curry. Recently, Cobreros, Egré, Ripley and van Rooij have put forward an approach based on a non-transitive notion of consequence which is suitable to deal with semantic paradoxes while having a transparent truth predicate together with classical logic. Nevertheless, there are some interesting issues concerning the set of metainferences validated by this (...)
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  • Anything Goes.David Ripley - 2015 - Topoi 34 (1):25-36.
    This paper consider Prior's connective Tonk from a particular bilateralist perspective. I show that there is a natural perspective from which we can see Tonk and its ilk as perfectly well-defined pieces of vocabulary; there is no need for restrictions to bar things like Tonk.
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  • Synonymy and Intra-Theoretical Pluralism.Patrick Allo - 2015 - Australasian Journal of Philosophy 93 (1):77-91.
    The starting point of this paper is a version of intra-theoretical pluralism that was recently proposed by Hjortland [2013]. In a first move, I use synonymy-relations to formulate an intuitively compelling objection against Hjortland's claim that, if one uses a single calculus to characterise the consequence relations of the paraconsistent logic LP and the paracomplete logic K3, one immediately obtains multiple consequence relations for a single language and hence a reply to the Quinean charge of meaning variance. In a second (...)
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  • (1 other version)Interpretace znalosti v substrukturálních rámcích.Ondrej Majer & Michal Peliš - 2013 - Organon F: Medzinárodný Časopis Pre Analytickú Filozofiu 20 (1):79-98.
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  • Logical discrimination (2nd edition).Lloyd Humberstone - 2005 - In Jean-Yves Béziau (ed.), Logica Universalis: Towards a General Theory of Logic. Boston: Birkhäuser Verlog. pp. 225–246.
    We discuss conditions under which the following ‘truism’ does indeed express a truth: the weaker a logic is in terms of what it proves, the stronger it is as a tool for registering distinctions amongst the formulas in its language.
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  • Logical Consequence and the Paradoxes.Edwin Mares & Francesco Paoli - 2014 - Journal of Philosophical Logic 43 (2-3):439-469.
    We group the existing variants of the familiar set-theoretical and truth-theoretical paradoxes into two classes: connective paradoxes, which can in principle be ascribed to the presence of a contracting connective of some sort, and structural paradoxes, where at most the faulty use of a structural inference rule can possibly be blamed. We impute the former to an equivocation over the meaning of logical constants, and the latter to an equivocation over the notion of consequence. Both equivocation sources are tightly related, (...)
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  • Two Flavors of Curry’s Paradox.Jc Beall & Julien Murzi - 2013 - Journal of Philosophy 110 (3):143-165.
    In this paper, we distinguish two versions of Curry's paradox: c-Curry, the standard conditional-Curry paradox, and v-Curry, a validity-involving version of Curry's paradox that isn’t automatically solved by solving c-curry. A unified treatment of curry paradox thus calls for a unified treatment of both c-Curry and v-Curry. If, as is often thought, c-Curry paradox is to be solved via non-classical logic, then v-Curry may require a lesson about the structure—indeed, the substructure—of the validity relation itself.
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  • Paraconsistency: Logic and Applications.Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.) - 2012 - Dordrecht, Netherland: Springer.
    A logic is called 'paraconsistent' if it rejects the rule called 'ex contradictione quodlibet', according to which any conclusion follows from inconsistent premises. While logicians have proposed many technically developed paraconsistent logical systems and contemporary philosophers like Graham Priest have advanced the view that some contradictions can be true, and advocated a paraconsistent logic to deal with them, until recent times these systems have been little understood by philosophers. This book presents a comprehensive overview on paraconsistent logical systems to change (...)
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  • Quine and Slater on paraconsistency and deviance.Francesco Paoli - 2003 - Journal of Philosophical Logic 32 (5):531-548.
    In a famous and controversial paper, B. H. Slater has argued against the possibility of paraconsistent logics. Our reply is centred on the distinction between two aspects of the meaning of a logical constant *c* in a given logic: its operational meaning, given by the operational rules for *c* in a cut-free sequent calculus for the logic at issue, and its global meaning, specified by the sequents containing *c* which can be proved in the same calculus. Subsequently, we use the (...)
