In this paper, we introduce the notion of intuitionistic fuzzy PMS-subalgebras under homomorphism and Cartesian product and investigate several properties. We study the homomorphic image and inverse image of the intuitionistic fuzzy PMS-subalgebras of a PMS-algebra, which are also intuitionistic fuzzy PMS-subalgebras of a PMS-algebra, and find some other interesting results. Furthermore, we also prove that the Cartesian product of intuitionistic fuzzy PMS-subalgebras is again an intuitionistic fuzzy PMS-subalgebra and characterize it in terms of its level sets. Finally, we (...) consider the strongest intuitionistic fuzzy PMS-relations on an intuitionistic fuzzy set in a PMS-algebra and demonstrate that an intuitionistic fuzzy PMS-relation on an intuitionistic fuzzy set in a PMS-algebra is an intuitionistic fuzzy PMS-subalgebra if and only if the corresponding intuitionistic fuzzy set in a PMS-algebra is an intuitionistic fuzzy PMS-subalgebra of a PMS-algebra. (shrink)

In an earlier paper, we introduced the following pre-order on the subgroups of a given Polish group: if G is a Polish group and \ are subgroups, we say H is homomorphism reducible to L iff there is a continuous group homomorphism \ such that \\). We previously showed that there is a \ subgroup L of the countable power of any locally compact Polish group G such that every \ subgroup of \ is homomorphism reducible to (...) L. In the present work, we show that this fails in the countable power of the group of increasing homeomorphisms of the unit interval. (shrink)

This paper is a critical response to Andreas Bartels’ sophisticated defense of a structural account of scientific representation. We show that, contrary to Bartels’ claim, homomorphism fails to account for the phenomenon of misrepresentation. Bartels claims that homomorphism is adequate in two respects. First, it is conceptually adequate, in the sense that it shows how representation differs from misrepresentation and non-representation. Second, if properly weakened, homomorphism is formally adequate to accommodate misrepresentation. We question both claims. First, we (...) show that homomorphism is not the right condition to distinguish representation from misrepresentation and non-representation: a “representational mechanism” actually does all the work, and it is independent of homomorphism – as of any structural condition. Second, we test the claim of formal adequacy against three typical kinds of inaccurate representation in science which, by reference to a discussion of the notorious billiard ball model, we define as abstraction, pretence, and simulation. We first point out that Bartels equivocates between homomorphism and the stronger condition of epimorphism, and that the weakened form of homomorphism that Bartels puts forward is not a morphism at all. After providing a formal setting for abstraction, pretence and simulation, we show that for each morphism there is at least one form of inaccurate representation which is not accommodated. We conclude that Bartels’ theory – while logically laying down the weakest structural requirements – is nonetheless formally inadequate in its own terms. This should shed serious doubts on the plausibility of any structural account of representation more generally. (shrink)

In this article, we investigate the status of the homomorphism preservation property amongst restricted classes of finite relational structures and algebraic structures. We show that there are many homomorphism-closed classes of finite lattices that are definable by a first-order sentence but not by existential positive sentences, demonstrating the failure of the homomorphism preservation property for lattices at the finite level. In contrast to the negative results for algebras, we establish a finite-level relativised homomorphism preservation theorem in (...) the relational case. More specifically, we give a complete finite-level characterisation of first-order definable finitely generated anti-varieties relative to classes of relational structures definable by sentences of some general forms. When relativisation is dropped, this gives a fresh proof of Atserias’s characterisation of first-order definable constraint satisfaction problems over a fixed template, a well known special case of Rossman’s Finite Homomorphism Preservation Theorem. (shrink)

Suppose G is a definably connected, definable group in an o-minimal expansion of an ordered group. We show that the o-minimal universal covering homomorphism equation image: equation image→ G is a locally definable covering homomorphism and π1 is isomorphic to the o-minimal fundamental group π of G defined using locally definable covering homomorphisms.

Man unterscheidet in der Organisation verschiedener Tiere folgende Kategorien von Parallelismen: 1) die Homologien, welche auf einen gemeinsamen Ursprung der betreffenden Organe hinweisen, 2) die Analogien, die als eine Folge von ähnlichen Funktionen oder der äusseren Wirkungen sekundär enstehen, 3) die Homomorphien, wodurch ich diejenigen Übereinstimmungen im Körperbau von verschiedenen Tieren bezeichne, welche auf Grund der allgemeinen Gesetze der Morphogenese zustande kommen. Das Studium der Homologien ist historischer Art, dasjenige der Homomorphien und Analogien typologischer Art.Man kann weiter unterscheiden: eine allgemeine (...) Homomorphie, welche sich im Tierreiche überall, wo dazu günstige Bedingungen vorhanden sind, offenbart , und eine spezielle Homomorphie, welche als eine der Möglichkeiten bei einer begrenzten Anzahl von Tierformen hervortritt . Die Grenze zwischen diesen beiden Kategorien ist natürlich nicht sehr deutlich, ebenso wie manchmal die Grenze zwischen Homologien, Homomorphien und Analogien. Alle diese Erscheinungen beruhen letzten Endes auf morphogenetischen Gesetzen, können also als Homomorphien im weitesten Sinne des Wortes bezeichnet werden.Dans l'organisation des divers animaux on peut distinguer les parallélismes suivants: 1) les homologies qui dénotent la descendance des porteurs des organes similaires d'un seul et même ancêtre, 2) les analogies qui se forment sous l'influence d'une fonction analogue ou des mêmes conditions extérieures, et 3) les homomorphies qui représentent la manifestation des propriétés fondamentales de la substance animée. Les homologies sont les phénomènes de l'ordre historique, tandis que les homomorphies et les analogies doivent être étudiées d'après une méthode typologique.Si une similitude homomorphique des formes se manifeste partout dans le règne animal ou au moins dans tous les cas où se trouvent des conditions favorables, il faut parler d'une homomorphie générale . Si au contraire on observe le parallélisme seulement dans les cas isolés, comme p. ex. les yeux composés chez les Arthropodes, les Vers et les Mollusques, il faut parler de l'homomorphie spéciale. La limite entre ces deux catégories des phénomènes n'est pas très précise. De même il est difficile parfois de définir strictement si nous avons à faire à une homologie, à une analogie ou à une homomorphie. Tous ces phénomènes-là dépendent finalement des lois morphogénètiques. C'est pourquoi qu'on peut les indiquer comme des homomorphies dans le sens le plus étendu de ce mot. (shrink)

