Relevant Logic Research Articles

Topics in Relevant Logic: A Semantic Perspective

Topics in Relevant Logic: A Semantic Perspective

Centering racial health equity in systematic reviews Paper 4: A systematic review on the use of logic models and frameworks for methodological conduct of evidence synthesis

ObjectiveTo identify evidence syntheses of health interventions addressing racial health equity reporting the use of equity-focused frameworks and logic models. Study Design and SettingThe search strategy included three sources; a search of three bibliographic databases to identify systematic reviews assessing interventions to improve racial health equity, semi-structured interviews with diverse group and a targeted organization website searches (e.g. NIH, USPSTF) to identify relevant logic models and frameworks. The searches were conducted between January 1, 2020, and January 25, 2023. We used a qualitative approach to identify and describe key characteristics of equity-focused logic models and frameworks used in evidence syntheses. ResultsOf the 153 racial health equity-focused evidence syntheses identified, 2 explicitly used logic models to describe the intervention mechanism. We identified seven existing health equity frameworks from semi-structured interviews and electronic search of key websites that were categorized by stated purpose as providing guidance for 1) research, 2) health policy, 3) digital healthcare solutions, and 4) clinical preventive services. Two out of 7 frameworks included guidance on integrating frameworks or logic models in evidence synthesis while the majority provided contextual information on how to define or consider race or racism as a structural determinant of health. ConclusionThere is limited use of logic models and frameworks in evidence syntheses addressing racial health equity. There is a need for more applied frameworks providing guidance for framing, conducting and interpreting findings of evidence syntheses addressing racial health equity.

Epistemic Logics for Relevant Reasoners

We present a neighbourhood-style semantic framework for modal epistemic logic modelling agents who process information using relevant logic. The distinguishing feature of the framework in comparison to relevant modal logic is that the environment the agent is situated in is assumed to be a classical possible world. This framework generates two-layered logics combining classical logic on the propositional level with relevant logic in the scope of modal operators. Our main technical result is a general soundness and completeness theorem.

Simplified Semantics for Further Relevant Logics I

This paper shows that the relevant logics E and Π′ are strongly sound and complete with regards to a version of the “simplified” Routley-Meyer semantics. Such a semantics for E has been thought impossible. Although it is impossible if an admissible rule of E  the rule of restricted assertion or equivalently Ackermann’s δ-rule  is solely added as a primitive rule, it is very much possible when E is axiomatized in the way Anderson and Belnap did. The simplified semantics for E and Π′ requires unreduced frames. Contra what has been claimed, however, no additional frame component is required over and above what’s required to model other relevant logics such as T and R. It is also shown how to modify the tonicity requirements of the ternary relation so as to allow for the standard truth condition for both fusion – the intensional conjunction ◦ – as well as the converse conditional ←.

Simplified semantics for further relevant logics II

It is shown how to model propositional constants within the simplified Routley-Meyer semantics. Various axioms and rules allowing the definition of modal operators, implicative negations, enthymematical conditionals, and propositions expressing various infinite conjunctions and disjunctions are set forth and shown to correspond to specific frame conditions. Two propositional constants which are both often designated as “the Ackermann constant” are shown to capture two such “infinite” propositions: The conjunction of every logical law and the conjunction of every truth –what Anderson and Belnap called the “world” constant.

Semiconic idempotent logic I: Structure and local deduction theorems

Semiconic idempotent logic is a common generalization of intuitionistic logic, relevance logic with mingle, and semilinear idempotent logic. It is an algebraizable logic and it admits a cut-free hypersequent calculus. We give a structural decomposition of its characteristic algebraic semantics, conic idempotent residuated lattices, showing that each of these is an ordinal sum of simpler partially ordered structures. This ordinal sum is indexed by a totally ordered residuated lattice, which serves as its skeleton and is both a subalgebra and nuclear image. We equationally characterize the totally ordered residuated lattices appearing as such skeletons. Further, we describe both congruence and subalgebra generation in conic idempotent residuated lattices, proving that every variety generated by these enjoys the congruence extension property. In particular, this holds for semilinear idempotent residuated lattices. Based on this analysis, we obtain a local deduction theorem for semiconic idempotent logic, which also specializes to semilinear idempotent logic.

One Variable Relevant Logics are S5ish

Here I show that the one-variable fragment of several first-order relevant logics corresponds to certain S5ish extensions of the underlying propositional relevant logic. In particular, given a fairly standard translation between modal and one-variable languages and a permuting propositional relevant logic L, a formula A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal {A}$$\\end{document} of the one-variable fragment is a theorem of LQ (QL) iff its translation is a theorem of L5 (L.5). The proof is model-theoretic. In one direction, semantics based on the Mares-Goldblatt [15] semantics for quantified L are transformed into ternary (plus two binary) relational semantics for S5-like extensions of L (for a general presentation, see Seki [26, 27]). In the other direction, a valuation is given for the full first-order relevant logic based on L into a model for a suitable S5 extension of L. I also discuss this work’s relation to finding a complete axiomatization of the constant domain, non-general frame ternary relational semantics for which RQ is incomplete [11].

