Varieties like groups, rings, or Boolean algebras have the property that, in any of their members, the lattice of congruences is isomorphic to a lattice of more manageable objects, for example normal subgroups of groups, two-sided ideals of rings, filters (or ideals) of Boolean algebras.algebraic logic can explain these phenomena at a rather satisfactory level of generality: in every member A of a τ-regular variety ������ the lattice of congruences of A is isomorphic to the lattice of deductive filters on (...) A of the τ-assertional logic of ������. Moreover, if ������ has a constant 1 in its type and is 1-subtractive, the deductive filters on A ∈ ������ of the 1-assertional logic of ������ coincide with the ������-ideals of A in the sense of Gumm and Ursini, for which we have a manageable concept of ideal generation. However, there are isomorphism theorems, for example, in the theories of residuated lattices, pseudointerior algebras and quasi-MV algebras that cannot be subsumed by these general results. The aim of the present paper is to appropriately generalise the concepts of subtractivity and τ-regularity in such a way as to shed some light on the deep reason behind such theorems. The tools and concepts we develop hereby provide a common umbrella for the algebraic investigation of several families of logics, including substructural logics, modal logics, quantum logics, and logics of constructive mathematics. (shrink)

LetA≤Bbe structures, and${\cal K}$a class of structures. An elementb∈BisdominatedbyArelative to${\cal K}$if for all${\bf{C}} \in {\cal K}$and all homomorphismsg,g':B → Csuch thatgandg'agree onA, we havegb=g'b. Our main theorem states that if${\cal K}$is closed under ultraproducts, thenAdominatesbrelative to${\cal K}$if and only if there is a partial functionFdefinable by a primitive positive formula in${\cal K}$such thatFB(a1,…,an) =bfor somea1,…,an∈A. Applying this result we show that a quasivariety of algebras${\cal Q}$with ann-ary near-unanimity term has surjective epimorphisms if and only if$\mathbb{S}\mathbb{P}_n \mathbb{P}_u \left( {\mathcal{Q}_{{\text{RSI}}} } \right)$has (...) surjective epimorphisms. It follows that if${\cal F}$is a finite set of finite algebras with a common near-unanimity term, then it is decidable whether the (quasi)variety generated by${\cal F}$has surjective epimorphisms. (shrink)

Substructural fuzzy logics are substructural logics that are complete with respect to algebras whose lattice reduct is the real unit interval [0.1]. In this paper, we introduce Uninorm logic UL as Multiplicative additive intuitionistic linear logic MAILL extended with the prelinearity axiom ((A → B) ∧ t) ∨ ((B → A) ∧ t). Axiomatic extensions of UL include known fuzzy logics such as Monoidal t-norm logic MTL and Gödel logic G, and new weakening-free logics. Algebraic semantics for these logics are (...) provided by subvarieties of (representable) pointed bounded commutative residuated lattices. Gentzen systems admitting cut-elimination are given in the framework of hypersequents. Completeness with respect to algebras with lattice reduct [0, 1] is established for UL and several extensions using a two-part strategy. First, completeness is proved for the logic extended with Takeuti and Titani's density rule. A syntactic elimination of the rule is then given using a hypersequent calculus. As an algebraic corollary, it follows that certain varieties of residuated lattices are generated by their members with lattice reduct [0, 1]. (shrink)

Substructural logics extending the full Lambek calculus FL have largely benefited from a systematical algebraic approach based on the study of their algebraic counterparts: residuated lattices. Recently, a nonassociative generalization of FL has been studied by Galatos and Ono as the logic of lattice-ordered residuated unital groupoids. This paper is based on an alternative Hilbert-style presentation for SL which is almost MP -based. This presentation is then used to obtain, in a uniform way applicable to most substructural logics, a form (...) of local deduction theorem, description of filter generation, and proper forms of generalized disjunctions. A special stress is put on semilinear substructural logics. Axiomatizations of the weakest semilinear logic over SL and other prominent substructural logics are provided and their completeness with respect to chains defined over the real unit interval is proved. (shrink)

This article presents a detailed formal approach to concepts and concept combination. Sense generation is a competence‐level theory that attempts to respect constraints from the various cognitive sciences, and postulates “quasi‐classical” conceptual structures where attributes receive only one value (but are defeasible and so do not represent necessary and sufficient conditions on category membership) and where classification is binary (but explicitly context‐sensitive). It is also argued that any general theory of concepts must account for “privative” combinations (e.g., stone lion, (...) fake gun, apparent friend) as extreme test‐cases of representational and classificatory flexibility. The approach presented therefore provides a treatment of these combinations. The approach differentiates between the “lexical concept” (the stable information represented in a mental lexicon) which acts as a base from which the various “senses” (flexible contents associated with words and phrases in context, and used in classification) are “generated.” Generation allows nonmonotonicity, so that in different circumstances, different attributes may be defeated or modified. Classification is treated as relative to the perspective adopted, so that a classification acceptable from one perspective may be unacceptable from another, without contradiction. The result is a view that assumes bottom‐up priority in concept combination, where the range of senses generated by bottom‐up rules of combination is tempered by pragmatic‐communicative constraints on classification. An account of the representational and classification behavior of privative combinations is outlined, and the article concludes with a discussion of some of the implications of the approach. (shrink)

We generalize the result of non-finite axiomatizability of totally categorical first-order theories from elementary model theory to homogeneous model theory. In particular, we lift the theory of envelopes to homogeneous model theory and develope theory of imaginaries in the case of ω-stable homogeneous classes of finite U-rank.