The case against analytical isomorphism is made within an evolutionary framework. The relevance to neural filling-in is discussed. Homomorphism is argued for as a conceptually superior substitute for isomorphism, and the implications for the personal/subpersonal distinction are explored.

Consciousness and Mind presents David Rosenthal's influential work on the nature of consciousness. Central to that work is Rosenthal's higher-order-thought theory of consciousness, according to which a sensation, thought, or other mental state is conscious if one has a higher-order thought that one is in that state. The first four essays develop various aspects of that theory. The next three essays present Rosenthal's homomorphism theory of mental qualities and qualitative consciousness, and show how that theory fits with and helps (...) sustain the HOT theory. A crucial feature of homomorphism theory is that it individuates and taxonomizes mental qualities independently of the way we're conscious of them, and indeed independently of our being conscious of them at all. So the theory accommodates the qualitative character not only of conscious sensations and perceptions, but also of those which fall outside our stream of consciousness. Rosenthal argues that, because this account of mental qualities makes no appeal to consciousness, it enables us to dispel such traditional quandaries as the alleged conceivability of undetectable quality inversion, and to disarm various apparent obstacles to explaining qualitative consciousness and understanding its nature. Six further essays build on the HOT theory to explain various important features of consciousness, among them the complex connections that hold in humans between consciousness and speech, the self-interpretative aspect of consciousness, and the compelling sense we have that consciousness is unified. Two of the essays, one an extended treatment of homomorphism theory, appear here for the first time. There is also a substantive introduction, which draws out the connections between the essays and highlights their implications. (shrink)

Angell's logic of analytic containment AC has been shown to be characterized by a 9-valued matrix NC by Ferguson, and by a 16-valued matrix by Fine. We show that the former is the image of a surjective homomorphism from the latter, i.e., an epimorphic image. The epimorphism was found with the help of MUltlog, which also provides a tableau calculus for NC extended by quantifiers that generalize conjunction and disjunction.

I show that the partial truth of a sentence in a partial structure is equivalent to the truth of that sentence in an expansion of a structure that corresponds naturally to the partial structure. Further, a mapping is a partial homomorphism/partial isomorphism between two partial structures if and only if it is a homomorphism/isomorphism between their corresponding structures. It is a corollary that the partial truth of a sentence in a partial structure is equivalent to the truth of (...) a specific Ramsey sentence in a corresponding structure. Hence the partial structures approach can be expressed in standard first or second-order model theory, and it can be captured in the received view on scientific theories as developed by Carnap and Hempel. (shrink)

This is a survey of work on set-theoretical invariance criteria for logicality. It begins with a review of the Tarski-Sher thesis in terms, first, of permutation invariance over a given domain and then of isomorphism invariance across domains, both characterized by McGee in terms of definability in the language L∞,∞. It continues with a review of critiques of the Tarski-Sher thesis, and a proposal in response to one of those critiques via homomorphism invariance. That has quite divergent characterization results (...) depending on its formulation, one in terms of FOL, the other by Bonnay in terms of L∞,∞, both without equality. From that we move on to a survey of Bonnay’s work on similarity relations between structures and his results that single out invariance with respect to potential isomorphism among all such. Turning to the critique that calls for sameness of meaning of a logical operation across domains, the paper continues with a result showing that the isomorphism invariant operations that are absolutely definable with respect to KPU−Inf are exactly those definable in full FOL; this makes use of an old theorem of Manders. The concluding section is devoted to a critical discussion of the arguments for set-theoretical criteria for logicality. (shrink)

In this paper we extend the theory of neutrosophic rings and neutrosophic fields to soft sets and construct soft neutrosophic rings and soft neutrosophic fields. We also extend neutrosophic ideal theory to form soft neutrosophic ideal over a neutrosophic ring and soft neutrosophic ideal of a soft neutrosophic ring . We have given many examples to illustrate the theory of soft neutrosophic rings and soft neutrosophic fields and display many properties of of these. At the end of this paper we (...) gave soft neutrosophic ring homomorphism. (shrink)

The aim of this paper is to defend the structural concept of representation, as defined by homomorphisms, against its main objections, namely: logical objections, the objection from misrepresentation, theobjection from failing necessity, and the copy theory objection. The logical objections can be met by reserving the relation.