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  • Univocity of Intuitionistic and Classical Connectives.Branden Fitelson & Rodolfo C. Ertola-Biraben - forthcoming - Bulletin of Symbolic Logic.
    In this paper, we show (among other things) that the conditional in Frege's Begriffsschrift is ambiguous.
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  • (1 other version)The original sin of proof-theoretic semantics.Francesco Paoli & Bogdan Dicher - 2018 - Synthese 198 (1):615-640.
    Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...)
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  • Inconsistency, Paraconsistency and ω-Inconsistency.Bruno Da Ré - 2018 - Principia: An International Journal of Epistemology 22 (1):171-188.
    In this paper I’ll explore the relation between ω-inconsistency and plain inconsistency, in the context of theories that intend to capture semantic concepts. In particular, I’ll focus on two very well known inconsistent but non-trivial theories of truth: LP and STTT. Both have the interesting feature of being able to handle semantic and arithmetic concepts, maintaining the standard model. However, it can be easily shown that both theories are ω- inconsistent. Although usually a theory of truth is generally expected to (...)
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  • Old Wine in (Somewhat Leaky) New Bottles: Some Comments on Beall.Graham Priest - 2016 - Australasian Journal of Logic 13 (5).
    Dialetheists concerning the paradoxes of self-refrence have often argued that the phenomeonon provides a choice between inconsistency and expressive incompleteness, and that inconsistency is the correct choice. In a recent paper 75: 573-84), JC Beall attacks this argument. This paper analyses his arguments, and argues that his paper simply provides a new spin on matters well known.
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  • Information and logical discrimination.Patrick Allo - 2012 - In S. Barry Cooper (ed.), How the World Computes. pp. 17--28.
    Informational conceptions of logic are barely novel. We find them in the work of John Corcoran, in several papers on substructural and constructive logics by Heinrich Wansing, and in the interpretation of the Routley-Meyer semantics for relevant logics in terms of Barwises and Perrys theory of situations. Allo & Mares [2] present an informational account of logical consequence that is based on the content-nonexpantion platitude, but that also relies on a double inversion of the standard direction of explanation (in- formation (...)
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  • Logical pluralism and semantic information.Patrick Allo - 2007 - Journal of Philosophical Logic 36 (6):659 - 694.
    Up to now theories of semantic information have implicitly relied on logical monism, or the view that there is one true logic. The latter position has been explicitly challenged by logical pluralists. Adopting an unbiased attitude in the philosophy of information, we take a suggestion from Beall and Restall at heart and exploit logical pluralism to recognise another kind of pluralism. The latter is called informational pluralism, a thesis whose implications for a theory of semantic information we explore.
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  • Truth and Falsehood: An Inquiry Into Generalized Logical Values.Yaroslav Shramko & Heinrich Wansing - 2011 - Dordrecht, Netherland: Springer.
    The book presents a thoroughly elaborated logical theory of generalized truth-values understood as subsets of some established set of truth values. After elucidating the importance of the very notion of a truth value in logic and philosophy, we examine some possible ways of generalizing this notion. The useful four-valued logic of first-degree entailment by Nuel Belnap and the notion of a bilattice constitute the basis for further generalizations. By doing so we elaborate the idea of a multilattice, and most notably, (...)
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  • Requiem for logical nihilism, or: Logical nihilism annihilated.Bogdan Dicher - 2020 - Synthese 198 (8):7073-7096.
    Logical nihilism is the view that the relation of logical consequence is empty: there are counterexamples to any putative logical law. In this paper, I argue that the nihilist threat is illusory. The nihilistic arguments do not work. Moreover, the entire project is based on a misguided interpretation of the generality of logic.
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  • Instability and Contraction: Méditations hégéliennes I.Elia Zardini - 2019 - Journal of Philosophical Logic 48 (1):155-188.
