Heinrich Wansing, One heresy and one orthodoxy: On dialetheism, dimathematism, and the non-normativity of logic, Erkenntnis 89, 2024, 181-205, published online 09 March 2022. DOI: https://doi.org/10.1007/s10670-022-00528-8, open access.
Abstract. In this paper, Graham Priest’s understanding of dialetheism, the view that there exist true contradictions, is discussed, and various kinds of metaphysical dialetheism are distinguished between. An alternative to dialetheism is presented, namely a thesis called ‘dimathematism’. It is pointed out that dimathematism enables one to escape a slippery slope argument for dialetheism that has been put forward by Priest. Moreover, dimathematism is presented as a thesis that is helpful in rejecting the claim that logic is a normative discipline.
Heinrich Wansing, Beyond paraconsistency. A plea for a radical breach with the Aristotelean orthodoxy in logic, to appear in: Walter Carnielli on Reasoning, Paraconsistency, and Probability, edited by Abilio Rodrigues, Henrique Antunes, and Alfredo Freire, 2022, Springer, to appear 2025.
Abstract. It is suggested to radically break with the time-honored Aristotelean tradition of complete banishment of contradictions in science. In particular, it is argued that it is theoretically rational to believe not only that there exist interesting or important non-trivial negation inconsistent theories but also that there exist interesting or important non-trivial negation inconsistent logics.
Hitoshi Omori and Heinrich Wansing, Varieties of negation and contra-classicality in view of Dunn semantics, in: Katalin Bimbó (ed.), Relevance Logics and other Tools for Reasoning. Essays in Honour of Michael Dunn, College Publications, London, 2022, 309-337. DOI: https://doi.org/10.13154/294-10519, open access.
Abstract. In this paper, we discuss J. Michael Dunn's foundational work on the semantics for First Degree Entailment logic (FDE), also known as Belnap-Dunn logic (or Sanjaya-Belnap-Smiley-Dunn Four-valued Logic, as suggested by Dunn himself). More specifically, by building on the framework due to Dunn, we sketch a broad picture towards a systematic understanding of contra-classicality. Our focus will be on a simple propositional language with negation, conjunction, and disjunction, and we will systematically explore variants of FDE, K3, and LP by tweaking the falsity condition for negation.
Heinrich Wansing and Hitoshi Omori, A note on "A Connexive Conditional", Logos & Episteme 13(3), 2022, 325-328. DOI: 0.5840/logos-episteme202213326, open access.
Abstract. In a recent article, Mario Günther presented a conditional that is claimed to be connexive. The aim of this short discussion note is to show that Günther's claim is not without problems.
Satoru Niki and Heinrich Wansing, On the provable contradictions of the connexive logics C and C3, Journal of Philosophical Logic, 52 (2023), 1355–1383. DOI: https://doi.org/10.1007/s10992-023-09709-4, open access.
Abstract. Despite the tendency to beotherwise, some non-classical logics are known to validate formulas that are invalid in classical logic. A subclass of such systems even possesses pairs of a formula and its negation as theorems, without becoming trivial. How should these provable contradictions be understood? The present paper aims to shed light on aspects of this phenomenon by taking the constructive connexive logic C and its non-constructive extension C3 as samples. The topics covered in this paper include: how new contradictions are found from provable contradictions; how to find constructive provable contradictions in C3; how contradictions can be seen from the viewpoint of strong implication; and generating provable contradictions in C3.
Grigory K. Olkhovikov, On the completeness of some first-order extensions of C, Journal of Applied Logics - IfCoLog Journal 10(1), 2023, 57-114. DOI: 10.13154/294-9815, open access.
Abstract. We show the completeness of several Hilbert-style systems resulting from extending the propositional connexive logics C and C3 by the set of Nelsonian quantifiers, both in the varying domain and in the constant domain setting. In doing so, we focus on countable signatures and proceed by variations of Henkin construction. In addition, we consider possible extensions of C and C3 with a non-Nelsonian universal quantifier preserving a specific rapport between the interpretation of conditionals and the interpretation of the universal quantification which is visible in both intuitionistic logic and Nelson’s logic but is lost if one adds the Nelsonian quantifiers on top of the propositional basis provided by C and C3. We briefly explore the completeness systems resulting from adding this non-Nelsonian quantifier either together with the Nelsonian ones or separately to the two propositional connexive logics.