We define notions of homomorphism, submodel, and sandwich of Kripke models, and we define two syntactic operators analogous to universal and existential closure. Then we prove an intuitionistic analogue of the generalized (dual of the) Lyndon-Łoś-Tarski Theorem, which characterizes the sentences preserved under inverse images of homomorphisms of Kripke models, an intuitionistic analogue of the generalized Łoś-Tarski Theorem, which characterizes the sentences preserved under submodels of Kripke models, and an intuitionistic analogue of the generalized Keisler Sandwich Theorem, which characterizes (...) the sentences preserved under sandwiches of Kripke models. We also define several intuitionistic formula hierarchies analogous to the classical formula hierarchies $\forall_n (= \Pi^0_n)$ and $\exists_n (=\Sigma^0_n)$ , and we show how our generalized syntactic preservation theorems specialize to these hierarchies. Each of these theorems implies the corresponding classical theorem in the case where the Kripke models force classical logic. (shrink)

Recent work in the philosophy of science has generated an apparent conflict between theories attempting to explicate the nature of scientific representation. On one side, there are what one might call 'informational' views, which emphasize objective relations (such as similarity, isomorphism, and homomorphism) between representations (theories, models, simulations, diagrams, etc.) and their target systems. On the other side, there are what one might call 'functional' views, which emphasize cognitive activities performed in connection with these targets, such as interpretation and (...) inference. The main sources of the impression of conflict here are arguments by some functionalists to the effect that informational theories are flawed: it is suggested that relations typically championed by informational theories are neither necessary nor sufficient for scientific representation, and that any theory excluding functions is inadequate. In this paper I critically examine these arguments, and contend that, as it turns out, informational and functional theories are importantly complementary. (shrink)

An interesting feature of some sets of representations is that their structure mirrors the structure of the items they represent. Founding an account of representational content on isomorphism, homomorphism or structural resemblance has proven elusive, however, largely because these relations are too liberal when the candidate structure over representational vehicles is unconstrained. Furthermore, in many cases where there is a clear isomorphism, it is not relied on in the way the representations are used. That points to a potential resolution: (...) that an isomorphism must be used, hence usable, if it is to be an ingredient in a theory of content. This paper argues that the class of exploitable isomorphisms can indeed play a content-constituting role. (shrink)

In their constructive reviews, Frances Egan, Randy Gallistel and Steven Gross have raised some important problems for the account of content advanced by Nicholas Shea in Representation in Cognitive Science. Here the author addresses their main challenges. Egan argues that the account includes an unrecognised pragmatic element; and that it makes contents explanatorily otiose. Gallistel raises questions about homomorphism and correlational information. Gross puts the account to work to resolve a dispute about probabilistic contents in perception, but argues that (...) a question remains about whether probabilities are found in the content or instead in the manner of representation. (shrink)

The claim that similarity plays a role in representation has been philosophically discredited. Psychologists, however, routinely analyse the success of mental representations for guiding behaviour in terms of a similarity between representation and the world. I provide a foundation for this practice by developing a philosophically responsible account of the relationship between similarity and representation in natural systems. I analyse similarity in terms of the existence of a suitable homomorphism between two structures. The key insight is that by restricting (...) attention to only those homomorphisms induced by causal processes, we can solve two philosophical problems with a single assumption. First, causal structure provides an adequate source for the bias required to ensure the similarity relation is non-trivial; second, it provides an adequate source for the directionality required to move from similarity to representation. I defend this account against objections by Goodman and van Fraassen and demonstrate that it is indeed the account of similarity’s role in representation assumed by psychological practice. (shrink)

Perceptual experience seems to involve distinct intentional and qualitative features. Inasmuch as one can visually perceive that there is a Coke can in front of one, perceptual experience must be intentional. But such experiences seem to differ from paradigmatic intentional states in having introspectible qualitative character. Peacocke argues that a perceptual experience’s qualitative character is determined by intrinsic, nonrepresentational properties. But and also argues that perceptual experiences have nonconceptual representational content in addition to conceptual content and nonrepresentational sensational properties. He (...) thus distinguishes between conceptual, nonrepresentational, and nonconceptual but representational aspects of perceptual experience. I will argue that Peacocke posits too much. Contrary to his arguments, the sensational properties Peacocke claims are nonrepresentational are best construed as representational; they are best explained in terms of their relation to the perceptible properties they enable us to perceive. Since sensational properties are arguably nonconceptual, they are best construed as nonconceptual representational properties. I offer the Homomorphism View of sensory qualities, pioneered by Sellars , as a unified account of qualitative character and nonconceptual sensory representation. According to this view, a sensory quality represents a perceptible stimulus property in virtue of resembling and differing from other sensory qualities in ways parallel to the ways the stimulus property resembles and differs from other perceptible properties. (shrink)

In this paper we defend structural representations, more specifically neural structural representation. We are not alone in this, many are currently engaged in this endeavor. The direction we take, however, diverges from the main road, a road paved by the mathematical theory of measure that, in the 1970s, established homomorphism as the way to map empirical domains of things in the world to the codomain of numbers. By adopting the mind as codomain, this mapping became a boon for all (...) those convinced that a representation system should bear similarities with what was being represented, but struggled to find a precise account of what such similarities mean. The euforia was brief, however, and soon homomorphism revealed itself to be affected by serious weaknesses, the primary one being that it included systems embarrassingly alien to representations. We find that the defense attempts that have followed, adopt strategies that share a common format: valid structural representations come as “homomorphism plus X”, with various “X”, provided in descriptive format only. Our alternative direction stems from the observation of the overlooked departure from homomorphism as used in the theory of measure and its later use in mental representations. In the former case, the codomain or the realm of numbers, is the most suited for developing theorems detailing the existence and uniqueness of homomorphism for a wide range of empirical domains. In the latter case, the codomain is the realm of the mind, possibly more vague and more ill-defined than the empirical domain itself. The time is ripe for articulating the mapping between represented domains and the mind in formal terms, by exploiting what is currently known about coding mechanisms in the brain. We provide a sketch of a possible development in this direction, one that adopts the theory of neural population coding as codomain. We will show that our framework is not only not in disagreement with the “plus X” proposals, but can lead to natural derivation of several of the “X”. (shrink)