    In other works, I’ve proposed a solution to the semantic paradoxes which, at the technical level, basically relies on failure of contraction. I’ve also suggested that, at the philosophical level, contraction fails because of the instability of certain states of affairs. In this paper, I try to make good on that suggestion.
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  • (1 other version)The original sin of proof-theoretic semantics.Bogdan Dicher & Francesco Paoli - 2020 - Synthese:1-26.
    Proof-theoretic semantics is an alternative to model-theoretic semantics. It aims at explaining the meaning of the logical constants in terms of the inference rules that govern their behaviour in proofs. We argue that this must be construed as the task of explaining these meanings relative to a logic, i.e., to a consequence relation. Alas, there is no agreed set of properties that a relation must have in order to qualify as a consequence relation. Moreover, the association of a consequence relation (...)
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  • Is multiset consequence trivial?Petr Cintula & Francesco Paoli - 2016 - Synthese 199 (Suppl 3):741-765.
    Dave Ripley has recently argued against the plausibility of multiset consequence relations and of contraction-free approaches to paradox. For Ripley, who endorses a nontransitive theory, the best arguments that buttress transitivity also push for contraction—whence it is wiser for the substructural logician to go nontransitive from the start. One of Ripley’s allegations is especially insidious, since it assumes the form of a trivialisation result: it is shown that if a multiset consequence relation can be associated to a closure operator in (...)
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  • MV-Algebras and Quantum Computation.Antonio Ledda, Martinvaldo Konig, Francesco Paoli & Roberto Giuntini - 2006 - Studia Logica 82 (2):245-270.
    We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers.
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  • (1 other version)Relevance logic.Edwin Mares - 2008 - Stanford Encyclopedia of Philosophy.
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  • A substructural analysis of embedded conditionals.Pilar Terrés Villalonga - 2020 - Synthese 199 (Suppl 3):571-595.
    The aim of this paper is to give a general solution to the paradoxes of the material conditional, including the paradoxes generated by embedded conditionals. The solution consists in a pragmatic reinterpretation of the formal languages of classical logic LK and relevant logic LR as presented in Paoli. In particular I argue that the material conditional in the classical logic LK captures the truth conditions of “if...then”, but ignores certain pragmatic enrichments that are associated to it, while relevant logic LR (...)
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  • On structural contraction and why it fails.Lucas Rosenblatt - 2019 - Synthese 198 (3):2695-2720.
    The goal of the paper is to discuss whether substructural non-contractive accounts of the truth-theoretic paradoxes can be philosophically motivated. First, I consider a number of explanations that have been offered to justify the failure of contraction and I argue that they are not entirely compelling. I then present a non-contractive theory of truth that I’ve proposed elsewhere. After looking at some of its formal properties, I suggest an explanation of the failure of structural contraction that is compatible with it.
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  • Substructural logics, pragmatic enrichment, and the inferential role of logical constants.Pilar Terrés Villalonga - 2020 - Inquiry: An Interdisciplinary Journal of Philosophy 63 (6):628-654.
    ABSTRACT My aim in this paper is to present a pluralist thesis about the inferential role of logical constants, which embraces classical, relevant, linear and ordered logic. That is, I defend that a logical constant c has more than one correct inferential role. The thesis depends on a particular interpretation of substructural logics' vocabulary, according to which classical logic captures the literal meaning of logical constants and substructural logics encode a pragmatically enriched sense of those connectives. The paper is divided (...)
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  • Validity, dialetheism and self-reference.Federico Matias Pailos - 2020 - Synthese 197 (2):773-792.
    It has been argued recently that dialetheist theories are unable to express the concept of naive validity. In this paper, we will show that LP\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}$$\end{document} can be non-trivially expanded with a naive validity predicate. The resulting theory, LPVal\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf {LP}^{\mathbf {Val}}$$\end{document} reaches this goal by adopting a weak self-referential procedure. We show that LPVal\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf (...)