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 can give a systematic diagnostic of the cases in which a conditional is pragmatically enriched and those cases in which it is not. This diagnostic shows the reason why the paradoxes seem unacceptable and why they are, nevertheless, truth-preserving. This reinterpretation will also cover the solution that Paoli gives to McGee’s paradoxes of the Modus Ponens. (shrink)

Bounded lattices (that is lattices that are both lower bounded and upper bounded) form a large class of lattices that include all distributive lattices, many nondistributive finite lattices such as the pentagon lattice N₅, and all lattices in any variety generated by a finite bounded lattice. Extending a theorem of Paris for distributive lattices, we prove that if L is an ℵ₀-algebraic bounded lattice, then every countable nonstandard model ������ of Peano Arithmetic has a cofinal elementary extension ������ such (...) that the interstructure lattice Lt(������ / ������) is isomorphic to L. (shrink)

Presburger arithmetic is the first-order theory of the natural numbers with addition. We characterize sets that can be defined by a Presburger formula as exactly the sets whose characteristic functions can be represented by rational generating functions; a geometric characterization of such sets is also given. In addition, ifp= are a subset of the free variables in a Presburger formula, we can define a counting functiong to be the number of solutions to the formula, for a givenp. We show that (...) every counting function obtained in this way may be represented as, equivalently, either a piecewise quasi-polynomial or a rational generating function. Finally, we translate known computational complexity results into this setting and discuss open directions. (shrink)

In this paper a uniform methodology to perform natural\ndeduction over the family of linear, relevance and intuitionistic\nlogics is proposed. The methodology follows the Labelled\nDeductive Systems (LDS) discipline, where the deductive process\nmanipulates {\em declarative units} -- formulas {\em labelled}\naccording to a {\em labelling algebra}. In the system described\nhere, labels are either ground terms or variables of a given {\em\nlabelling language} and inference rules manipulate formulas and\nlabels simultaneously, generating (whenever necessary)\nconstraints on the labels used in the rules. A set of natural\ndeduction style (...) inference rules is given, and the notion of a\n{\em derivation} is defined which associates a labelled natural\ndeduction style ``structural derivation'' with a set of generated\nconstraints. Algorithmic procedures, based on a technique called\n{\em resource abduction\/}, are defined to solve the constraints\ngenerated within a structural derivation, and their termination\nconditions discussed. A natural deduction derivation is then\ndefined to be {\em correct} with respect to a given substructural\nlogic, if, under the condition that the algorithmic procedures\nterminate, the associated set of constraints is satisfied with\nrespect to the underlying labelling algebra. Finally, soundness\nand completeness of the natural deduction system are proved with\nrespect to the LKE tableaux system \cite{daga:LAD}.\footnote{Full\nversion of a paper presented at the {\em 3rd Workshop on Logic,\nLanguage, Information and Computation\/} ({\em WoLLIC'96\/}), May\n8--10, Salvador (Bahia), Brazil, organised by Univ.\ Federal de\nPernambuco (UFPE) and Univ.\ Federal da Bahia (UFBA), and\nsponsored by IGPL, FoLLI, and ASL.}. (shrink)

In this paper, we show that the finite model property fails for certain non‐integral semilinear substructural logics including Metcalfe and Montagna's uninorm logic and involutive uninorm logic, and a suitable extension of Metcalfe, Olivetti and Gabbay's pseudo‐uninorm logic. Algebraically, the results show that certain classes of bounded residuated lattices that are generated as varieties by their linearly ordered members are not generated as varieties by their finite members.

We develop a general algebraic and proof-theoretic study of substructural logics that may lack associativity, along with other structural rules. Our study extends existing work on substructural logics over the full Lambek Calculus [34], Galatos and Ono [18], Galatos et al. [17]). We present a Gentzen-style sequent system that lacks the structural rules of contraction, weakening, exchange and associativity, and can be considered a non-associative formulation of . Moreover, we introduce an equivalent Hilbert-style system and show that the logic associated (...) with and is algebraizable, with the variety of residuated lattice-ordered groupoids with unit serving as its equivalent algebraic semantics. Overcoming technical complications arising from the lack of associativity, we introduce a generalized version of a logical matrix and apply the method of quasicompletions to obtain an algebra and a quasiembedding from the matrix to the algebra. By applying the general result to specific cases, we obtain important logical and algebraic properties, including the cut elimination of and various extensions, the strong separation of , and the finite generation of the variety of residuated lattice-ordered groupoids with unit. (shrink)

