We study positive bilinear forms on a Hilbert space which are not necessarily bounded nor induced by some positive operator. We show when different families of bilinear forms can be described as a generalized effect algebra. In addition, we present families which are or are not monotone downwards (Dedekind upwards) σ-complete generalized effect algebras.

We aim to construct exact and explicit solutions to a generalized Bogoyavlensky-Konopelchenko equation through the Maple computer algebra system. The considered nonlinear equation is transformed into a Hirota bilinear form, and symbolic computations are made for solving both the nonlinear equation and the corresponding bilinear equation. A few classes of exact and explicit solutions are generated from different ansätze on solution forms, including traveling wave solutions, two-wave solutions, and polynomial solutions.

We relate so-called spin factors and generalized Hermitian (GH-) algebras, both of which are partially ordered special Jordan algebras. Our main theorem states that positive-definite spin factors of dimension greater than one are mathematically equivalent to generalized Hermitian algebras of rank two.

We present a general derivation of the Duffin-Kemmer-Petiau (D.K.P) equation on the relativistic phase space proposed by Bohm and Hiley. We consider geometric algebras and the idea of algebraic spinors due to Riesz and Cartan. The generators βμ (p) of the D.K.P algebras are constructed in the standard fashion used to construct Clifford algebras out of bilinear forms. Free D.K.P particles and D.K.P particles in a prescribed external electromagnetic field are analized and general Liouville type equations for these cases (...) are obtained. Choosing particular values for the label p we classify the different types of the D.K.P Liouville operators. (shrink)

Linear Logic is a versatile framework with diverse applications in computer science and mathematics. One intriguing fragment of Linear Logic is Multiplicative-Additive Linear Logic (MALL), which forms the exponential-free component of the larger framework. Modifying MALL, researchers have explored weaker logics such as Noncommutative MALL (Bilinear Logic, BL) and Cyclic MALL (CyMALL) to investigate variations in commutativity. In this paper, we focus on Cyclic Nonassociative Bilinear Logic (CyNBL), a variant that combines noncommutativity and nonassociativity. We introduce a sequent (...) system for CyNBL, which includes an auxiliary system for incorporating nonlogical axioms. Notably, we establish the cut elimination property for CyNBL. Moreover, we establish the strong conservativeness of CyNBL over Full Nonassociative Lambek Calculus (FNL) without additive constants. The paper highlights that all proofs are constructed using syntactic methods, ensuring their constructive nature. We provide insights into constructing cut-free proofs and establishing a logical relationship between CyNBL and FNL. (shrink)

The geometro-stochastic quantization of a gauge theory for extended objects based on the (4, 1)-de Sitter group is used for the description of quantized matter in interaction with gravitation. In this context a Hilbert bundle ℋ over curved space-time B is introduced, possessing the standard fiber ℋ $_{\bar \eta }^{(\rho )} $ , being a resolution kernel Hilbert space (with resolution generator $\tilde \eta $ and generalized coherent state basis) carrying a spin-zero phase space representation of G=SO(4, 1) belonging to (...) the principal series of unitary irreducible representations determined by the parameter ρ. The bundle ℋ, associated to the de Sitter frame bundle P(B, G), provides a geometric arena with built-in fundamental length parameter R (taken to be of the order of 10−13 cm characterizing hadron physics) yielding, in the presence of gravitation, a quantum kinematical framework for the geometro-stochastic description of spinless matter described in terms of generalized quantum mechanical wave functions, Ψ x ρ (ξ, ζ), defined on #x210B;. By going over to a nonlinear realization of the de Sitter group with the help of a section ξ(x) on the soldered bundle E, associated to P, with homogeneous fiber V′4⋍G/H, one is able to recover gravitation in a de Sitter gauge invariant manner as a gauge theory related to the Lorentz subgroup H of G. ξ(x) plays the dual role of a symmetry-reducing and an extension field. After introducing covariant bilinear source currents in the fields Ψ x ρ (ξ, ζ) and their adjoints determined by G-invariant integration over the local fibers in ℋ, a quantum fiber dynamical (QFD) framework is set up for the dynamics at small distances in B determining the geometric quantities beyond the classical metric of Einstein's theory through a set of current-curvature field equations representing the source equations for axial vector torsion and the de Sitter boost contributions to the bundle connection (the latter defining the soldering forms of the Cartan connection in P(B, G) in the nonlinear gauge). The presented bundle framework yields a theory for quantized material objects in interaction with gravitation, the long-range metrical part of which remains classical. (shrink)