In this paper we will study the properties of the least extension n(Λ) of a given intermediate logic Λ by a strong negation. It is shown that the mapping from Λ to n(Λ) is a homomorphism of complete lattices, preserving and reflecting finite model property, frame-completeness, interpolation and decidability. A general characterization of those constructive logics is given which are of the form n(Λ). This summarizes results that can be found already in [13, 14] and [4]. Furthermore, we determine (...) the structure of the lattice of extensions of n(LC). (shrink)

Grammatical theory has long wrestled with the fact that causative constructions exhibit properties of both single words and complex phrases. However, as Paul Kiparsky has observed, the distribution of such properties of causatives is not arbitrary: ‘construal’ phenomena such as honorification, anaphor and pronominal binding, and quantifier ‘floating’ typically behave as they would if causatives were syntactically complex, embedding constructions; whereas case marking, agreement and word order phenomena all point to the analysis of causatives as single lexical items.1 Although an (...) analysis of causatives in terms of complex syntactic structures has frequently been adopted in an attempt to simplify the mapping to semantic structure, we believe that motivating syntactic structure based on perceived semantics is questionable because in general a syntax/semantics homomorphism cannot be maintained without vitiating syntactic theory (Miller 1991). Instead, we sketch a strictly lexical theory of Japanese causatives that deals with the evidence offered for a complex phrasal analysis. Such an analysis makes the phonology, morphology and syntax parallel, while a mismatch occurs with the semantics. The conclusions we will reach are given in (1). (shrink)

This paper develops an order-theoretic generalization of Blok and Pigozziʼs notion of an algebraizable logic. Unavoidably, the ordered model class of a logic, when it exists, is not unique. For uniqueness, the definition must be relativized, either syntactically or semantically. In sentential systems, for instance, the order algebraization process may be required to respect a given but arbitrary polarity on the signature. With every deductive filter of an algebra of the pertinent type, the polarity associates a reflexive and transitive relation (...) called a Leibniz order, analogous to the Leibniz congruence of abstract algebraic logic . Some core results of AAL are extended here to sentential systems with a polarity. In particular, such a system is order algebraizable if the Leibniz order operator has the following four independent properties: it is injective, it is isotonic, it commutes with the inverse image operator of any algebraic homomorphism, and it produces anti-symmetric orders when applied to filters that define reduced matrix models. Conversely, if a sentential system is order algebraizable in some way, then the order algebraization process naturally induces a polarity for which the Leibniz order operator has properties –. (shrink)

How, if at all, does the internal structure of human phenomenological color space map onto the internal structure of objective reflectance‐profile space, in such a fashion as to provide a useful and accurate representation of that objective feature space? A prominent argument (due to Hardin, among others) proposes to eliminate colors as real, objective properties of objects, on grounds that nothing in the external world (and especially not surface‐reflectance‐profiles) answers to the well‐known and quite determinate internal structure of human phenomenological (...) color space. The present paper proposes a novel way to construe the objective space of possible reflectance profiles so that (1) its internal structure becomes evident, and (2) that structure’s homomorphism with the internal structure of human phenomenological color space becomes obvious. The path is thus reopened to salvage the objective reality of colors, in the same way that we preserved the objective reality of such features as temperature, pitch, and sourness—by identifying them with some objective feature recognized in modern physical theory. (shrink)

In this paper we defend structural representations, more specifically neural structural representation. We are not alone in this, many are currently engaged in this endeavor. The direction we take, however, diverges from the main road, a road paved by the mathematical theory of measure that, in the 1970s, established homomorphism as the way to map empirical domains of things in the world to the codomain of numbers. By adopting the mind as codomain, this mapping became a boon for all (...) those convinced that a representation system should bear similarities with what was being represented, but struggled to find a precise account of what such similarities mean. The euforia was brief, however, and soon homomorphism revealed itself to be affected by serious weaknesses, the primary one being that it included systems embarrassingly alien to representations. We find that the defense attempts that have followed, adopt strategies that share a common format: valid structural representations come as “homomorphism plus X”, with various “X”, provided in descriptive format only. Our alternative direction stems from the observation of the overlooked departure from homomorphism as used in the theory of measure and its later use in mental representations. In the former case, the codomain or the realm of numbers, is the most suited for developing theorems detailing the existence and uniqueness of homomorphism for a wide range of empirical domains. In the latter case, the codomain is the realm of the mind, possibly more vague and more ill-defined than the empirical domain itself. The time is ripe for articulating the mapping between represented domains and the mind in formal terms, by exploiting what is currently known about coding mechanisms in the brain. We provide a sketch of a possible development in this direction, one that adopts the theory of neural population coding as codomain. We will show that our framework is not only not in disagreement with the “plus X” proposals, but can lead to natural derivation of several of the “X”. (shrink)