A quasivariety of algebras has the joint embedding property (JEP) if and only if it is generated by a single algebra A. It is structurally complete if and only if the free ℵ0‐generated algebra in can serve as A. A consequence of this demand, called ‘passive structural completeness’ (PSC), is that the nontrivial members of all satisfy the same existential positive sentences. We prove that if is PSC then it still has the JEP, and if it has the (...) JEP and its nontrivial members lack trivial subalgebras, then its relatively simple members all belong to the universal class generated by one of them. Under these conditions, if is relatively semisimple then it is generated by one ‐simple algebra. We also prove that a quasivariety of finite type, with a finite nontrivial member, is PSC if and only if its nontrivial members have a common retract. The theory is then applied to the variety of De Morgan monoids, where we isolate the sub(quasi)varieties that are PSC and those that have the JEP, while throwing fresh light on those that are structurally complete. The results illuminate the extension lattices of intuitionistic and relevance logics. (shrink)

The value of testimony as a source of knowledge has been a subject of epistemological debates. The "trust theory of testimony" suggests that human testimony is based on an affective relationship supported by social norms. However, the advent of generative artificial intelligence challenges our understanding of genuine testimony. The concept of "quasi-testimony" seeks to characterize utterances produced by non-human entities that mimic testimony but lack certain fundamental attributes. This article analyzes these issues in depth, exploring philosophical perspectives on testimony (...) and the implications of conversational AI technologies on our epistemic practices. (shrink)

Universality has been an important concept in computable structure theory. A class C of structures is universal if, informally, for any structure of any kind there is a structure in C with the same computability-theoretic properties as the given structure. Many classes such as graphs, groups, and fields are known to be universal. This paper is about the class of finitely generated groups. Because finitely generated structures are relatively simple, the class of finitely generated groups has no (...) hope of being universal. We show that finitely generated groups are as universal as possible, given that they are finitely generated: for every finitely generated structure, there is a finitely generated group which has the same computability-theoretic properties. The same is not true for finitely generated fields. We apply the results of this investigation to quasi Scott sentences, and also answer a question of Alvir, Knight, and McCoy. (shrink)

Quasi-Nelson logic (QNL) was recently introduced as a common generalisation of intuitionistic logic and Nelson's constructive logic with strong negation. Viewed as a substructural logic, QNL is the axiomatic extension of the Full Lambek Calculus with Exchange and Weakening by the Nelson axiom, and its algebraic counterpart is a variety of residuated lattices called quasi-Nelson algebras. Nelson's logic, in turn, may be obtained as the axiomatic extension of QNL by the double negation (or involutivity) axiom, and intuitionistic logic (...) as the extension of QNL by the contraction axiom. A recent series of papers by the author and collaborators initiated the study of fragments of QNL, which correspond to subreducts of quasi-Nelson algebras. In the present paper we focus on fragments that contain the connectives forming a residuated pair (the monoid conjunction and the so-called strong Nelson implication), these being the most interesting ones from a substructural logic perspective. We provide quasi-equational (whenever possible, equational) axiomatisations for the corresponding classes of algebras, obtain twist representations for them, study their congruence properties and take a look at a few notable subvarieties. Our results specialise to the involutive case, yielding characterisations of the corresponding fragments of Nelson's logic and their algebraic counterparts. (shrink)

We characterize the modal logics of elementary classes of Kripke frames as precisely those modal logics that are axiomatized by modal axioms synthesized in a certain effective way from "quasi-positive" sentences of hybrid logic. These are pure positive hybrid sentences with arbitrary existential and relativized universal quantification over nominals. The proof has three steps. The first step is to use the known result that the modal logic of any elementary class of Kripke frames is also the modal logic of (...) the closure of this class under disjoint unions, generated subframes, bounded morphic images, and ultraroots. This latter class can be defined by the first-order sentences of a special syntactic form (called pseudo-equations by Goldblatt) that are valid in the former class. The second step is to translate these pseudo-equations into equivalent quasi-positive hybrid sentences. In the third and main step, we show that any quasi-positive sentence S generates an infinite set of modal formulas called "approximants," which together axiomatize a canonical modal logic that is sound and complete for the class of frames validating S. The proof is analogous to standard proofs of Sahlqvist's theorem. It generalizes to sets of quasi-positive sentences. The main result now follows. (shrink)

The present research paper aimed to identify the effectiveness of exploratory activities based on engineering and science practices of Next Generation Science Standards (NGSS) in developing exploratory thinking among elementary students in Mecca, Saudi Arabia. The author utilized the quasi-experimental method based on the control and experimental groups. Moreover, the sample consisted of (64) 4th grade elementary female students. The "Unit of Energy" was restructured based on engineering and science practices of NGSS among the 4th grade elementary students. A (...) teacher guide and a student notebook concerning the activities of the "Unit of Energy" were prepared. Moreover, an exploratory thinking test was developed and applied to the participants over 6 weeks. The results showed statically significant differences at the level of ≤0.01 between the mean scores of the experimental and control groups at exploratory thinking post-test and in each domain. The study recommends the need for teacher preparation programs at Colleges of Education on preparing the pre-service teachers according to NGSS that should be involved in teaching practices to evaluate pre-service teachers’ performance in practicum. (shrink)