Heinrich Wansing and Sara Ayhan, Logical multilateralism, Journal of Philosophical Logic 52 (2023),1603–1636. DOI: https://doi.org/10.1007/s10992-023-09720-9, open access.
Abstract. In this paper we will consider the existing notions of bilateralism in the context of proof-theoretic semantics and propose, based on our understanding of bilateralism, an extension to logical multilateralism. This approach differs from what has been proposed under this name before in that we do not consider multiple speech acts as the core of such a theory but rather multiple consequence relations. We will argue that for this aim the most beneficial proof-theoretical realization is to use sequent calculi with multiple sequent arrows satisfying some specific conditions, which we will lay out in this paper. We will unfold our ideas with the help of a case study in logical tetralateralism and present an extension of Almukdad and Nelson’s propositional constructive four-valued logic by unary operations of meaningfulness and nonsensicality. We will argue that in sequent calculi with multiple sequent arrows it is possible to maintain certain features that are desirable if we assume an understanding of the meaning of connectives in the spirit of proof-theoretic semantics. The use of multiple sequent arrows will be justified by the presence of congruentiality-breaking unary connectives.
Satoru Niki, Double negation as minimal negation, Journal of Logic, Language and Information 32(5) , 2023, 861-886. DOI: https://doi.org/10.1007/s10849-023-09413-1, open access.
Abstract. N. Kamide introduced a pair of classical and constructive logics, each with a peculiar type of negation: its double negation behaves as classical and intuitionistic negation, respectively. A consequence of this is that the systems prove contradictions but are non-trivial. The present paper aims at giving insights into this phenomenon by investigating subsystems of Kamide's logics, with a focus on a system in which the double negation behaves as the negation of minimal logic. We establish the negation inconsistency of the system and embeddability of contradictions from other systems. In addition, we attempt at an informational interpretation of the negation using the dimathematical framework of H. Wansing.
Heinrich Wansing, Remarks on semantic information and logic. From semantic tetralateralism to the pentalattice 65536_5, Logica Yearbook 2022, Igor Sedlár (ed.), College Publications, London, 2023, 165-186. DOI: https://doi.org/10.13154/294-12570, open access.
Abstract. A 16-element lattice 16inf of generalized semantical values pre-ordered by set-inclusion as an information order is presented. The propositional logic Inf of that lattice is axiomatized and a generalization of 16inf toa 65536-element pentalattice is suggested.
Heinrich Wansing, Constructive logic is connexive and contradictory, Logic and Logical Philosophy, 27 pp., published online 02 January 2024. DOI: 10.12775/LLP.2024.001, open access.
Abstract. This paper deals with the constructiveness of the contra-classical, connexive, paraconsistent, and contradictory non-trivial first-order logic QC, which is a connexive variant of QN4. It is shown that there is a sense in which QC is even more constructive than QN4. The argument focuses on a problem that is mirror-inverted to Raymond Smullyan's drinker paradox, namely the invalidity of what will be called the drinker truism and its dual in QN4 (and QInt), and on a version of the Brouwer-Heyting-Kolmogorov interpretation of the logical operations that treats proofs and disproofs on a par. The validity of the drinker truism and its dual together with the greater constructiveness of QC in comparison to QN4 may serve as further motivation for the study of connexive logics and suggests that constructive logic is connexive and contradictory (the latter understood as being negation inconsistent).
Heinrich Wansing and Zach Weber, Quantifiers in connexive logic (in general and in particular), Logic Journal of the IGPL, published online October 30, 2024, DOI: https://doi.org/10.1093/jigpal/jzae115, open access.
Abstract. Connexive logic has room for two pairs of universal and particular quantifiers: one pair, ∀ and ∃, are standard quantifiers; the other pair, A and E, are unorthodox, but we argue, are well-motivated in the context of connexive logic. Both non-standard quantifiers have been introduced previously, but in the context of connexive logic they have a natural semantic and proof theoretic place, and plausible natural language readings. The result are logics which are negation inconsistent but non-trivial.