We examine, from the partial structures perspective, two forms of applicability of mathematics: at the “bottom” level, the applicability of theoretical structures to the “appearances”, and at the “top” level, the applicability of mathematical to physical theories. We argue that, to accommodate these two forms of applicability, the partial structures approach needs to be extended to include a notion of “partial homomorphism”. As a case study, we present London's analysis of the superfluid behavior of liquid helium in terms of (...) Bose‐Einstein statistics. This involved both the introduction of group theory at the top level, and some modeling at the “phenomenological” level, and thus provides a nice example of the relationships we are interested in. We conclude with a discussion of the “autonomy” of London's model. (shrink)

The paper starts with an examination and critique of Tarski’s wellknown proposed explication of the notion of logical operation in the type structure over a given domain of individuals as one which is invariant with respect to arbitrary permutations of the domain. The class of such operations has been characterized by McGee as exactly those definable in the language L∞,∞. Also characterized similarly is a natural generalization of Tarski’s thesis, due to Sher, in terms of bijections between domains. My main (...) objections are that on the one hand, the Tarski-Sher thesis thus assimilates logic to mathematics, and on the other hand fails to explain the notion of same logical operation across domains of different sizes. A new notion of homomorphism invariant operation over functional type structures (with domains M0 of individuals and {T, F} at their base) is introduced to accomplish the latter. The main result is that an operation is definable from.. (shrink)

It is known that a countable $\omega $ -categorical structure interprets all finite structures primitively positively if and only if its polymorphism clone maps to the clone of projections on a two-element set via a continuous clone homomorphism. We investigate the relationship between the existence of a clone homomorphism to the projection clone, and the existence of such a homomorphism which is continuous and thus meets the above criterion.

Starting from the familiar observation that no straightforward treatment of pure quotation can be compositional in the standard (homomorphism) sense, we introduce general compositionality, which can be described as compositionality that takes linguistic context into account. A formal notion of linguistic context type is developed, allowing the context type of a complex expression to be distinct from those of its constituents. We formulate natural conditions under which an ordinary meaning assignment can be non-trivially extended to one that is sensitive (...) to context types and satisfies general compositionality. As our main example we work out a Fregean treatment of pure quotation, but we also indicate that the method applies to other kinds of context, e.g. intensional contexts. (shrink)

본 논고는 대한민국 사회를 관통하고 있는 불법촬영물이라는 특정 포획물을 기반으로 분포하고 있는 ‘관음충’에 대한 형태발생학적인(morphogenetic) 고찰이다. 형태발생학적 고찰이란 대한민국의 사회문화적 환경 안에서 디지털 성범죄 시스템을 추동시키는 ‘관음충’이라는 특정 군집구성체(population)가 어떠한 젠더와 조건을 중심으로 발생과 생장, 증식을 거듭하는지를 추적함을 의미한다. 필자는 한남유충-관음충-한남충이라는 용어가 배태하고 있는 곤충 군집체의 형태발생학적 착상(conception, idea)을 적극적으로 활용하여 본 논의의 배경(background)으로 삼고자 한다. 그리하여 한남충을 알-유충-성충의 단계에서 탈피와 성장을 거듭하지만 형태상으로 비슷한 상태를 유지하는 ‘불완전변태(homomorphism)’의 모델로 분석하고자 하는 것이다. 또한 ‘한남유충’에서 ‘한남충’으로의 변태(metamorphosis) 과정의 추이가 ‘관음충’의 지수(factor)를 (...) 통해 구체적으로 어떠한 방식으로 단계적으로 진화 가능한지를 첨예하게 드러내고자 한다. 이를 위해 필자는 미국의 신물질주의(New materialism) 이론의 선두주자이자 들뢰즈의 현대적 계승자인 마뉴엘 데란다(Manuel De Landa)의 이론적 틀을 창의적으로 재해석함으로써 관음충 군집체의 발생과 진화과정, 그것의 잠재적 궤적 방향과 현실적 양태에 대한 비판적 분석을 시도할 것이다. 그러하기에 첫째, 데란다가 제시한 ‘군집구성체적 사고(population thinking)’ 틀을 통해 한국에서 태어난 남아가 어떻게 ‘관음충’으로 집단적으로 생장, 진화하는가를 분석하고자 사회문화적으로 다양한 자가복제 기제들(replicators)을 들여다보도록 하겠다. 둘째, ‘강렬도의 사고(intensive thinking)’ 틀을 통해 관음충의 형태발생학적 변화 과정을 ‘영토화(territorialisation)와 코드화(coding)’라는 두 가지 기준척도를 통해 각각의 변이국면의 주요 특이점들을 파악하고 고찰할 것이다. 셋째, ‘위상학적 사고(Topological thinking)’ 틀을 통해 가부장제 자본주의 사회지평 내 관음충 군집체가 주파할 잠재적 궤도 방향과 메커니즘을 분석, 고찰하고 대한민국 사회가 이 궤도로부터 어떻게 이탈 가능할지를 페미니즘적으로 사유하도록 하겠다. (shrink)

This paper is about partially ordered multisets (pomsets for short). We investigate a particular class of pomsets that we call order-deterministic, properly including all partially ordered sets, which satisfies a number of interesting properties: among other things, it forms a distributive lattice under pomset prefix (hence prefix closed sets of order-deterministic pomsets are prime algebraic), and it constitutes a reflective subcategory of the category of all pomsets. For the order-deterministic pomsets we develop an algebra with a sound and (-) complete (...) equational theory. The operators in the algebra are concatenation and join, the latter being a variation on the more usual disjoint union of pomsets. This theory is then extended in order to capture refinement of pomsets by incorporating homomorphisms between models as objects in the algebra and homomorphism application as a new operator. (shrink)