Quasi-MV algebras are generalisations of MV algebras arising in quantum computational logic. Although a reasonably complete description of the lattice of subvarieties of quasi-MV algebras has already been provided, the problem of extending this description to the setting of quasivarieties has so far remained open. Given its apparent logical repercussions, we tackle the issue in the present paper. We especially focus on quasivarieties whose generators either are subalgebras of the standard square quasi-MV algebra S , or can (...) be obtained therefrom through the addition of some fixpoints for the inverse. (shrink)

A first-order sentence is quasi-modal if its class of models is closed under the modal validity preserving constructions of disjoint unions, inner substructures and bounded epimorphic images. It is shown that all members of the proper class of canonical structures of a modal logic Λ have the same quasi-modal first-order theory Ψ Λ . The models of this theory determine a modal logic Λ e which is the largest sublogic of Λ to be determined by an elementary class. (...) The canonical structures of Λ e also have Ψ Λ as their quasi-modal theory. In addition there is a largest sublogic Λ c of Λ that is determined by its canonical structures, and again the canonical structures of Λ c have Ψ Λ are their quasi-modal theory. Thus Ψ Λ = Ψ Λ c = Ψ Λ e . Finally, we show that all finite structures validating Λ are models of Ψ Λ , and that if Λ is determined by its finite structures, then Ψ Λ is equal to the quasi-modal theory of these structures. (shrink)

For John Forrester, the ‘case’, particularly in its psychoanalytic version, makes possible a science of the particular – knowledge open to the differences of individuals and situations. This article takes up that aspect of Forrester’s account that linked the psychoanalytic case with forms of autobiography – new narrations of that particular self. After Freud, many authors – literary and psychoanalytic – have taken up the challenge of narrating subjectivity in new forms, engaging a quasi-psychoanalytic framework (H. D., Walter Benjamin, (...) Frantz Fanon, Eve Kosofsky Sedgwick are examples). Focusing on Luisa Passerini’s text Autobiography of a Generation, which deals with the Italian experience of 1968, the article examines some of the features of such hybrid texts, and argues that psychoanalysis makes a contribution not just to the forms of self-investigation they pursue, but more significantly to the search for a radically new methodology of narration. Such models end up as ‘impossible’ cases, but in so doing they explore new interdisciplinary means for understanding the historical shaping of subjectivity. (shrink)

This is the second of a series of papers that investigate fragments of quasi-Nelson logic (QNL) from an algebraic logic standpoint. QNL, recently introduced as a common generalization of intuitionistic and Nelson’s constructive logic with strong negation, is the axiomatic extension of the substructural logic |$FL_{ew}$| (full Lambek calculus with exchange and weakening) by the Nelson axiom. The algebraic counterpart of QNL (quasi-Nelson algebras) is a class of commutative integral residuated lattices (a.k.a. |$FL_{ew}$|-algebras) that includes both Heyting and (...) Nelson algebras and can be characterized algebraically in several alternative ways. The present paper focuses on the algebraic counterpart (a class we dub quasi-Nelson implication algebras, QNI-algebras) of the implication–negation fragment of QNL, corresponding to the connectives that witness the algebraizability of QNL. We recall the main known results on QNI-algebras and establish a number of new ones. Among these, we show that QNI-algebras form a congruence-distributive variety (Cor. 3.15) that enjoys equationally definable principal congruences and the strong congruence extension property (Prop. 3.16); we also characterize the subdirectly irreducible QNI-algebras in terms of the underlying poset structure (Thm. 4.23). Most of these results are obtained thanks to twist representations for QNI-algebras, which generalize the known ones for Nelson and quasi-Nelson algebras; we further introduce a Hilbert-style calculus that is algebraizable and has the variety of QNI-algebras as its equivalent algebraic semantics. (shrink)

We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety of such quasi-MV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasi-MV algebras generate ,we prove a standard completeness theorem for w.r.t. an algebra over the complex numbers.

We present some equivalent conditions for a quasivariety \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {K}}$$\end{document} of structures to be generated by a single structure. The first such condition, called the embedding property was found by A.I. Mal′tsev in [6]. It says that if \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf A}, {\bf B} \in \mathcal {K}}$$\end{document} are nontrivial, then there exists \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\bf C} \in (...) \mathcal{K}}$$\end{document} such that A and B are embeddable into C. One of our equivalent conditions states that the set of quasi-identities valid in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal{K}}$$\end{document} is closed under a certain Gentzen type rule which is due to J. Łoś and R. Suszko [5]. (shrink)