Satoru Niki, A note on negation inconsistent variants of FDE-negation, The Australasian Journal of Logic. 21(2), 2024, 64--90. DOI: https://doi.org/10.26686/ajl.v21i2.8202, open access.
Abstract. H. Omori and H. Wansing introduced in a recent paper possible alternatives for the negation of the logic of first-degree entailment. One of their observations with regard to these alternative negations is that some of them turn out to induce negation inconsistency, meaning that some contradictions become provable (under an arbitrary premise) when used in place of the original negation. Omori and Wansing also considered a nondeterministic generalisation of such operators, but it was left open whether the generalised negation similarly induces negation inconsistency. In this paper, we provide an answer to this question in the positive, and moreover look into further generalisation and characterisation of non-deterministic operators which satisfy the formal criteria of negation inconsistency and its pair notion of negation incompleteness in the setting of Omori and Wansing.
Satoru Niki, Intuitionistic views on connexive constructible falsity, Journal of Applied Logics - IfCoLog Journal, 11(2), 2024, 125–157. DOI: https://doi.org/10.13154/294-12564, open access.
Abstract. Intuitionistic logicians generally accept that a negation can be understood as an implication to absurdity. An alternative account of constructive negation is to define it in terms of a primitive notion of falsity. This approach was originally suggested by D. Nelson, who called the operator constructible falsity, as complementing certain constructive aspects of negation. For intuitionistic logicians to be able to understand this new notion, however, it is desirable that constructible falsity has a comprehensive relationship with the traditional intuitionistic negation. This point is especially pressing in H. Wansing's framework of connexive constructible falsity, which exhibits unusual behaviours. From this motivation, this paper enquires what kind of interaction between the two operators can be satisfactory in the framework. We focus on a few natural-looking candidates for such an interaction, and evaluate their relative merits through analyses of their formal properties with both proof-theoretic and semantical means. We in particular note that some interactions allow connexive constructible falsity to provide a different solution to the problem of the failure of the constructible falsity property in intuitionistic logic. An emerging perspective in the end is that intuitionistic logicians may have different preferences depending on whether absurdity is to be understood as the falsehood.
Sara Ayhan and Heinrich Wansing, On synonymy in proof-theoretic semantics. The case of 2Int, Bulletin of the Section of Logic 52 (2023), 187–237. DOI: https://doi.org/10.18778/0138-0680.2023.18, open access.
Abstract. We consider an approach to propositional synonymy in proof-theoretic semanticsthat is defined with respect to a bilateral G3-style sequent calculus SC2Int for the bi-intuitionistic logic 2Int. A distinctive feature of SC2Int is that it makesuse of two kinds of sequents, one representing proofs, the other representingrefutations. The structural rules ofSC2Int, in particular its cut rules, are shownto be admissible. Next, interaction rules are defined that allow transitions fromproofs to refutations, and vice versa, mediated through two different negationconnectives, the well-knownimplies-falsity negationand the less well-knownco-implies-truth negationof 2Int. By assuming that the interaction rules have noimpact on the identity of derivations, the concept of inherited identity betweenderivations in SC2Int is introduced and the notions of positive and negativesynonymy of formulas are defined. Several examples are given of distinct formulasthat are either positively or negatively synonymous. It is conjectured that thetwo conditions cannot be satisfied simultaneously.
Grigory K. Olkhovikov, An intuitionistically complete system of basic intuitionistic conditional logic, Journal of Philosophical Logic, 53 (2024) 1199-1240. DOI: https://doi.org/10.1007/s10992-024-09763-6. open access
Abstract. We introduce a basic intuitionistic conditional logic IntCK that we show to be complete both relative to a special type of Kripke models and relative to a standard translation into first-order intuitionistic logic. We show that IntCK stands in a very natural relation to other similar logics, like the basic classical conditional logic CK and the basic intuitionistic modal logic IK. As for the basic intuitionistic conditional logic ICK proposed by Y. Weiss, IntCK, extends its language with a diamond-like conditional modality, but its diamond-conditional-free fragment is also a proper extension of ICK. We briefly discuss the resulting gap between the two candidate systems of basic intuitionistic conditional logic and the possible pros and cons of both candidates.
