Results for 'Logics of formal inconsistency'

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  1. 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 (...)
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  2. Towards a Philosophical Understanding of the Logics of Formal Inconsistency.Walter Carnielli & Abílio Rodrigues - 2015 - Manuscrito 38 (2):155-184.
    In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also (...)
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  3. 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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  4. On Philosophical Motivations for Paraconsistency: An Ontology-Free Interpretation of the Logics of Formal Inconsistency.Walter Carnielli & Abilio Rodrigues - manuscript
    In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non- contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We (...)
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  5. On the Philosophical Motivations for the Logics of Formal Consistency and Inconsistency.Walter Carnielli & Rodrigues Abilio - manuscript
    We present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language. We shall defend the view according to which logics of formal inconsistency are theories of logical consequence of normative and epistemic character. This approach not only allows us to make inferences in the presence of contradictions, but offers a philosophically (...)
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  6. Formal Inconsistency and Evolutionary Databases.Walter A. Carnielli, João Marcos & Sandra De Amo - 2000 - Logic and Logical Philosophy 8 (2):115-152.
    This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics (...)
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  7.  93
    Non-Deterministic Algebraization of Logics by Swap Structures1.Marcelo E. Coniglio, Aldo Figallo-Orellano & Ana Claudia Golzio - 2020 - Logic Journal of the IGPL 28 (5):1021-1059.
    Multialgebras have been much studied in mathematics and in computer science. In 2016 Carnielli and Coniglio introduced a class of multialgebras called swap structures, as a semantic framework for dealing with several Logics of Formal Inconsistency that cannot be semantically characterized by a single finite matrix. In particular, these LFIs are not algebraizable by the standard tools of abstract algebraic logic. In this paper, the first steps towards a theory of non-deterministic algebraization of logics by swap (...)
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  8. Paraconsistent Belief Revision Based on a Formal Consistency Operator.Rafael R. Testa, Marcelo E. Coniglio & Márcio M. Ribeiro - 2015 - CLE E-Prints 15 (8):01-11.
    In this paper two systems of AGM-like Paraconsistent Belief Revision are overviewed, both defined over Logics of Formal Inconsistency (LFIs) due to the possibility of defining a formal consistency operator within these logics. The AGM° system is strongly based on this operator and internalize the notion of formal consistency in the explicit constructions and postulates. Alternatively, the AGMp system uses the AGM-compliance of LFIs and thus assumes a wider notion of paraconsistency - not necessarily (...)
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  9.  70
    Defining LFIs and LFUs in Extensions of Infectious Logics.Szmuc Damian Enrique - 2016 - Journal of Applied Non-Classical Logics 26 (4):286-314.
    The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the -fragment of the logics of nonsense, such as the ones due to Bochvar and Halldén, among others. Here, we extend these logics with classical negations, and we furthermore show that some of these extended systems can be properly regarded as logics of formal inconsistency and logics of (...) undeterminedness. (shrink)
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  10. Swap Structures Semantics for Ivlev-Like Modal Logics.Marcelo E. Coniglio & Ana Claudia Golzio - 2019 - Soft Computing 23 (7):2243-2254.
    In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap (...)
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  11.  63
    Normality Operators and Classical Recapture in Extensions of Kleene Logics.Ciuni Roberto & Massimiliano Carrara - forthcoming - Logic Journal of the IGPL.
    In this paper, we approach the problem of classical recapture for LP and K3 by using normality operators. These generalize the consistency and determinedness operators from Logics of Formal Inconsistency and Underterminedness, by expressing, in any many-valued logic, that a given formula has a classical truth value (0 or 1). In particular, in the rst part of the paper we introduce the logics LPe and Ke3 , which extends LP and K3 with normality operators, and we (...)
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  12. Recovery Operators, Paraconsistency and Duality.Walter A. Carnielli, Marcelo E. Coniglio & Abilio Rodrigues Filho - forthcoming - Logic Journal of the IGPL.