In A. Kumar, & M. Banerjee [(2012). Definable and rough sets in covering-based approximation spaces. In T. Li. (eds.), Rough sets and knowledge technology (pp. 488–495). Springer-Verlag], A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], authors proposed a pair of lower and upper approximation operators based on granules generated by quasiorders. This work is an extension of algebraic results presented therein. A characterisation has been presented (...) for those quasiorder-generated covering-based approximation spaces whose corresponding collections of definable and rough sets form Stone algebras. The notion of rough lattice was proposed in A. Kumar, & M. Banerjee [(2015). Algebras of definable and rough sets in quasi order-based approximation spaces. Fundamenta Informaticae, 141(1), 37–55], A. Kumar [(2020). A Study of Algebras and Logics of Rough Sets Based on Classical and Generalized Approximation Spaces. In Transactions on Rough Sets XXII, LNCS (Vol. 12485, pp. 123–251). Springer]. Some special rough lattices are introduced in this work, viz. rough Stone algebra, ∼1-complemented and ∼2-complemented rough lattices. Representations of these algebras in terms of rough sets are obtained. Moreover, logics for these algebras are shown to be sound and complete with respect to rough set semantics. (shrink)

With the wide application of computers and digital technologies, online information searching is being integrated into students’ learning process. Improving students’ creative question generation through online information searching is an emerging research topic in the creativity and pedagogy field. Online information searching brings diversified information, but it also leads to cognitive load brought by a large amount of online information. Using online information searching to generate creative questions depends on students’ cognitive properties. However, the existing literature ignores the joint influence (...) of students’ online information searching strategies and cognitive properties on their creative question generation. This study puts forward three hypotheses: first, the two strategies of students’ online information searching will increase their creative question generation; second, the impact of “keywords” is negatively moderated by students’ need for cognitive closure ; third, the impact of “Web page exploration” is positively moderated by NFCC. The main reason is that high NFCC prevents students from obtaining diversified perspectives by using different keywords, but it helps to avoid distractions caused by a large amount of online information and promote the persistency of their reading information. Based on the data of quasi-experimental tasks completed by 90 students in Grade 7 and Grade 8, the results support the above hypothesis. The contributions of creative question generation theory and NFCC theory, as well as important issues of future study, are discussed. (shrink)

We study quasi-characterizing inference rules (this notion was introduced into consideration by A. Citkin (1977). The main result of our paper is a complete description of all self-admissible quasi-characterizing inference rules. It is shown that a quasi-characterizing rule is self-admissible iff the frame of the algebra generating this rule is not rigid. We also prove that self-admissible rules are always admissible in canonical, in a sense, logics S4 or IPC regarding the type of algebra generating rules.

The first two steps of the construction of motivic integration in the fundamental work of Hrushovski and Kazhdan [8] have been presented in Yin [12]. In this paper we present the final third step. As in Yin [12], we limit our attention to the theory of algebraically closed valued fields of pure characteristic 0 expanded by a -generated substructure S in the language . A canonical description of the kernel of the homomorphism is obtained.

We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV algebras and $\sqrt{^{\prime }}$ quasi-MV algebras - first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et al. 200+} and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of $\sqrt{^{\prime }}$ quasi-MV algebras; we give a representation of semisimple $\sqrt{^{\prime }}$ quasi-MV algebras in (...) terms of algebras of functions; finally, we describe the structure of free algebras with one generator in both varieties. (shrink)

Instead of paralysing readers with a technical account of its nature and genealogy, I aim to accumulate a sense of Derrida's quasi-transcendental thinking over a series of expositions. I begin with a critical account of the most prevalent misreading of Derrida's work, generated by attempts, such as Rorty's, to place it on one side of a clear duality that sets old-fashioned “philosophical” foundationalism against contemporary anti-foundationalist “textuality.” In contrast, through an analogy between what occurs in the giving of (...) a gift and the happening of différance, I shall try to articulate the more complex, quasi-transcendental “logic” of Derrida's thinking, which refuses a clear-cut “either/or” choice between the poles of this duality, precisely because these alternatives stand in a relation, not of analytical contradiction, but of aporia, or dilemma. If this exposition proves to be too abstruse and metaphysical for some, a second, more practical, example concerning the aporias of ethical decision- making should go some way to wards compensation. Through these expositions, I aim to show that a complex, quasi-transcendental way of thinking serves as a more sophisticated and accurate key to the interpretation of Derrida's texts than attempts to reduce it to the anti-foundationalist side of supposedly contradictory opposites. To support this claim, I return with a critical eye to Rorty's rejection of Jonathan Culler's argument that Derrida must and does maintain a philosophy/literature distinction, and of Christopher Norris's explanation for Derrida's claim that one cannot escape philosophy. I also try to answer Rorty's rejection of the very idea of quasi-transcendentality by reducing this mode of thinking to a mere restatement of the co-implication of binaries. I conclude with a brief outline of what deconstructive practice amounts to when understood in the light of quasi-transcendental thinking. S. Afr. J. Philos. Vol.23(3) 2004: 244-266. (shrink)

This paper examines collective decision-making with an infinite-time horizon setting. First, we establish a result on the collection of decisive sets: if there are at least four alternatives and Arrow’s axioms are satisfied on the selfish domain, then the collection of decisive sets forms an ultrafilter. Second, we impose generalized versions of stationarity axiom for social preferences, which are substantially weaker than the standard version. We show that if any of our generalized versions are satisfied in addition to Arrow’s axioms, (...) then some generation is dictatorial. Moreover, we specify a very weak stationarity axiom that guarantees a possibility result. (shrink)

In this paper we exhibit a non-finitely based, finitely generated quasi-variety of De Morgan algebras and determine the bottom of the lattices of sub-quasi-varieties of Kleene and De Morgan algebras.