Heinrich Wansing and Hitoshi Omori, Connexive Logic, Connexivity, and Connexivism: Remarks on terminology, Studia Logica 112 (2024), 1–35. DOI: https://doi.org/10.1007/s11225-023-10082-1, open access.
Abstract. Over the past ten years, the community researching connexive logics is rapidly growing and a number of papers have been published. However, when it comes to the terminology used in connexive logic, it seems to be not without problems. In this introduction, we aim at making a contribution towards both unifying and reducing the terminology. We hope that this can help making it easier to survey and access the field from outside the community of connexive logicians. Along the way, we will make clear the context to which the papers in this special issue on Frontiers of Connexive Logic belong and contribute.
Yaroslav Shramko and Heinrich Wansing, Connexive exclusion, Erkenntnis, published online August 27, 2024. DOI: https://doi.org/10.1007/s10670-024-00842-3, open access.
Abstract. We present a logic which deals with connexive exclusion. Exclusion (also called “co-implication”) is considered to be a propositional connective dual to the connective of implication. Similarly to implication, exclusion turns out to be non-connexive in both classical and intuitionistic logics, in the sense that it does not satisfy certain principles that express such connexivity. We formulate these principles for connexive exclusion, which are in some sense dual to the well-known Aristotle’s and Boethius’ theses for connexive implication. A logical system in a language containing exclusion and negation can be called a logic of connexive exclusion if and only if it obeys these principles, and, in addition, the connective of exclusion in it is asymmetric, thus being different from a simple mutual incompatibility of propositions. We will develop a certain approach to such a logic of connexive exclusion based on a semantic justification of the connective in question. Our paradigm logic of connexive implication will be the connexive logic C, and exactly like this logic the logic of connexive exclusion turns out to be contradictory though not trivial
Heinrich Wansing and Hitoshi Omori, A note on the historiography of pre-modern connexive logic, in: Hitoshi Omori and Heinrich Wansing (eds), 60 Years of Connexive Logic, Springer, 2025, 1–22, DOI: https://doi.org/10.1007/978-3-031-82994-9_1, open access.
Abstract. The historiography of connexive logic has seen some pitfalls. In the present note, we show that the reception of principles characteristic of connexive logic provides an example of how an unwarranted bias in favor of what is now called ‘classical logic’ and an often accompanying aversion against contradictions can negatively affect the historiography of logic. Moreover, we briefly outline the coverage of the present volume 60 Years of Connexive Logic.
Hitoshi Omori and Heinrich Wansing, Another generalization of connexive logic C, in: Hitoshi Omori and Heinrich Wansing (eds), 60 Years of Connexive Logic, Springer, 2025, 225–240, DOI: https://doi.org/10.1007/978-3-031-82994-9_9, open access.
Abstract. The present article aims at generalizing the approach to connexive logic that was initiated in (Egré and Politzer 2013), by following the work by Paul Egré and Guy Politzer. To this end, a variant of the connexive modal logic CK is introduced and some basic results including soundness and completeness results are established.
Hitoshi Omori and Heinrich Wansing, Ten open problems in connexive logic, in: Hitoshi Omori and Heinrich Wansing (eds), 60 Years of Connexive Logic, Springer, 2025, 241–252, DOI: https://link.springer.com/chapter/10.1007/978-3-031-82994-9_10, open access.
Abstract. In this short note, which is the final chapter of the volume 60 Years of Connexive Logic, we list ten open problems. Some of these problems are technical and precisely stated, while others are less technical and even speculative. We hope that the list inspires some readers to contribute to the field by tackling one or many of the problems.
Sara Ayhan, Notions of Proof and Refutation in ‘Gentzensemantik’: Franz von Kutschera as an Early Proponent of (Bilateralist) Proof-Theoretic Semantics, History and Philosophy of Logic 46(3), 2025, 449–455. DOI: https://doi.org/10.1080/01445340.2024.2393964, open access.