In this paper we define a suitable version of the notion of homomorphism for Kripke models of intuitionistic first-order logic and characterize theories that are preserved under images and also those that are preserved under inverse images of homomorphisms. Moreover, we define a notion of union of chain for Kripke models and define a class of formulas that is preserved in unions of chains. We also define similar classes of formulas and investigate their behavior in Kripke models. An application (...) to intuitionistic first-order arithmetic is also given. (shrink)

The topics approached in the 52 papers included in this book are: neutrosophic sets; neutrosophic logic; generalized neutrosophic set; neutrosophic rough set; multigranulation neutrosophic rough set (MNRS); neutrosophic cubic sets; triangular fuzzy neutrosophic sets (TFNSs); probabilistic single-valued (interval) neutrosophic hesitant fuzzy set; neutro-homomorphism; neutrosophic computation; quantum computation; neutrosophic association rule; data mining; big data; oracle Turing machines; recursive enumerability; oracle computation; interval number; dependent degree; possibility degree; power aggregation operators; multi-criteria group decision-making (MCGDM); expert set; soft sets; LA-semihypergroups; single (...) valued trapezoidal neutrosophic number; inclusion relation; Q-linguistic neutrosophic variable set; vector similarity measure; fundamental neutro-homomorphism theorem; neutro-isomorphism theorem; quasi neutrosophic triplet loop; quasi neutrosophic triplet group; BE-algebra; cloud model; Maclaurin symmetric mean; pseudo-BCI algebra; hesitant fuzzy set; photovoltaic plan; decision-making trial and evaluation laboratory (DEMATEL); Choquet integral; fuzzy measure; clustering algorithm; and many more. (shrink)

Graph theory is a specific concept that has numerous applications throughout many industries. Despite the advancement of this technique, graph theory can still yield ambiguous and imprecise results. In order to cut down on these indeterminate factors, neutrosophic logic has emerged as an applicable solution that is gaining significant attention in solving many real-life decision-making problems that involve uncertainty, impreciseness, vagueness, incompleteness, inconsistency, and indeterminacy. However, empirical research on this specific graph set is lacking. Neutrosophic Graph Theory and Algorithms is (...) a collection of innovative research on the methods and applications of neutrosophic sets and logic within various fields including systems analysis, economics, and transportation. While highlighting topics including linear programming, decision-making methods, and homomorphism, this book is ideally designed for programmers, researchers, data scientists, mathematicians, designers, educators, researchers, academicians, and students seeking current research on the various methods and applications of graph theory. (shrink)

The book is a collection of papers and aims to unify the questions of syntax and semantics of language, which are included in logic, philosophy and ontology of language. The leading motif of the presented selection of works is the differentiation between linguistic tokens (material, concrete objects) and linguistic types (ideal, abstract objects) following two philosophical trends: nominalism (concretism) and Platonizing version of realism. The opening article under the title “The Dual Ontological Nature of Language Signs and the Problem of (...) Their Mutual Relations” provides a broad introduction into the problem area connected with this differentiation, while the logic-formal characteristics of the distinction are framed in the work entitled “On the Type-Token Relationships” (Chapter 1). The basic part of the book deals with issues relating to syntax (Chapters 2-4) and semantics of language (Chapters 5-6), as well as pertaining to syntactic-semantic pragmatic questions (Chapters 7-13). Throughout the book, language, categorial language, is characterized syntactically as generated by classical categorial grammar (Chapter 2) and formalized on two opposing levels: as language of expression-tokens (level of tokens) and language of expression-types (level of types). The author’s considerations contained in Chapters 2 and 4 lead to the important philosophical conclusion that in formal-logical syntactic studies on language the assumption that expression-types constitute the primary language layer while expression-tokens make the secondary one, can be neglected; thus, this speaks in favour of the opposing standpoint—the concretistic one—in the ontology of language syntax. In the works “Meaning and Interpretations”, Parts I and II (Chapters 5 and 6), it is underlined, however, that such semantic concepts as: meaning, denotation and interpretation are defined on the types level, yet their formal definitions require making use of notions of the tokens level. The semantic notions introduced in the above-mentioned articles are also used in the following works of the present selection, under the titles: “Three Principles of Compositionality” and “On Metaknowledge and Truth” (Chapters 7 and 8). They formalize two principles of compositionality that are well known in the literature on the subject, deriving from Frege, i.e. those of meaning and of denotation; they are related to the syntactic principle of compositionality which was introduced by the author. All the three principles are, at the same time, three conditions of homomorphism of categorial language algebra into three kinds of non-standard models of language (one syntactic and two semantic ones: intensional and extensional), which allows introducing three definitions of truthfulness into these models. The next two works in the collection, entitled: “On Language Adequacy” and “What is the Sense in Logic and Philosophy of Language” (Chapters 9 and 10) concern adequacy of categorial language syntax along with its dual semantics: intensional and extensional, and categorial compatibility of any of its syntactic categories with two corresponding semantic categories: intensional and extensional, based on the compatibility the syntactic category of each language expression with the ontological category assigned to its denotatum. The well-known problem of categorial compatibility for first-order quantifiers finds its solution in the paper “Categories of First-Order Quantifiers” (Chapter 11). In the work “Logic and Ontology of Language” (Chapter 12), being in a sense a summary of the considerations presented in the preceding chapters of the book, language is treated as an ontological being, characterized in compliance with the logical conception of language proposed by Ajdukiewicz. Application—like throughout the book—of tools of classical logic and set theory has resulted in emergence of a general formal logical theory of syntax, semantics and pragmatics of language, which takes into account duality in the understanding of linguistic expressions as tokens (concretes) and types (abstract objects). In terms that take into account a functional approach to language itself, there comes out an ontological neutrality of logic with respect to existential assumptions relating to the ontological nature of linguistic expressions and their extra-linguistic ontological counterparts. The issues connected with applying logic while explaining the manner of using linguistic tokens and linguistic types to determine notions of language communication are raised and illustrated in the last chapter of the work, bearing the title “A Logical Conceptualization of Knowledge on the Notion of Language Communication”. (shrink)