Fraïssé studied countable structures S through analysis of the age of S i.e., the set of all finitely generated substructures of S. We investigate the effectiveness of his analysis, considering effectively presented lists of finitely generated structures and asking when such a list is the age of a computable structure. We focus particularly on the Fraïssé limit. We also show that degree spectra of relations on a sufficiently nice Fraïssé limit are always upward closed unless the relation is (...) definable by a quantifier-free formula. We give some sufficient or necessary conditions for a Fraïssé limit to be spectrally universal. As an application, we prove that the computable atomless Boolean algebra is spectrally universal. (shrink)

In the present paper we continue the investigation of the lattice of subvarieties of the variety of √′ P quasi-MV algebras, already started in [6]. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a long-standing open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra D r is not finitely based, and we provide an infinite equational basis for (...) the same variety. (shrink)

The wind is the topic of a desirable pathic aesthetics and neophenomenology of air. More specifically, it is a good example of an atmospheric ephemeral quasi-thing, because, as religions have always recognized, it blows where it wishes. It involves us on the affective and felt-bodily level as an atmospheric feeling poured out into pre-dimensional space: that is, as a very concrete experience, significantly both climatic and affective, physical and felt-bodily. Unlike full-fledged things, the wind is not edged, discrete, cohesive, (...) or solid; it does not possess immanent and regular tendencies; it can appear in a partial form, without doing so through fragments and sides; it is (felt as) more immediate and intrusive than things, generating inhibiting or attracting motor suggestions; it dies down with the same inexplicable immediacy with which it rises; it does not have a threefold causality (cause-action-effect) but a twofold one (cause/action-effect). Given these quasi-thingly wind characteristics, the paper sketches a review of the main types of felt-bodily resonance, within a range whose two extremes are narrowness and vastness, triggered by windy atmospheres (for example sudden gust of wind, breeze, shallow wind, stormy wind and calm). (shrink)

The youngest generation of students prefers a more active learning style. Sandwich teaching may suit their learning style by alternating between active individual learning and passive collective learning. Sandwich teaching has been rarely applied to the Community Nursing Course for nursing students, and its teaching effects on this course remain unclear. This study applied Sandwich teaching to the Community Nursing Course for Chinese nursing undergraduates and investigated its effects on students' critical thinking, self-learning ability, course experience, and academic performance. This (...) is a quasi-experimental study with 72 Chinese nursing undergraduates. Students receiving traditional teaching were enrolled in the control group, and those who received Sandwich teaching were recruited into the experimental group. Both groups received the 12-week, 90-min Community Nursing Course. Our main outcome variable, including students' critical thinking, self-learning ability, and course experience, was assessed by specific questionnaire. The paired t-tests were applied to compare the differences of the same group in the pre-test and the post-test, and the independent-sample t-tests were used to compare the differences between the two groups. We observed that nursing students' critical thinking ability and self-learning ability were significantly improved after receiving Sandwich teaching. Students' course experience of Sandwich teaching was significantly better than that of traditional teaching. The final exam score in the experimental group was not significantly higher than that in the control group. These results suggest that Sandwich teaching in Community Nursing Course improved Chinese nursing undergraduates' critical thinking, self-learning ability, and course experience, but failed in improving academic performance. (shrink)

This interview with the philosopher Bernard Stiegler was conducted in Paris on 28 January 2015, and first appeared in Dutch translation in the journal De uil van Minerva. The conversation begins by discussing the fundamental place occupied by the concept of ‘technics’ in Stiegler’s work, and how the ‘constitutivity’ of technics does and does not relate to Kant and Husserl. Stiegler is then asked about his relationship with Deleuze, and he responds by focusing on the concept of quasi-causality, but (...) also by arguing that there is a certain trajectory in Deleuze’s thought, situating his own philosophy in relation to its various moments. Stiegler is then asked to respond to the Charlie Hebdo terrorist attacks carried out three weeks prior to the interview. After making a couple of precautionary remarks, Stiegler relates such occurrences to the problem of what he calls ‘spiritual poverty’, to the intensification of ‘negative sublimation’ that can occur when there is a disconnection between the generations, and more generally to the growth of nihilism. All of these phenomena relate to the exploitation of technology by a virulent capitalism that irrationally believes that only the market is rational. After consideration of the complex historical relationship between Islam and modernization, and of both of these to Nietzsche’s ‘death of God’, and after recalling the destructive role played by the West in the rise of fundamentalism and jihadism, Stiegler concludes by reflecting on the fact that, ultimately, ‘intellectuals’ have failed to use technologies in ways that produce alternatives to consumerism. (shrink)