Abstract. This is a comment on a translation of Franz von Kutschera's paper ‘Ein verallgemeinerter Widerlegungsbegriff für Gentzenkalküle’, which was published in German in 1969. The paper is an important predecessor of what is nowadays called ‘proof-theoretic semantics’, which describes the view that the meaning of logical connectives is determined by the rules governing their use in a proof system. Von Kutschera adopts this view in this paper, and more specifically, a bilateralist view on this subject in that his aim is to give a general framework that provides generalized rule schemata for arbitrary connectives both for proving and refuting and to use this as a reference to prove completeness of certain systems of operators purely proof-theoretically. The main logical system in focus here has been shown to be equivalent to N4, Nelson's constructive logic with strong negation. In order to understand the translated paper better, a contextualizing comment is offered referring and relating it to a preceding paper by von Kutschera.
Grigory K. Olkhovikov, A basic system of paraconsistent Nelsonian logic of conditionals, Journal of Logic, Language and Information, 33 (2024), 299–337, 41 pp. DOI: https://doi.org/10.1007/s10849-024-09421-9, open access.
Abstract. We define a Kripke semantics for a conditional logic based on the propositional logic N4, the paraconsistent variant of Nelson's logic of strong negation; we axiomatize the minimal system induced by this semantics. The resulting logic, which we call N4CK, shows strong connections both with the basic intuitionistic logic of conditionals IntCK introduced earlier in [Grigory K. Olkhovikov, An intuitionistically complete system of basic intuitionistic conditional logic, submitted for publication] and with the N4-based modal logic FSK^d introduced in [S. Odintsov, H. Wansing. Constructive predicate logic and constructive modal logic. Formal duality versus semantical duality. In: V. Hendricks et al., eds, First-Order Logic Revisited, 269--286, Berlin, Logos. (2004)] as one of the possible counterparts to the classical modal system K. We map these connections by looking into the embeddings which obtain between the aforementioned systems.
Edoardo Canonica, Inferring from negated conditionals connexively; an experimental investigation of a Boethian inference, submitted for publication.
Abstract. In his sixth century commentary on Cicero’s Topics Boethius presents four examples of what he takes to be valid inferences involving a negated conditional, the form of which we generalise informally as “if ∼(A → B) and A, then ∼B”. We argue that Boethius’ endorsement of these inferences provides evidence of his likely endorsement of reversed variants of Boethius’ Thesis, e.g., ∼(A → B) → (A → ∼B), a principle which is validated by some connexive logics, however is classically invalid. It has furthermore been claimed that connexively valid principles are not only highly intuitive, but that human reasoning can plausibly be characterised as connexive in virtue of this. We investigate the first part of this claim via an experiment in which participants infer outcomes of a simulated game. We conclude that there is good evidence for the intuitiveness of inferences along the lines of reversed variants of Boethius’ Thesis.
Satoru Niki, Correspondence of Contradictions in the Constructive Connexive Calculus C, submitted for publication.
Abstract. The calculus C was introduced by H. Wansing as a constructive logic with strong negation. In addition, C validates the theses of connexive logic that are attributed to Aristotle and Boethius. A further remarkable property of C is that it is a non-trivial but negation inconsistent system: it has a formula and its negation as theorems. From a bilateralist-minded perspective, such a contradiction can be seen as the existence of both a verification and a falsification of one and the same formula. Relatedly, it has been noted by Wansing that there seems to be a kind of correspondence between these two types of derivations when it comes to a proof of contradiction. Following this observation, we attempt in this paper to introduce a precise notion for such a correspondence. We thence establish that this correspondence obtains in propositional and first-order versions of C, via formulations of suitable sequent and tableau calculi.
Heinrich Wansing, Satoru Niki, and Sergey Drobyshevich, Bi-connexive logic, bilateralism, and negation inconsistency, Review of Symbolic Logic, 18 (2025), 859-899, published online March 12, 2025. DOI: 10.1017/S1755020324000248, open access.