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  • An informational interpretation of weak relevant logic and relevant property theory.Edwin Mares - 2017 - Synthese 199 (Suppl 3):547-569.
    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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  • The very idea of a substructural approach to paradox.Lionel Shapiro - 2016 - Synthese 199 (Suppl 3):767-786.
    This paper aims to call into question the customary division of logically revisionary responses to the truth-theoretic paradoxes into those that are “substructural” and those that are “ structural.” I proceed by examining, as a case study, Beall’s recent proposal based on the paraconsistent logic LP. Beall formulates his response to paradox in terms of a consequence relation that obeys all standard structural rules, though at the price of the language’s lacking a detaching conditional. I argue that the same response (...)
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  • (1 other version)Paraconsistencia pura.Bruno Da Ré - 2019 - Revista de Humanidades de Valparaíso 13:90-101.
    Dentro del conjunto de las lógicas no clásicas, las lógicas paraconsistentes han suscitado de manera particular el interés de diversos filósofos. Además de las definiciones tradicionales, en los últimos años, se han propuesto nuevas maneras de caracterizar a la paraconsistencia. Lo que tienen en común todas estas definiciones es que alguna forma de la regla o de la metarregla de explosión debe ser rechazada. En este artículo, presentaré dichas definiciones y evaluaré el rol que juegan la negación y la transitividad (...)
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  • (1 other version)Relevant Agents.Marta Bílková, Ondrej Majer, Michal Peliš & Greg Restall - 1998 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 22-38.
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  • From Natural to Formal Language: A Case for Logical Pluralism.Pilar Terrés Villalonga - 2019 - Topoi 38 (2):333-345.
    I argue for a version of logical pluralism based on the plurality of legitimate formalizations of the logical vocabulary. In particular, I argue that the apparent rivalry between classical and relevant logic can be resolved, given that both logics capture and formalize normative and legitimate senses of logical consequence: classical logic encodes “follows from” as truth preservation and captures the truth conditions of the logical constants, while relevant logic encodes a notion of “follows from” which, apart from preserving truth, avoids (...)
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  • Truth, Pretense and the Liar Paradox.Bradley Armour-Garb & James A. Woodbridge - 2015 - In T. Achourioti, H. Galinon, J. Martínez Fernández & K. Fujimoto (eds.), Unifying the Philosophy of Truth. Dordrecht: Imprint: Springer. pp. 339-354.
    In this paper we explain our pretense account of truth-talk and apply it in a diagnosis and treatment of the Liar Paradox. We begin by assuming that some form of deflationism is the correct approach to the topic of truth. We then briefly motivate the idea that all T-deflationists should endorse a fictionalist view of truth-talk, and, after distinguishing pretense-involving fictionalism (PIF) from error- theoretic fictionalism (ETF), explain the merits of the former over the latter. After presenting the basic framework (...)
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  • The nature of entailment: an informational approach.Yaroslav Shramko & Heinrich Wansing - 2019 - Synthese 198 (S22):5241-5261.
    In this paper we elaborate a conception of entailment based on what we call the Ackermann principle, which explicates valid entailment through a logical connection between sentences depending on their informational content. We reconstruct Dunn’s informational semantics for entailment on the basis of Restall’s approach, with assertion and denial as two independent speech acts, by introducing the notion of a ‘position description’. We show how the machinery of position descriptions can effectively be used to define the positive and the negative (...)
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  • Substructural epistemic logics.Igor Sedlár - 2015 - Journal of Applied Non-Classical Logics 25 (3):256-285.
    The article introduces substructural epistemic logics of belief supported by evidence. The logics combine normal modal epistemic logics with distributive substructural logics. Pieces of evidence are represented by points in substructural models and availability of evidence is modelled by a function on the point set. The main technical result is a general completeness theorem. Axiomatisations are provided by means of two-sorted Hilbert-style calculi. It is also shown that the framework presents a natural solution to the problem of logical omniscience.
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  • Implicational paradoxes and the meaning of logical constants.Francesco Paoli - 2007 - Australasian Journal of Philosophy 85 (4):553 – 579.