The Digital Humanities project ‘CANTUS NETWORK. Libri ordinarii of the Salzburg metropolitan province’ undertakes research around the liturgy and music of the churches and monasteries of the medieval ecclesiastical province of Salzburg. Key sources are the liturgical ‘prompt books’, called libri ordinarii, which include a short form of more or less the entire rite of a diocese or a monastery. The workflow of the project is set in an environment called GAMS, a humanities research data repository built for long-term storage (...) and presentation of data coming from the humanities. Digital editions of the libri ordinarii of the province were generated with the aim of enabling a comparative analysis of the various different traditions. As a first step, the books were transcribed with strict rule-based tags in Microsoft Word and transformed to TEI using the community’s XSLT stylesheets and a Java-based script. Subsequently, Semantic Web technologies were deployed to foster graph-based search and analysis of the structured data. Possible future work on the topic is facilitated by the dissemination of content levels as Linked Open Data. Further analysis is conducted with the help of Natural Language Processing methods in order to find text similarities and differences between the libri ordinarii. (shrink)

Habermas' claim to provide a critique of reification by means other than marxian ones requires him to transpose not only meaningful freedom, but also a dialectical view of social becoming, into terms com patible with linguistically mediated intersubjectivity. In order to remain critical of reification as colonization, he thus finds himself committed to the view that colonization is the outcome of the development of two perma nent and competing principles of sociation. Compelled to draw upon the resources both of the (...) dialectical tradition and of transcendental pragmat ics, the theory of communicative action is thereby constrained to remain both quasi-dialectical and quasi-transcendental. This founding gesture generates, in turn, at least two unavoidable aporias. The first can be under stood as a radical and structural deficit for critical judgement concerning the interplay among the decentered cognitive value spheres. The second is an inversion of the apparent claim of accessing a 'reason beyond reason' of which he accuses Horkheimer and Adorno. It shows up in the logical and epistemological problems surrounding the relation between performative contradiction and the status of his theory. Taken together, these theories signal that the theory of communicative action, rather than amounting to a transcendence of earlier approaches to reification, is simply a parallel, but one which becomes less than fully two-dimensional. Key Words: Adorno • .communicative action • .dialectic • .Habermas • . Horkheimer • . performative contradiction • . * reason • . reification. (shrink)

We present two of the three major steps in the construction of motivic integration, that is, a homomorphism between Grothendieck semigroups that are associated with a first-order theory of algebraically closed valued fields, in the fundamental work of Hrushovski and Kazhdan [8]. We limit our attention to a simple major subclass of V-minimal theories of the form ACV FS, that is, the theory of algebraically closed valued fields of pure characteristic 0 expanded by a -generated substructure S in (...) the language . The main advantage of this subclass is the presence of syntax. It enables us to simplify the arguments with many different technical details while following the major steps of the Hrushovski–Kazhdan theory. (shrink)

A structure is locally finite if every finitely generated substructure is finite; local sentences are universal sentences all models of which are locally finite. The stretching theorem for local sentences expresses a remarkable reflection phenomenon between the finite and the infinite models of local sentences. This result in part requires strong axioms to be proved; it was studied by the second named author, in a paper of this Journal, volume 53. Here we correct and extend this paper; in (...) particular we show that the stretching theorem implies the existence of inaccessible cardinals, and has precisely the consistency strength of Mahlo cardinals of finite order. And we present a sequel due to the first named author: (i) decidability of the spectrum $\operatorname{Sp}(\varphi)$ of a local sentence φ, below ω ω ; where $\operatorname{Sp}(\varphi)$ is the set of ordinals α such that φ has a model of order type α (ii) proof that $\operatorname{beth}_\omega = \sup\{\operatorname{Sp}(\varphi): \varphi \text{local sentence with a bounded spectrum}\}$ (iii) existence of a local sentence φ such that $\operatorname{Sp}(\varphi)$ contains all infinite ordinals except the inaccessible cardinals. (shrink)

We study the notion of weak amalgamation in the context of diagonal conjugacy classes. Generalizing results of Kechris and Rosendal, we prove that for every countable structure M, Polish group G of permutations of M, and \, G has a comeager n-diagonal conjugacy class iff the family of all n-tuples of G-extendable bijections between finitely generated substructures of M, has the joint embedding property and the weak amalgamation property. We characterize limits of weak Fraïssé classes that are not homogenizable. (...) Finally, we investigate 1- and 2-diagonal conjugacy classes in groups of ball-preserving bijections of certain ordered ultrametric spaces. (shrink)

In recent years, the Audit Pilot of Natural Resources Assets (APNRA) pilot program has been implemented by the Chinese government to strengthen the protection of natural resources and the ecological environment. Based on the APNRA pilot program, we use the multi-period differences–in–differences model to investigate the response of corporate environmental responsibility to external governance pressure. We find that firms significantly improve their environmental investment and performance after the implementation of the APNRA pilot program. Sewage charges (including green fees) and ecological (...) protection incentives constitute the two main channels that explain the positive relationship. We further find that the impact of the program on corporate environmental investment and performance is more pronounced for firms in regions with poor environmental quality, and for firms in heavy-polluting industries. This paper introduces the role of government governance in generating positive externality for firms and provides a valuable understanding of environmental governance in an emerging market. (shrink)

We show that if a class K of finite relational structures is closed under quasi-substructures, then there is no saturated K-generic structure that is superstable but not ω -stable.