Abstract. In this paper we study logical bilateralism understood as a theory of two primitive derivability relations, namely provability and refutability, in a language devoid of a primitive toggling negation and without a falsum constant, ⊥, and a verum constant, ⊤ There is thus no negation that toggles between provability and refutability, and there are no primitive constants that are used to define an “implies falsity” negation and a “co-implies truth” co-negation. This reduction of expressive power notwithstanding, there remains some interaction between provability and refutability due to the presence of (i) a conditional and the refutability condition of conditionals and (ii) a co-implication and the provability condition of co-implications. Moreover, assuming a hyperconnexive understanding of refuting conditionals and a dual understanding of proving co-implications, neither non-trivial negation inconsistency nor hyperconnexivity is lost for unary negation connectives definable by means of certain surrogates of falsum and verum. Whilst a critical attitude towards ⊥ and ⊤ can be justified by problematic aspects of the Brouwer-Heyting-Kolmogorov interpretation of the logical operations for these constants, the aim to reduce the availability of a toggling negation and observations on undefinability may also give further reasons to abandon ⊥ and ⊤.
Satoru Niki, A Note on Contradictions in Francez-Weiss Logics, Logic and Logical Philosophy 34 (2025), 387–416, published online December 12, 2024. DOI: https://doi.org/10.12775/LLP.2024.031, open access.
Abstract. It is an unusual property for a logic to prove a formula and its negation without ending up in triviality. Some systems have nonetheless been observed to satisfy this property: one group of such non-trivial negation inconsistent logics has its archetype in H. Wansing's constructive connexive logic, whose negation-implication fragment already proves contradictions. N. Francez and Y. Weiss subsequently investigated relevant subsystems of this fragment, and Weiss in particular showed that they remain negation inconsistent. In this note, we take a closer look at this phenomenon in the systems of Francez and Weiss, and point out two types of necessary conditions, one proof-theoretic and one relevant, which any contradictory formula must satisfy. As a consequence, we propose a nine-fold classification of provable contradictions for the logics.
Satoru Niki and Hitoshi Omori, Kamide is in America, Moisil and Leitgeb are in Australia, in: Andrzej Indrzejczak and Michał Zawidzki (eds.), Proceedings Eleventh International Conference on Non-Classical Logics. Theory and Applications, Electronic Proceedings in Theoretical Computer Science 415, 2024, pp. 180–194. DOI: http://dx.doi.org/10.4204/EPTCS.415.17, open access.
Abstract. It is not uncommon for a logic to be invented multiple times, hinting at its robustness. This trend is followed also by the expansion BD+ of Belnap-Dunn logic by Boolean negation. Ending up in the same logic, however, does not mean that the semantic interpretations are always the same as well. In particular, different interpretations can bring us to different logics, once the basic setting is moved from a classical one to an intuitionistic one. For BD+, two such paths seem to have been taken; one (BDi) by N. Kamide along the so-called American plan, and another (HYPE) by G. Moisil and H. Leitgeb along the so-called Australian plan. The aim of this paper is to better understand this divergence. This task is approached mainly by (i) formulating a semantics for first-order BD+ that provides an Australian view of the system; (ii) showing connections of the less explored (first-order) BDi with neighbouring systems, including an intermediate logic and variants of Nelson's logics.
Sara Ayhan and Hrafn Valtýr Oddsson, Proof-Theoretic Functional Completeness for the Connexive Logic C, Studia Logica, published online July 8, 2025, https://doi.org/10.1007/s11225-025-10200-1, open access.
Abstract. We show the functional completeness for the connectives of the non-trivial negation inconsistent logic C by using a well-established method implementing purely proof-theoretic notions only. Firstly, given that C contains a strong negation, expressing a notion of direct refutation, the proof needs to be applied in a bilateralist way in that not only higher-order rule schemata for proofs but also for refutations need to be considered. Secondly, given that C is a connexive logic we need to take a connexive understanding of inference as a basis, leading to a different conception of (higher-order) refutation than is usually employed.
Sara Ayhan, Problems and consequences of bilateral notions of (meta-)derivability, Erkenntnis, forthcoming.