    There are two foundational, but not fully developed, ideas in paraconsistency, namely, the duality between paraconsistent and intuitionistic paradigms, and the introduction of logical operators that express meta-logical notions in the object language. The aim of this paper is to show how these two ideas can be adequately accomplished by the Logics of Formal Inconsistency (LFIs) and by the Logics of Formal Undeterminedness (LFUs). LFIs recover the validity of the principle of explosion in a paraconsistent (...)
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  13. AGM-Like Paraconsistent Belief Change.Rafael R. Testa, Marcelo E. Coniglio & Marcio M. Ribeiro - 2017 - Logic Journal of the IGPL 25 (4):632-672.
    Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the (...)
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  14. Extensions of Priest-da Costa Logic.Thomas Macaulay Ferguson - 2014 - Studia Logica 102 (1):145-174.
    In this paper, we look at applying the techniques from analyzing superintuitionistic logics to extensions of the cointuitionistic Priest-da Costa logic daC (introduced by Graham Priest as “da Costa logic”). The relationship between the superintuitionistic axioms- definable in daC- and extensions of Priest-da Costa logic (sdc-logics) is analyzed and applied to exploring the gap between the maximal si-logic SmL and classical logic in the class of sdc-logics. A sequence of strengthenings of Priest-da Costa logic is examined and (...)
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  15. Twist-Valued Models for Three-Valued Paraconsistent Set Theory.Walter Carnielli & Marcelo E. Coniglio - manuscript
    Boolean-valued models of set theory were independently introduced by Scott, Solovay and Vopěnka in 1965, offering a natural and rich alternative for describing forcing. The original method was adapted by Takeuti, Titani, Kozawa and Ozawa to lattice-valued models of set theory. After this, Löwe and Tarafder proposed a class of algebras based on a certain kind of implication which satisfy several axioms of ZF. From this class, they found a specific 3-valued model called PS3 which satisfies all the axioms of (...)
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  16. Modal Logic S4 as a Paraconsistent Logic with a Topological Semantics.Marcelo E. Coniglio & Leonardo Prieto-Sanabria - 2017 - In Carlos Caleiro, Francisco Dionisio, Paula Gouveia, Paulo Mateus & João Rasga (eds.), Logic and Computation: Essays in Honour of Amilcar Sernadas. London, UK: College Publications. pp. 171-196.
    In this paper the propositional logic LTop is introduced, as an extension of classical propositional logic by adding a paraconsistent negation. This logic has a very natural interpretation in terms of topological models. The logic LTop is nothing more than an alternative presentation of modal logic S4, but in the language of a paraconsistent logic. Moreover, LTop is a logic of formal inconsistency in which the consistency and inconsistency operators have a nice topological interpretation. This constitutes a (...)
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  17. Meeting Hintikka's Challenge to Paraconsistentism.Walter Carnielli - 2009 - Principia: An International Journal of Epistemology 13 (3):283-297.
    Jaakko Hintikka, in a series of talks in Brazil in 2008, defended that IF logic and paraconsistent logic are, in a sense, very similar. Having sketched the proposal of a new paraconsistent system, he maintains that several achievements of IF logic could be reproducible in paraconsistent logic. One of the major difficulties, left as a challenge, would be to formulate some truth conditions for this new paraconsistent first-order language in order to make IF logic and paraconsistent logic more inter-related. My (...)
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  18. Some Investigations on mbC and mCi.Marcelo E. Coniglio & Tarcísio G. Rodrígues - 2014 - In Cezar A. Mortari (ed.), Tópicos de lógicas não clássicas. NEL/UFSC. pp. 11-70.
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  19. A Model-Theoretic Analysis of Fidel-Structures for mbC.Marcelo E. Coniglio - 2020 - In Can Baskent and Thomas Ferguson (ed.), Graham Priest on Dialetheism and Paraconsistency. Springer. pp. 189-216.