Logics that do not have a deduction-detachment theorem (briefly, a DDT) may still possess a contextual DDT —a syntactic notion introduced here for arbitrary deductive systems, along with a local variant. Substructural logics without sentential constants are natural witnesses to these phenomena. In the presence of a contextual DDT, we can still upgrade many weak completeness results to strong ones, e.g., the finite model property implies the strong finite model property. It turns out that a finitary system has a contextual (...) DDT iff it is protoalgebraic and gives rise to a dually Brouwerian semilattice of compact deductive filters in every finitely generated algebra of the corresponding type. Any such system is filter distributive, although it may lack the filter extension property. More generally, filter distributivity and modularity are characterized for all finitary systems with a local contextual DDT, and several examples are discussed. For algebraizable logics, the well-known correspondence between the DDT and the equational definability of principal congruences is adapted to the contextual case. (shrink)

In recent years restitution scholars have expended considerable energy in attempting to reveal the logical structure of the law of proprietary remedies. That project advances on the assumption that the strange rhetoric that pervades this area of law can be stripped away to reveal restitutionary principles. However, the doctrines in question have proved resistant to such endeavors. An appreciation of why this is so requires recognition of the very real anxiety generated by the judicial readjustment of property rights that (...) takes place in this area of law. The use of metaphors, fictions and evidential presumptions that characterizes the law tracing, subrogation and the provision of proprietary relief for wrongs serves to assuage this anxiety by manufacturing the appearance that these remedies are perfectly conventional instances of the enforcement of pre-existing property or consensual transfers of property. However, these property rites have a logic of their own - a logic that influences and constrains the development of the law of proprietary remedies and makes it impossible to neatly reduce this field to a set of restitutionary principles. This is illustrated by the work of Professor Peter Birks, which represents the most comprehensive attempt to cut away the abstruse rhetoric found in this area and reveal the restitutionary substructure of the law of proprietary remedies and makes it impossible to neatly reduce this field to a set of restitutionary principles. This is illustrated by the work of Professor Peter Birks, which represents the most comprehensive attempt to cut away the substructure of the law of proprietary remedies. In Birks' work this process has merely resulted in old metaphors being replaced with new ones. Ultimately, we must accept that if re are to rationalize this area we must be prepared to engage directly with the policy issues that arise in this context. (shrink)

[Significantly updated in Chapter 6 of Awareness and the Substructure of Knowledge] In order for a reason to justify an action or attitude it must be one that is possessed by an agent. Knowledge-centric views of possession ground our possession of reasons, at least partially, either in our knowledge of them or in our being in a position to know them. On virtually all accounts, knowing P is some kind of non-accidental true belief that P. This entails that knowing (...) P is a kind of non-accidental true representation that P. I outline a novel theory of the epistemic requirement on possession in terms of this more general state of non-accidental true representation. It is just as well placed to explain the motivations behind knowledge-centric views of possession, and it is also better placed to explain the extent of the reasons we possess in certain cases of deductive belief-updates and cases involving environmental luck. I conclude with three reflections. First, I indicate how my arguments generate a dilemma for Errol Lord’s view that possessing reasons is just a matter of being in a position to manifest one’s knowledge how to use them. Second, I explain how my view can simultaneously manage cases of environmental luck without falling prey to lottery cases. Finally, I sketch the direction for a further range of counterexamples to knowledge-centric theories of possession. (shrink)

The possibility that zitterbewegung opens a window to particle substructure in quantum mechanics is explored by constructing a particle model with structural features inherent in the Dirac equation. This paper develops a self-contained dynamical model of the electron as a lightlike particle with helical zitterbewegung and electromagnetic interactions. The model admits periodic solutions with quantized energy, and the correct magnetic moment is generated by charge circulation. It attributes to the electron an electric dipole moment rotating with ultrahigh frequency, (...) and the possibility of observing this directly as a resonance in electron channeling is analyzed in detail. Correspondence with the Dirac equation is discussed. A modification of the Dirac equation is suggested to incorporate the rotating dipole moment. (shrink)

A logical constant is weakly disharmonious if its elimination rules are weaker than its introduction rules. Substructural weak disharmony is the weak disharmony generated by structural restrictions on the eliminations. I argue that substructural weak disharmony is not a defect of the constants which exhibit it. To the extent that it is problematic, it calls into question the structural properties of the derivability relation. This prompts us to rethink the issue of controlling the structural properties of a logic by (...) means of harmony. I argue that such a control is possible and desirable. Moreover, it is best achieved by global tests of harmony. (shrink)