NEMO means Network Mobility which is the extension of Mipv6 and it is invented for accessing internet for the group of people when they are travelling in Vehicle as Network group. During handoff while exchanging Binding Updates between the Mobile Network Node, Correspondent Node and Home Agent, many security threats are present during those messages exchange. It may prone to several standard malicious attacks on the BU and Binding Acknowledgement. An efficient end-to-end security method is required to protect the BU (...) Exchange between MNN, HA and CN. In this paper, a secure architecture is proposed to provide authentication and confidentiality at each level of communication using a 3-Party Key Exchange called 3-PKE-NEMO with the help of Bilinear Pairing Theorem. Handoff delay is reduced without compromising security strength. The whole experimentation of this proposed work is carried out using NS2 simulation tool and authentication proof is given using BAN logic between all the nodes in NEMO. The proposed security architecture is compared with related existing solutions and found to be more secure. (shrink)

Compact Bilinear Logic , introduced by Lambek [14], arises from the multiplicative fragment of Noncommutative Linear Logic of Abrusci [1] by identifying times with par and 0 with 1. In this paper, we present two sequent systems for CBL and prove the cut-elimination theorem for them. We also discuss a connection between cut-elimination for CBL and the Switching Lemma from [14].

"L'oeuvre d'art est une tentative vers l'unique, elle s'affirme comme un tout, comme un absolu et, en même temps, elle appartient à un système de relations complexes [...]. Elle est matière et elle est esprit, elle est forme et elle est contenu [...]. Elle est créatrice de l'homme, créatrice du monde et elle installe dans l'histoire un ordre qui ne se réduit à rien d'autre." Un Eloge de la main complète ce texte. "La main arrache le toucher à sa passivité (...) réceptive, elle l'organise pour l'expérience et pour l'action [...]. Elle se mesure avec la matière qu'elle métamorphose, avec la forme qu'elle transfigure. Educatrice de l'homme, elle le multiplie dans l'espace et dans le temps." [Source : 4e de couv.]. (shrink)

It is possible to define a combinatorial closure on alternating bilinear maps with few relations similar to that in [2]. For the ℵ 0 - categorical case we show that this closure is part of the algebraic closure.

Bilinear Logic of Lambek amounts to Noncommutative MALL of Abrusci. Lambek proves the cut–elimination theorem for a one-sided sequent system for this logic. Here we prove an analogous result for the nonassociative version of this logic. Like Lambek, we consider a left-sided system, but the result also holds for its right-sided version, by a natural symmetry. The treatment of nonassociative sequent systems involves some subtleties, not appearing in associative logics. We also prove the PTime complexity of the multiplicative fragment (...) of NBL. (shrink)

In this paper we study the algebraic structure ofω-stable bilinear maps, arbitrary rings, and nilpotent groups. We will also provide rather complete structure theorems for the above structures in the finite Morley rank case.

Grishin algebras are a generalisation of Boolean algebras that provide algebraic models for classical bilinear logic with two mutually cancelling negation connectives. We show how to build complete Grishin algebras as algebras of certain subsets (“propositions”) of cover systems that use an orthogonality relation to interpret the negations. The variety of Grishin algebras is shown to be closed under MacNeille completion, and this is applied to embed an arbitrary Grishin algebra into the algebra of all propositions of some cover (...) system, by a map that preserves all existing joins and meets. This representation is then used to give a cover system semantics for a version of classical bilinear logic that has first-order quantifiers and infinitary conjunctions and disjunctions. (shrink)

Logical Forms explains both the detailed problems involved in finding logical forms and also the theoretical underpinnings of philosophical logic. In this revised edition, exercises are integrated throughout the book. The result is a genuinely interactive introduction which engages the reader in developing the argument. Each chapter concludes with updated notes to guide further reading.