Phrasal Coordination Relatedness Logic

I presented a sub-classical relating logic based on a relating via an NL-inspired relating relation Rcss. The relation Rcss is motivated by the NL-phenomenon of phrasal (subsentential) coordination, exhibiting an important aspect of contents relating among the arguments of binary connectives. The resulting logic Lcss can be viewed as a relevance logic exhibiting a contents related relevance, stronger than the variable-sharing property of other relevance logics like R. Note that relating here is not “tailored” to justify some predetermined logic; rather, the relating relation is independently justified, and induces a logic not previously investigated.

Routes to relevance: Philosophies of relevant logics

AbstractRelevant logics are a family of non‐classical logics characterized by the behavior of their implication connectives. Unlike some other non‐classical logics, such as intuitionistic logic, there are multiple philosophical views motivating relevant logics. Further, different views seem to motivate different logics. In this article, we survey five major views motivating the adoption of relevant logics: Use Criterion, sufficiency, meaning containment, theory construction, and truthmaking. We highlight the philosophical differences as well as the different logics they support. We end with some questions for future research.

Logic in the deep end

Abstract Weak enough relevant logics are often closed under depth substitutions. To determine the breadth of logics with this feature, we show there is a largest sublogic of R closed under depth substitutions and that this logic can be recursively axiomatized.

(What) Is Feminist Logic? (What) Do We Want It to Be?

‘Feminist logic’ may sound like an impossible, incoherent, or irrelevant project, but it is none of these. We begin by delineating three categories into which projects in feminist logic might fall: philosophical logic, philosophy of logic, and pedagogy. We then defuse two distinct objections to the very idea of feminist logic: the irrelevance argument and the independence argument. Having done so, we turn to a particular kind of project in feminist philosophy of logic: Valerie Plumwood's feminist argument for a relevance logic ( L Plum ) . Plumwood's work serves as our primary case study as we turn to the project of considering three different ways we might understand her argument and revisionist arguments like it: as a priori theorizing, as ameliorative conceptual engineering, or as instances of anti-exceptionalist approaches to logic. After arguing that the anti-exceptionalist approach seems to provide the most promising means of understanding the kind of project undertaken in a feminist challenge to classical logic, we briefly address the consequences that this might have for logic instruction. Here, we argue for the perhaps unexpected conclusion that feminist programs ought to offer more, not less, instruction in logic for those who take interest.

Some Remarks on the Logic of Probabilistic Relevance

In this paper we deepen some aspects of the statistical approach to relevance by providing logics for the syntactical treatment of probabilistic relevance relations. Specifically, we define conservative expansions of Classical Logic endowed with a ternary connective ⇝ - indeed, a constrained material implication - whose intuitive reading is “x materially implies y and it is relevant to y under the evidence z”. In turn, this ensures the definability of a formula in three-variables R(x, z, y) which is the representative of relevance in the object language. We outline the algebraic semantics of such logics, and we apply the acquired machinery to investigate some termdefined weakly connexive implications with some intuitive appeal. As a consequence, a further motivation of (weakly) connexive principles in terms of relevance and background assumptions obtains.

Discussion on the Origin of Chinese Modernization from the Perspective of Classical Marxist Theory

Chinese modernization is socialist modernization with Chinese characteristics under the leadership of the Communist Party of China, and it is the contemporary form of Chinese socialist modernization under the grand historical vision, which has considerable research value. This paper mainly combines the theoretical vision with the historical vision, studies and discusses the origin of Chinese modernization, from China’s “Oriental society,” a modern prehistoric social form, to modern China stepping on the socialist road under the basic circumstances of world history, and takes the initiative to master the relevant logic of the historical trend. This paper also presents the research and discussion on why it is possible for modern China to realize Chinese modernization, and to solve the problem of the origin of Chinese modernization in theory and historical logic.

Bisequent Calculus for Four-Valued Quasi-Relevant Logics: Cut Elimination and Interpolation

We present a uniform syntactical characterisation of the class of quasi-relevant logics which are four-valued extensions of the basic relevant logic B of Meyer and Routley. All these logics are obtained by the addition of suitable quasi-relevant implications to the four-valued logic of First Degree Entailment FDE. So far they were characterised axiomatically and semantically in several ways but did not obtain a special proof-theoretic treatment. To this aim a generalised form of sequent calculus called bisequent calculus (BSC) is applied. In BSC rules operate on the ordered pairs of ordinary sequents. It may be treated as the weakest kind of system in the rich family of generalised sequent calculi operating on items which are some collections of ordinary sequents, like hypersequents or nested sequents. It is shown that all logics under consideration have cut-free characterisation in BSC which satisfies the subformula property and yields decidability. It is also shown that the interpolation theorem holds for these logics if their language is enriched with additional negation.