    In this paper the class of Fidel-structures for the paraconsistent logic mbC is studied from the point of view of Model Theory and Category Theory. The basic point is that Fidel-structures for mbC (or mbC-structures) can be seen as first-order structures over the signature of Boolean algebras expanded by two binary predicate symbols N (for negation) and O (for the consistency connective) satisfying certain Horn sentences. This perspective allows us to consider notions and results from Model Theory in order to (...)
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  20.  76
    Flaws of Formal Relationism.Mahrad Almotahari - 2013 - Thought: A Journal of Philosophy 2 (4):367-376.
    Formal relationism in the philosophy of mind is the thesis that folk psychological states should be individuated, at least partially, in terms of the purely formal inference-licensing relations between underlying mental representations. It's supposed to provide a Russellian alternative to a Fregean theory of propositional attitudes. I argue that there's an inconsistency between the motivation for formal relationism and the use to which it's put in defense of Russellian propositions. Furthermore, I argue that formal relationism (...)
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  21. Strengths and Limitations of Formal Ontologies in the Biomedical Domain.Barry Smith - 2009 - Electronic Journal of Communication, Information and Innovation in Health 3 (1):31-45.
    We propose a typology of representational artifacts for health care and life sciences domains and associate this typology with different kinds of formal ontology and logic, drawing conclusions as to the strengths and limitations for ontology in a description logics framework. The four types of domain representation we consider are: (i) lexico-semantic representation, (ii) representation of types of entities, (iii) representations of background knowledge, and (iv) representation of individuals. We advocate a clear distinction of the four kinds of (...)
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  22.  58
    Fractal Images of Formal Systems.Paul St Denis & Patrick Grim - 1997 - Journal of Philosophical Logic 26 (2):181-222.
    Formal systems are standardly envisaged in terms of a grammar specifying well-formed formulae together with a set of axioms and rules. Derivations are ordered lists of formulae each of which is either an axiom or is generated from earlier items on the list by means of the rules of the system; the theorems of a formal system are simply those formulae for which there are derivations. Here we outline a set of alternative and explicitly visual ways of envisaging (...)
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  23. Constructing Formal Semantics From an Ontological Perspective. The Case of Second-Order Logics.Thibaut Giraud - 2014 - Synthese 191 (10):2115-2145.
    In a first part, I defend that formal semantics can be used as a guide to ontological commitment. Thus, if one endorses an ontological view \(O\) and wants to interpret a formal language \(L\) , a thorough understanding of the relation between semantics and ontology will help us to construct a semantics for \(L\) in such a way that its ontological commitment will be in perfect accordance with \(O\) . Basically, that is what I call constructing formal (...)
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  24. Curry’s Paradox and Ω -Inconsistency.Andrew Bacon - 2013 - Studia Logica 101 (1):1-9.
    In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic (...)
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  25. Many-Valued Logics. A Mathematical and Computational Introduction.Luis M. Augusto - 2020 - London: College Publications.
    2nd edition. Many-valued logics are those logics that have more than the two classical truth values, to wit, true and false; in fact, they can have from three to infinitely many truth values. This property, together with truth-functionality, provides a powerful formalism to reason in settings where classical logic—as well as other non-classical logics—is of no avail. Indeed, originally motivated by philosophical concerns, these logics soon proved relevant for a plethora of applications ranging from switching theory (...)
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  26. Maximality in Finite-Valued Lukasiewicz Logics Defined by Order Filters.Marcelo E. Coniglio, Francesc Esteva, Joan Gispert & Lluis Godo - 2019 - Journal of Logic and Computation 29 (1):125-156.
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  27. A Road Map of Interval Temporal Logics and Duration Calculi.Valentin Goranko, Angelo Montanari & Guido Sciavicco - 2004 - Journal of Applied Non-Classical Logics 14 (1-2):9-54.
    We survey main developments, results, and open problems on interval temporal logics and duration calculi. We present various formal systems studied in the literature and discuss their distinctive features, emphasizing on expressiveness, axiomatic systems, and (un)decidability results.
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  28.  95
    On Partial and Paraconsistent Logics.Reinhard Muskens - 1999 - Notre Dame Journal of Formal Logic 40 (3):352-374.