Few notions are more central to Aquinas’s thought than those of matter and form. Although he invokes these notions in a number of different contexts, and puts them to a number of different uses, he always assumes that in their primary or basic sense they are correlative both with each other and with the notion of a “hylomorphic compound”—that is, a compound of matter (hyle) and form (morphe). Thus, matter is an entity that can have form, (...) class='Hi'>form is an entity that can be had by matter, and a hylomorphic compound is an entity that exists when the potentiality of some matter to have form is actualized.1 What is more, Aquinas assumes that the matter of a hylomorphic compound explains certain of its general characteristics, whereas its form explains certain of its more specific characteristics. Thus, the matter of a bronze statue explains the fact that it is bronze, whereas its form explains the fact that it is a statue. Again, the matter of a human being explains the fact that it is a material object, whereas its form explains the specific type of material object it is (namely, human). My aim in this chapter is to provide a systematic introduction to Aquinas’s primary or basic notions of matter and form. To accomplish this aim, I focus on the two main theoretical contexts in which he deploys them—namely, his theory of change and his theory of individuation. In both contexts, as we shall see, Aquinas appeals to matter and form to account for relations of sameness and difference holding between distinct individuals. (shrink)

In this article, I critically reassess Iris Marion Young's late works, which centre on the distinction between liability and social connection responsibility. I concur with Young's diagnosis that structural injustices call for a new conception of responsibility, but I reject several core assumptions that underpin her distinction between two models and argue for a different way of conceptualising responsibility to address structural injustices. I show that Young's categorical separation of guilt and responsibility is not supported by the writings of Hannah (...) Arendt, which Young draws on, and that it is also untenable on independent systematic grounds. Furthermore, I argue that several of Young's other criteria fail to clearly demarcate two distinct phenomena. I therefore propose to transcend Young's distinction between two models in favour of a related, but conceptually different distinction between two forms of responsibility: interactional and structural. Embracing this terminology facilitates the conceptualisation of the general features of responsibility that are shared by both forms, including their retrospective and prospective time-direction and their applicability to individual, joint and group agency. The distinction between interactional and structural responsibility also yields a more compelling general account of the role of background structures, and of blame within ascriptions of political responsibility. (shrink)

00 In this innovative analysis, Plato's four eleatic dialogues are treated as a continuous argument. In Kenneth Dorter's view, Plato reconsiders the theory of forms propounded in his earlier dialogues and through an examination of the theory's limitations reaffirms and proves it essential. Contradicted are both those philosophers who argue that Plato espoused his theory of forms uncritically and those who argue that Plato in some sense rejected the theory and moved toward the categorical analysis developed byAristotle. Dorter's reexamination of (...) Plato's insights implies an important new direction for modern philosophical inquiry. In this innovative analysis, Plato's four eleatic dialogues are treated as a continuous argument. In Kenneth Dorter's view, Plato reconsiders the theory of forms propounded in his earlier dialogues and through an examination of the theory's limitations reaffirms and proves it essential. Contradicted are both those philosophers who argue that Plato espoused his theory of forms uncritically and those who argue that Plato in some sense rejected the theory and moved toward the categorical analysis developed byAristotle. Dorter's reexamination of Plato's insights implies an important new direction for modern philosophical inquiry. (shrink)

In dialogue with afro-caribbean philosophy, this book seeks in Cassirer's philosophy of symbolic forms a new vocabulary for approaching central intellectual and ...

Form of Thought and Presentational Gesture in Karl Popper and E. H. Gombrich The paper deals with common elements and differences in Popper and Gombrich, especially concerning their forms of thought and presentational gesture. Among others it considers the model of common sense which was basal for both of them as well as the similarities of searchlight theory (Popper) and some postulates of Gestalt psychology (Gombrich). At the end it analyses their approaches to historiography with special focusing on Gombrich's (...) comments on the concept of social history of art. (shrink)

In _Form, Matter, Substance_, Kathrin Koslicki defends a hylomorphic analysis of concrete particular objects (e.g., living organisms). The Aristotelian doctrine of hylomorphism holds that those entities that fall under it are compounds of matter (hulē) and form (morphē or eidos). Koslicki argues that a hylomorphic analysis of concrete particular objects is well-equipped to compete with alternative approaches when measured against a wide range of criteria of success. A successful application of the doctrine of hylomorphism to the special case of (...) concrete particular objects, however, hinges on how hylomorphists conceive of the matter composing a concrete particular object, its form, and the hylomorphic relations which hold between a matter-form compound, its matter and its form. Through the detailed answers to these questions Koslicki develops in this book, matter-form compounds, despite their metaphysical complexity, emerge as occupying the privileged ontological status traditionally associated with substances, due in particular to their high degree of unity. (shrink)