On Pretabular Extensions of Relevance Logic

We exhibit infinitely many semisimple varieties of semilinear De Morgan monoids (and likewise relevant algebras) that are not tabular, but which have only tabular proper subvarieties. Thus, the extension of relevance logic by the axiom (p→q)∨(q→p)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(p\\rightarrow q)\\vee (q\\rightarrow p)$$\\end{document} has infinitely many pretabular axiomatic extensions, regardless of the presence or absence of Ackermann constants.

Topic Transparency and Variable Sharing in Weak Relevant Logics

Topic Transparency and Variable Sharing in Weak Relevant Logics

Polysiloxane-Based Molecular Logic Gate for Dual-Channel Visualizing Mitochondrial pH and Sulphite Changes during Cuproptosis.

Intracellular Cu-induced regulated cell death, characterized by the aggregation of lipidizing mitochondrial enzymes, is called cuproptosis. Mitochondria play a vital role in the metabolic regulation of cell injury and stressful immune responses. The pH levels and sulfur dioxide (SO2) content in mitochondria have important indicative roles in the regulation of cuproptosis. However, fluorescent probes that simultaneously detect changes in pH and SO2 in mitochondria during cuprotosis have not been reported. To fill this blank, in this study, we dexterously used functional polysiloxane as a fluorescent platform to propose a molecular logic gate probe P0-pH-SO2 for detecting changes in intramitochondrial pH and SO2 content through a dual-channel mode. In addition, we defined a new function to reflect the cellular state of the elesclomol-induced cuproptosis process based on the input and output of the relevant logic relationship. This new fluorescent molecular logic gate probe P0-pH-SO2 can be rapidly activated by mitochondrial sulfites to induce green fluorescence, while the red fluorescence is quenched with the proton in the mitochondria. Overall, this study developed a novel logic-gated molecular probe that provided a versatile strategy for monitoring the role played by intramitochondrial sulfites and H+ in cuproptosis. This work will open the way to broaden the applications of molecular logic gates and fluorescent polysiloxanes.

A Variety of DeMorgan Negations in Relevant Logics

The present paper is inspired by Sylvan and Plumwood’s logicBM defined in “Non-normal relevant logics” and by their treatmentof negation with the ∗-operator in “The semantics of first-degree en-tailment”. Given a positive logic L including Routley and Meyer’sbasic positive logic and included in either the positive fragment of Eor in that of RW, we investigate the essential De Morgan negation ex-pansions of L and determine all the deductive relations they maintainto each other. A Routley-Meyer semantics is provided for each logicdefined in the paper.

Val (Routley) Plumwood: Work in Logic

Val Plumwood (nee Morrell) is best known in the logic community for her work on relevant logics published jointly with Richard Sylvan. Together, as `"Val and Richard Routley", they worked at the center of the Canberra Logic Group from 1971 to 1981 before they divorced and changed names, whereupon Val shifted her focus to issues in environmental philosophy. Her writing in that latter field drew so much attention, in fact, that most people familiar with her philosophical work know her solely for contributions there and are quite often surprised to hear of her work in non-classical logic. While her ``fame as an environmental philosopher overshadowed her work in logic, this work included significant contributions to the emerging study of non-classical logics and relevant logics in particular. Like Sylvan, she later turned to applications of this non-classical thinking in other areas, eventually in areas traditionally deemed beyond the reach of logical innovation.

From Excluded Middle to Homogenization in Plumwood’s Feminist Critique of Logic


 
 
 A key facet of Valerie Plumwood’s feminist critique of logic is her analysis of classical negation. On Plumwood’s reading, the exclusionary features of classical negation generate hierarchical dualisms, i.e., dichotomies in which dominant groups’ primacy is reinforced while underprivileged groups are oppressed. For example, Plumwood identifies the system collapse following from ex contradictione quodlibet—that a theory including both φ and ∼φ trivializes—as a primary source of many of these features. Although Plumwood considers the principle of excluded middle to be compatible with her goals, that she identifies relevant logics as systems lacking a hierarchical negation—whose first-degree fragments are both paraconsistent and paracomplete—suggests that excluded middle plays some role in hierarchical dualisms as well. In these notes, I examine the role of excluded middle in generating oppressive homogenization and try to clarify the relationship between Plumwood’s critique and this principle from several contemporary perspectives. Finally, I examine the matter of whether Plumwood’s critique requires relevance or whether a non-relevant logic could satisfy her criteria and serve as a liberatory logic of difference.