    In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent (...) once the right set-up is chosen. Our logic L4 has a semantics that also underlies Belnap’s [4] and is related to the logic of bilattices. L4 is in focus most of the time, but it is also shown how results obtained for L4 can be transferred to several variants. (shrink)
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  29.  65
    Combining Algebraizable Logics.A. Jánossy, Á Kurucz & Á. E. Eiben - 1996 - Notre Dame Journal of Formal Logic 37 (2):366-380.
    The general methodology of "algebraizing" logics is used here for combining different logics. The combination of logics is represented as taking the colimit of the constituent logics in the category of algebraizable logics. The cocompleteness of this category as well as its isomorphism to the corresponding category of certain first-order theories are proved.
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  30.  39
    Relevant Logics, Counterfactual Worlds, and the Understanding of Narrative.Luis Galván - 2019 - In Matei Chihaia & Katharina Rennhak (eds.), Relevance and Narrative Research. Lanham, USA / London: Lexington Books. pp. 37-60.
    The aim of this paper is to explore what insights relevant logics may provide for the understanding of literary fictional narrative. To date, hardly anyone has reflected on the intersection of relevant logics and narratology, and some could think that there is good reason for it. On the one hand, relevance has been a prominent issue in pragmatics, in the tradition of Grice, and Sperber and Wilson; thus framed, relevance is highly context-sensitive, so it seems unsuitable for (...) analysis. On the other hand, the very idea of a logic of narrative has been criticized, arguing that logic brings to a stasis the time of human action (Ricœur, II: 29-60), or that its emphasis on rules misses the creative, unpredictable character of literature (De Man)... First, I will briefly introduce relevant logics, with an eye to showing their interest for narratological concerns, rather than to here providing a coherent (let alone comprehensive) survey. Secondly, lest I get drawn into purely abstract discussion, I will analyse several stories in order to give some instances of the kind of topics congenial to narratology that may be addressed with a relevantist toolkit. Thirdly (and lastly), I will expand in more theoretical fashion on certain issues raised in the second section and bring them into connection with pragmatic relevance theory. (shrink)
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  31. Notes on the Model Theory of DeMorgan Logics.Thomas Macaulay Ferguson - 2012 - Notre Dame Journal of Formal Logic 53 (1):113-132.
    We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, (...)
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  32.  20
    Modeling the Interaction of Computer Errors by Four-Valued Contaminating Logics.Roberto Ciuni, Thomas Macaulay Ferguson & Damian Szmuc - 2019 - In Rosalie Iemhoff, Michael Moortgat & Ruy de Queiroz (eds.), Logic, Language, Information, and Computation. Berlín, Alemania: pp. 119-139.
    Logics based on weak Kleene algebra (WKA) and related structures have been recently proposed as a tool for reasoning about flaws in computer programs. The key element of this proposal is the presence, in WKA and related structures, of a non-classical truth-value that is “contaminating” in the sense that whenever the value is assigned to a formula ϕ, any complex formula in which ϕ appears is assigned that value as well. Under such interpretations, the contaminating states represent occurrences of (...)
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  33.  61
    Non Classical Concept Representation and Reasoning in Formal Ontologies.Antonio Lieto - 2012 - Dissertation, Università Degli Studi di Salerno
    Formal ontologies are nowadays widely considered a standard tool for knowledge representation and reasoning in the Semantic Web. In this context, they are expected to play an important role in helping automated processes to access information. Namely: they are expected to provide a formal structure able to explicate the relationships between different concepts/terms, thus allowing intelligent agents to interpret, correctly, the semantics of the web resources improving the performances of the search technologies. Here we take into account a (...)
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  34. Identity Logics.John Corcoran & Stanley Ziewacz - 1979 - Notre Dame Journal of Formal Logic 20 (4):777-784.
    In this paper we prove the completeness of three logical systems I LI, IL2 and IL3. IL1 deals solely with identities {a = b), and its deductions are the direct deductions constructed with the three traditional rules: (T) from a = b and b = c infer a = c, (S) from a = b infer b = a and (A) infer a = a(from anything). IL2 deals solely with identities and inidentities {a ± b) and its deductions include both (...)