Abstract. A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a system with two derivability relations is obtained, which can be quite naturally expressed in a proof system of natural deduction but which faces obstacles in a sequent calculus representation. Since in a sequent calculus there are two derivability relations inherent, one expressed by the sequent sign and one by the horizontal lines holding \emph{between sequents}, in a truly bilateral calculus both need to be dualized. While dualizing the sequent sign is rather straightforwardly corresponding to dualizing the horizontal lines in natural deduction, dualizing the horizontal lines in sequent calculus, uncovers problems that, as will be argued in this paper, shed light on deeper conceptual issues concerning an imbalance between the notions of proof vs. refutation. The roots of this problem will be further analyzed and possible solutions on how to retain a bilaterally desired balance in our system are presented.
Satoru Niki and Heinrich Wansing, Abelian logic on the Bochum Plan (and the American Plan as well), Studia Logica, published online 13 September 2025, https://doi.org/10.1007/s11225-025-10208-7, open access.
Abstract. In this paper, we introduce two new semantic presentations of Abelian logic, the non-trivial negation inconsistent logic of Abelian lattice-ordered groups, which was independently developed by Ettore Casari, and by Robert Meyer and John Slaney. Abelian logic is presented through a methodology that combines elements of what is sometimes referred to as the “Bochum Plan” and the “American Plan.” While the Bochum Plan is an approach to defining contra-classical logics, the American Plan–developed by Nuel Belnap and Michael Dunn–in particular offers a conception of negation that invites an application of the Bochum Plan. The
first semantics is a ternary frame Kripke semantics, and the second is based on ideas from Edwin Mares’ work. Thereby emerges a condition for the falsity of Abelian implication to be supported, which we analyse further in the separate context of the first-degree entailment logic. The perspectives are united in the end to provide a defence against the scepticism concerning the status of the Abelian negation as a negation.
Daniel Skurt and Heinrich Wansing, Solving a New Paradox of Deontic Logic (and a dozen other paradoxes) with RNmatrices for
MC-based Modal Logics, submitted for publication.
Abstract. In this paper it is shown that every extension of the minimal connexive propositional modal logic mMC by a global inference rule is characterized by a restricted non-deterministic matrix (RNmatrix). This result is used to solve a seemingly hitherto unnoticed paradox of deontic logic. In order to further highlight the flexibility of RNmatrices, it is noted that factual detachment of conditional obligations can be characterized by making use of RNmatrices.
Sara Ayhan, Queer feminist logic and contradictions: Or how logic and feminism can be relevant to each other, Synthese, forthcoming.
Abstract. Work in the field of feminist logic is still rather scarce and the field itself remains a contested area of study, but still, it is developing. One approach concentrates on analyzing logical systems with respect to structural features that may perpetuate sexism and oppression or, on the other hand, features that may be helpful for resisting and opposing these social phenomena. Upon this assumption, I want to investigate possible applications of queer feminist views on (philosophy of) logic with respect to a very specific group, namely contradictory logics, i.e., logical systems containing contradictions in their set of theorems. I want to show that, on the one hand, the formal set-up of contradictory logics makes them well-suited from the perspectives of feminist logic and, on the other hand, that queer feminist theories provide a relevant, and so far undeveloped, conceptual motivation for contradictory logics. Thus, bringing together contradictory logics and queer feminist theories may prove fruitful both as a ‘real-life’ motivation for these peripheral logical systems and as a formal basis for a philosophical field that is still characterized by a distrust of formalism.
Heinrich Wansing, Über überconsistent logics and dialetheism, to appear in: Crítica: Revista Hispanoamericana de Filosofía.
Abstract. In this paper, Graham Priest’s claim is discussed that, on balance, the existence of well-motivated non-trivial contradictory logics seems to strengthen the case for dialetheism. It is expounded that to arrive at this conclusion, a relationship must be established between dialetheism and the concept of valid inference as defined in model theory. It is argued that through this relationship, and under variants of a certain assumption that relates model-theoretic structures to reality, proponents of Priest’s dialetheism can obtain the conclusion that the existence of convincingly motivated contradictory logics supports their position. Moreover, it is pointed out that certain logics with valid contradictions and their state-based semantics can be seen as exemplifying a claim that has been called ‘strong dimathematism’ and that avoids the mentioned assumption that relates model-theoretic structures to reality.