We study the lattice of extensions of four-valued Belnap–Dunn logic, called super-Belnap logics by analogy with superintuitionistic logics. We describe the global structure of this lattice by splitting it into several subintervals, and prove some new completeness theorems for super-Belnap logics. The crucial technical tool for this purpose will be the so-called antiaxiomatic (or explosive) part operator. The antiaxiomatic (or explosive) extensions of Belnap–Dunn logic turn out to be of particular interest owing to their connection to graph theory: the lattice (...) of finitary antiaxiomatic extensions of Belnap–Dunn logic is isomorphic to the lattice of upsets in the homomorphism order on finite graphs (with loops allowed). In particular, there is a continuum of finitary super-Belnap logics. Moreover, a non-finitary super-Belnap logic can be constructed with the help of this isomorphism. As algebraic corollaries we obtain the existence of a continuum of antivarieties of De Morgan algebras and the existence of a prevariety of De Morgan algebras which is not a quasivariety. (shrink)

Given a Polish groupG, let$E(G)$be the right coset equivalence relation$G^{\omega }/c(G)$, where$c(G)$is the group of all convergent sequences inG. The connected component of the identity of a Polish groupGis denoted by$G_0$.Let$G,H$be locally compact abelian Polish groups. If$E(G)\leq _B E(H)$, then there is a continuous homomorphism$S:G_0\rightarrow H_0$such that$\ker (S)$is non-archimedean. The converse is also true whenGis connected and compact.For$n\in {\mathbb {N}}^+$, the partially ordered set$P(\omega )/\mbox {Fin}$can be embedded into Borel equivalence relations between$E({\mathbb {R}}^n)$and$E({\mathbb {T}}^n)$.

It is generally accepted that, in the cognitive and neural sciences, there are both computational and mechanistic explanations. We ask how computational explanations can integrate into the mechanistic hierarchy. The problem stems from the fact that implementation and mechanistic relations have different forms. The implementation relation, from the states of an abstract computational system to the physical, implementing states is a homomorphism mapping relation. The mechanistic relation, however, is that of part/whole; the explaining features in a mechanistic explanation are (...) the components of the explanandum phenomenon and their causal organization. Moreover, each component in one level of mechanism is constituted and explained by components of an underlying level of mechanism. Hence, it seems, computational variables and functions cannot be mechanistically explained by the medium-dependent states and properties that implement them. How then, do the computational and the implementational integrate to create the mechanistic hierarchy? After explicating the general problem, we further demonstrate it through a concrete example, of reinforcement learning, in the cognitive and neural sciences. We then examine two possible solutions. On one solution, the mechanistic hierarchy embeds at the same levels computational and implementational properties. This picture fits with the view that computational explanations are mechanistic sketches. On the other solution, there are two separate hierarchies, one computational and another implementational, which are related by the implementation relation. This picture fits with the view that computational explanations are functional and autonomous explanations. It is less clear how these solutions fit with the view that computational explanations are full-fledged mechanistic explanations. Finally, we argue that both pictures are consistent with the reinforcement learning example, but that scientific practice does not align with the view that computational models are merely mechanistic sketches. (shrink)

We show that the existential preservation theorem fails for two-variable first-order logic FO2. It is known that for all k ≥ 3, FOk does not have an existential preservation theorem, so this settles the last open case, answering a question of Andreka, van Benthem, and Németi. In contrast, we prove that the homomorphism preservation theorem holds for FO2.

This study provides an innovative approach to neutrosophic algebraic structures by introducing a new structure called Neutrosophic Soft Cubic T-ideal (NSCTID), which combines T-ideal (TID) and neutrosophic Soft Cubic Sets (NSCSs) within the framework of PS-Algebra. Within the already-existing neutrosophic cubic structures, the addition of soft sets with the characteristics of TID makes this structure more desirable. The theoretical development of the proposed structure includes the application of fundamental ideas as union, intersection, the Cartesian product, and homomorphism. We also (...) introduce the notions of NSCTID-translation and NSCTID-multiplication to further enhance the structure of NSCTID. By applying the idea of translation and multiplication, we offer improved algorithm for neutrosophic cubic sets to deal with different parameters that are satisying the TID’s distinctive characteristics. Through this thorough research, we offer an elementary understanding of NSCTID and its capabilities, providing the way to new algebraic structures. (shrink)

Cooper storage is a widespread technique for associating sentences with their meanings, used in diverse linguistic and computational linguistic traditions. This paper encodes the data structures and operations of cooper storage in the simply typed linear \-calculus, revealing the rich categorical structure of a graded applicative functor. In the case of finite cooper storage, which corresponds to ideas in current transformational approaches to syntax, the semantic interpretation function can be given as a linear homomorphism acting on a regular set (...) of trees, and thus generation can be done in polynomial time. (shrink)