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  35.  76
    Introduction: Formal Approaches to Multi-Agent Systems: Special Issue of Best Papers of FAMAS 2009.B. Dunin-Keplicz & R. Verbrugge - 2013 - Logic Journal of the IGPL 21 (3):404-406.
    This special issue of the Logic Journal of the IGPL includes revised and updated versions of the best work presented at the fourth edition of the workshop Formal Ap- proaches to Multi-Agent Systems, FAMAS'09, which took place in Turin, Italy, from 7 to 11 September, 2009, under the umbrella of the Multi-Agent Logics, Languages, and Organisations Federated Workshops (MALLOW). -/- Just like its predecessor, research reported in this FAMAS 2009 special issue is very much inspired by practical concerns. (...)
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  36.  54
    Introduction: Formal Approaches to Multi-Agent Systems: Special Issue of Best Papers of FAMAS 2007.B. Dunin-Keplicz & R. Verbrugge - 2013 - Logic Journal of the IGPL 21 (3):309-310.
    Over the last decade, multi-agent systems have come to form one of the key tech- nologies for software development. The Formal Approaches to Multi-Agent Systems (FAMAS) workshop series brings together researchers from the fields of logic, theoreti- cal computer science and multi-agent systems in order to discuss formal techniques for specifying and verifying multi-agent systems. FAMAS addresses the issues of logics for multi-agent systems, formal methods for verification, for example model check- ing, and formal approaches (...)
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  37. Normalizing Medical Ontologies Using Basic Formal Ontology.Thomas Bittner & Barry Smith - 2004 - In K. Versorgung & V. Forschung (eds.), Ubiquitäre Information (Proceedings of GMDS 2004). Videel OHG. pp. 199-201.
    Description Logics are nowadays widely accepted as formalisms which provide reasoning facilities which allow us to discover inconsistencies in ontologies in an automatic fashion. Where ontologies are developed in modular fashion, they allow changes in one module to propogated through the system of ontologies automatically in a way which helps to maintain consistency and stability. For this feature to be utilized effectively, however, requires that domain ontologies be represented in a normalized form.
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  38.  62
    Using Cross-Lingual Information to Cope with Underspecification in Formal Ontologies.Werner Ceusters, Ignace Desimpel, Barry Smith & Stefan Schulz - 2003 - Studies in Health Technology and Informatics 95:391-396.
    Description logics and other formal devices are frequently used as means for preventing or detecting mistakes in ontologies. Some of these devices are also capable of inferring the existence of inter-concept relationships that have not been explicitly entered into an ontology. A prerequisite, however, is that this information can be derived from those formal definitions of concepts and relationships which are included within the ontology. In this paper, we present a novel algorithm that is able to suggest (...)
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  39. Eliminating Undecidability and Incompleteness in Formal Systems.Pete Olcott - manuscript
    To eliminate incompleteness, undecidability and inconsistency from formal systems we only need to convert the formal proofs to theorem consequences of symbolic logic to conform to the sound deductive inference model. -/- Within the sound deductive inference model there is a (connected sequence of valid deductions from true premises to a true conclusion) thus unlike the formal proofs of symbolic logic provability cannot diverge from truth.
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  40. 2007. Notes on the Founding of Logics and Metalogic: Aristotle, Boole, and Tarski. Eds. C. Martínez Et Al. Current Topics in Logic and Analytic Philosophy / Temas Actuales de Lógica y Filosofía Analítica. Imprenta Univeridade Santiago de Compostela.John Corcoran - 2007 - In C. Martínez (ed.), Current Topics in Logic and Analytic Philosophy /. pp. 145-178.
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  41. A General Semantics for Logics of Affirmation and Negation.Fabien Schang - 2021 - Journal of Applied Logics - IfCoLoG Journal of Logics and Their Applications 8 (2):593-609.