    I discuss paradoxes of implication in the setting of a proof-conditional theory of meaning for logical constants. I argue that a proper logic of implication should be not only relevant, but also constructive and nonmonotonic. This leads me to select as a plausible candidate LL, a fragment of linear logic that differs from R in that it rejects both contraction and distribution.
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  • On Polarity Frames: Applications to Substructural and Lattice-based Logics.Tomoyuki Suzuki - 2014 - In Rajeev Goré, Barteld Kooi & Agi Kurucz (eds.), Advances in Modal Logic, Volume 10: Papers From the Tenth Aiml Conference, Held in Groningen, the Netherlands, August 2014. London, England: CSLI Publications. pp. 533-552.
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  • Investigations into a left-structural right-substructural sequent calculus.Lloyd Humberstone - 2007 - Journal of Logic, Language and Information 16 (2):141-171.
    We study a multiple-succedent sequent calculus with both of the structural rules Left Weakening and Left Contraction but neither of their counterparts on the right, for possible application to the treatment of multiplicative disjunction against the background of intuitionistic logic. We find that, as Hirokawa dramatically showed in a 1996 paper with respect to the rules for implication, the rules for this connective render derivable some new structural rules, even though, unlike the rules for implication, these rules are what we (...)
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  • Wittgenstein on Incompleteness Makes Paraconsistent Sense.Francesco Berto - 2012 - In Francesco Berto, Edwin Mares, Koji Tanaka & Francesco Paoli (eds.), Paraconsistency: Logic and Applications. Dordrecht, Netherland: Springer. pp. 257--276.
    I provide an interpretation of Wittgenstein's much criticized remarks on Gödel's First Incompleteness Theorem in the light of paraconsistent arithmetics: in taking Gödel's proof as a paradoxical derivation, Wittgenstein was right, given his deliberate rejection of the standard distinction between theory and metatheory. The reasoning behind the proof of the truth of the Gödel sentence is then performed within the formal system itself, which turns out to be inconsistent. I show that the models of paraconsistent arithmetics (obtained via the Meyer-Mortensen (...)
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  • Residuated Structures and Orthomodular Lattices.D. Fazio, A. Ledda & F. Paoli - 2021 - Studia Logica 109 (6):1201-1239.
    The variety of residuated lattices includes a vast proportion of the classes of algebras that are relevant for algebraic logic, e.g., \-groups, Heyting algebras, MV-algebras, or De Morgan monoids. Among the outliers, one counts orthomodular lattices and other varieties of quantum algebras. We suggest a common framework—pointed left-residuated \-groupoids—where residuated structures and quantum structures can all be accommodated. We investigate the lattice of subvarieties of pointed left-residuated \-groupoids, their ideals, and develop a theory of left nuclei. Finally, we extend some (...)
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  • Correction to: Variations on intra-theoretical logical pluralism: internal versus external consequence.Bogdan Dicher - 2020 - Philosophical Studies 177 (3):687-687.
    In the original publication of the article, in Definition 4, the sixth line which reads as.
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  • From consequence operator to universal logic: a survey of general abstract logic.Jean-Yves Beziau - 2005 - In Jean-Yves Béziau (ed.), Logica Universalis: Towards a General Theory of Logic. Boston: Birkhäuser Verlog. pp. 3--17.
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  • Informational Semantics as a Third Alternative?Patrick Allo & Edwin Mares - 2011 - Erkenntnis 77 (2):167-185.
    Informational semantics were first developed as an interpretation of the model-theory of substructural (and especially relevant) logics. In this paper we argue that such a semantics is of independent value and that it should be considered as a genuine alternative explication of the notion of logical consequence alongside the traditional model-theoretical and the proof-theoretical accounts. Our starting point is the content-nonexpansion platitude which stipulates that an argument is valid iff the content of the conclusion does not exceed the combined content (...)
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  • Nikolaos Galatos.Hiroakira Ono - 2006 - Studia Logica 83 (1-3):1-32.
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