In abstract algebraic logic, many systems, such as those paraconsistent logics taking inspiration from da Costa's hierarchy, are not algebraizable by even the broadest standard methodologies, as that of Blok and Pigozzi. However, these logics can be semantically characterized by means of non-deterministic algebraic structures such as Nmatrices, RNmatrices and swap structures. These structures are based on multialgebras, which generalize algebras by allowing the result of an operation to assume a non-empty set of values. This leads to an interest in (...) exploring the foundations of multialgebras applied to the study of logic systems. It is well known from universal algebra that, for every signature \, there exist algebras over \ which are absolutely free, meaning that they do not satisfy any identities or, alternatively, satisfy the universal mapping property for the class of \-algebras. Furthermore, once we fix a cardinality of the generating set, they are, up to isomorphisms, unique, and equal to algebras of terms. Equivalently, the forgetful functor, from the category of \-algebras to Set, has a left adjoint. This result does not extend to multialgebras. Not only multialgebras satisfying the universal mapping property do not exist, but the forgetful functor \, from the category of \-multialgebras to Set, does not have a left adjoint. In this paper we generalize, in a natural way, algebras of terms to multialgebras of terms, whose family of submultialgebras enjoys many properties of the former. One example is that, to every pair consisting of a function, from a submultialgebra of a multialgebra of terms to another multialgebra, and a collection of choices, there corresponds a unique homomorphism, what resembles the universal mapping property. Another example is that the multialgebras of terms are generated by a set that may be viewed as a strong basis, which we call the ground of the multialgebra. Submultialgebras of multialgebras of terms are what we call weakly free multialgebras. Finally, with these definitions at hand, we offer a simple proof that multialgebras with the universal mapping property for the class of all multialgebras do not exist and that \ does not have a left adjoint. (shrink)

In this paper, we study natural language constructions which were first examined by Barwise: The richer the country, the more powerful some of its officials. Guided by Barwise’s observations, we suggest that conceivable interpretations of such constructions express the existence of various similarities between partial orders such as homomorphism or embedding. Semantically, we interpret the constructions as polyadic generalized quantifiers restricted to finite models. We extend the results obtained by Barwise by showing that similarity quantifiers are not expressible in (...) elementary logic over finite models. We also investigate whether the proposed readings are sound from the cognitive perspective. We prove that almost all similarity quantifiers are intractable. This leads us to first-order variants, which only approximate the strong readings, but are cognitively more plausible. Driven by the question of ambiguity, we recall Barwise’s argumentation in favour of strong readings, enriching it with some arguments of our own. Given that Barwise-like sentences are indeed ambiguous, we use a generalized Strong Meaning Hypothesis to derive predictions for their verification. Finally, we propose a hypothesis according to which conflicting pressures of communication and cognition might give rise to an ambiguous construction, provided that different semantic variants of the construction withstand different pressures involved in its usage. (shrink)

That diagrams are analog, i.e., homomorphic, representations of some kind, and sentential representations are not, is a generally held intuition. In this paper, we develop a formal framework in which the claim can be stated and examined, and certain puzzles resolved. We start by asking how physical things can represent information in some target domain. We lay a basis for investigating possible homomorphisms by modeling both the physical medium and the target domain as sets of variables, each with a constraint (...) structure. When a homomorphism exists, the causality of the physical medium can provide a “free ride,” automatically determining the information that is needed to solve a problem. The modeling technique enables us to show how in sentential representations the structure of the 2-D space is used non-homomorphically to define tokens, and to provide a minimal homomorphism with respect to the ordering of the arguments for n-ary functions, predicates, and operators, but otherwise there is no homomorphism with the target domain. Our treatment also characterizes diagrams as a type of a more general class of physical representations in which physical causality plays a role in providing the information needed to solve a problem. (shrink)

A residuated lattice is said to be integrally closed if it satisfies the quasiequations \ and \, or equivalently, the equations \ and \. Every integral, cancellative, or divisible residuated lattice is integrally closed, and, conversely, every bounded integrally closed residuated lattice is integral. It is proved that the mapping \\backslash {\mathrm {e}}\) on any integrally closed residuated lattice is a homomorphism onto a lattice-ordered group. A Glivenko-style property is then established for varieties of integrally closed residuated lattices with (...) respect to varieties of lattice-ordered groups, showing in particular that integrally closed residuated lattices form the largest variety of residuated lattices admitting this property with respect to lattice-ordered groups. The Glivenko property is used to obtain a sequent calculus admitting cut-elimination for the variety of integrally closed residuated lattices and to establish the decidability, indeed PSPACE-completenes, of its equational theory. Finally, these results are related to previous work on BCI-algebras, semi-integral residuated pomonoids, and Casari’s comparative logic. (shrink)

A relational structure \ is called reversible iff each bijective homomorphism from \ onto \ is an isomorphism, and linear orders are prototypical examples of such structures. One way to detect new reversible structures of a given relational language L is to notice that the maximal or minimal elements of isomorphism-invariant sets of interpretations of the language L on a fixed domain X determine reversible structures. We isolate certain syntactical conditions providing that a satisfiable \-theory defines a class of (...) interpretations having extreme elements on a fixed domain and detect several classes of reversible structures. For some of these classes, we characterize the corresponding reversible extreme interpretations. In particular, we characterize the reversible countable ultrahomogeneous graphs. (shrink)