    A general framework for translating various logical systems is presented, including a set of partial unary operators of affirmation and negation. Despite its usual reading, affirmation is not redundant in any domain of values and whenever it does not behave like a full mapping. After depicting the process of partial functions, a number of logics are translated through a variety of affirmations and a unique pair of negations. This relies upon two preconditions: a deconstruction of truth-values as ordered and (...)
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  42. Frege and the Idea of Formal Language.Taskashi Iida - 2003 - Annals of the Japan Association for Philosophy of Science 12 (1):15-23.
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  43. Logical Consequence in Modal Logic II: Some Semantic Systems for S4.George Weaver - 1974 - Notre Dame Journal of Formal Logic 15:370.
    ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen (...)
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  44. Logics of Rejection: Two Systems of Natural Deduction.Allard Tamminga - 1994 - Logique Et Analyse 146:169-208.
    This paper presents two systems of natural deduction for the rejection of non-tautologies of classical propositional logic. The first system is sound and complete with respect to the body of all non-tautologies, the second system is sound and complete with respect to the body of all contradictions. The second system is a subsystem of the first. Starting with Jan Łukasiewicz's work, we describe the historical development of theories of rejection for classical propositional logic. Subsequently, we present the two systems of (...)
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  45. The Formal-Structural View Of Logical Consequence.Gila Sher - 2001 - Philosophical Review 110 (2):241-261.
    This paper offers a response to William’s Hanson’s criticism of Sher’s formal-structural conception of logical consequence and logical constants.
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  46.  78
    Proof Theory of Finite-Valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued (...)
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  47. Two Adaptive Logics of Norm-Propositions.Mathieu Beirlaen & Christian Straßer - 2013 - Journal of Applied Logic 11 (2):147-168.
    We present two defeasible logics of norm-propositions (statements about norms) that (i) consistently allow for the possibility of normative gaps and normative conflicts, and (ii) map each premise set to a sufficiently rich consequence set. In order to meet (i), we define the logic LNP, a conflict- and gap-tolerant logic of norm-propositions capable of formalizing both normative conflicts and normative gaps within the object language. Next, we strengthen LNP within the adaptive logic framework for non-monotonic reasoning in order to (...)
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  48. On the Application of Formal Principles to Life Science Data: A Case Study in the Gene Ontology.Jacob Köhler, Anand Kumar & Barry Smith - 2004 - In Proceedings of DILS 2004 (Data Integration in the Life Sciences), (Lecture Notes in Bioinformatics 2994). Berlin: Springer. pp. 79-94.
    Formal principles governing best practices in classification and definition have for too long been neglected in the construction of biomedical ontologies, in ways which have important negative consequences for data integration and ontology alignment. We argue that the use of such principles in ontology construction can serve as a valuable tool in error-detection and also in supporting reliable manual curation. We argue also that such principles are a prerequisite for the successful application of advanced data integration techniques such as (...)
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  49. The Cornucopia of Formal-Ontological Relations.Barry Smith & Pierre Grenon - 2004 - Dialectica 58 (3):279–296.
    The paper presents a new method for generating typologies of formal-ontological relations. The guiding idea is that formal relations are those sorts of relations which hold between entities which are constituents of distinct ontologies. We provide examples of ontologies (in the spirit of Zemach’s classic “Four Ontologies” of 1970), and show how these can be used to give a rich typology of formal relations in a way which also throws light on the opposition between threeand four-dimensionalism.
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  50. The Independence Thesis: When Individual and Social Epistemology Diverge.Conor Mayo-Wilson, Kevin J. S. Zollman & David Danks - 2011 - Philosophy of Science 78 (4):653-677.
    In the latter half of the twentieth century, philosophers of science have argued (implicitly and explicitly) that epistemically rational individuals might compose epistemically irrational groups and that, conversely, epistemically rational groups might be composed of epistemically irrational individuals. We call the conjunction of these two claims the Independence Thesis, as they together imply that methodological prescriptions for scientific communities and those for individual scientists might be logically independent of one another. We develop a formal model of scientific inquiry, define (...)
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