All forms of consequentialism make the moral assessment of alternatives depend in some way on the value of the alternatives, but they form a heterogeneous family of moral theories. Some employ subjective assumptions about value, while others employ objective assumptions. Some assess the value of alternatives directly, while others assess value indirectly. Some direct agents to maximize value, while others direct agents to satisfice. Some, such as utilitarianism, are impartial and concerned to promote agent-neutral value, while others, such as (...) self-referential altruism and perfectionist egoism, are partial and concerned to promote agent-relative value. This chapter focuses on the contrast between agent-neutral and agent-relative consequentialism. The chief attraction of agent-neutral consequentialism lies in its interpretation of impartiality. This interpretation is robust, and has the resources to answer criticisms that it cannot accommodate agent-relative constraints and options. However, it is difficult to fit associated duties into the intellectual net of agent-neutral consequentialism. Accommodating partiality requires an agent-relative form of consequentialism. (shrink)

Hylomorphism is the Aristotelian theory according to which substances are composites of matter and form. If my house is a substance, then its matter would be a collection of bricks and timbers and its form something like a structure that unites those bricks and timbers into a single substance. Contemporary hylomorphists are divided on how to understand forms best, but a prominent group of theorists argue that forms are emergent powers. According to such views, when material components are (...) arranged appropriately, a novel substance emerges with the power to impose unity on its components through time. I argue that these accounts of form fall prey to a bootstrapping problem, and so, suffer from issues of redundancy, given plausible assumptions about inherence. In their place, I suggest an ontologically minimalist conception of forms as collective manifestations of the powers of matter. (shrink)

Logical form has always been a prime concern for philosophers belonging to the analytic tradition. For at least one century, the study of logical form has been widely adopted as a method of investigation, relying on its capacity to reveal the structure of thoughts or the constitution of facts. This book focuses on the very idea of logical form, which is directly relevant to any principled reflection on that method. Its central thesis is that there is no (...) such thing as a correct answer to the question of what is logical form: two significantly different notions of logical form are needed to fulfil two major theoretical roles that pertain respectively to logic and to semantics. This thesis has a negative and a positive side. The negative side is that a deeply rooted presumption about logical form turns out to be overly optimistic: there is no unique notion of logical form that can play both roles. The positive side is that the distinction between two notions of logical form, once properly spelled out, sheds light on some fundamental issues concerning the relation between logic and language. (shrink)

This inaugural lecture, delivered on 17 November 2021 at the University of Neuchâtel, addresses the question: Are material objects analyzable into more basic constituents and, if so, what are they? It might appear that this question is more appropriately settled by empirical means as utilized in the natural sciences. For example, we learn from physics and chemistry that water is composed of H2O-molecules and that hydrogen and oxygen atoms themselves are composed of smaller parts, such as protons, which are in (...) turn composed of yet smaller parts, such as quarks, and so on. While the question at the center of this lecture might thus appear to fall more appropriately into the empirical domain of natural science, I argue that metaphysics in fact has an important role to play in determining how best to answer the question before us. More concretely, I propose that the Aristotelian doctrine of hylomorphism, when appropriately interpreted, provides the best metaphysical answer to the question of whether and how material objects are analyzable into more basic constituents. Hylomorphism holds that those entities to which this doctrine applies are, in some sense, compounds of matter (“hylē”) and form (“morphē” or “eidos”). Thus, the title of this lecture, “Form, Matter, Substance”, refers to the claim that lies at the center of the doctrine of hylomorphism, as applied to the domain of material objects, namely that sensible substances are the result of combining matter and form in the right sort of way; or, for short, “form + matter = substance”. I begin in Section II by providing some historical background which brings out Aristotle’s motivations for proposing the doctrine of hylomorphism in the context of his analysis of change. Section III turns to some of the main features of the contemporary hylomorphic theory I have defended especially in Koslicki (2008) and Koslicki (2018). Section IV discusses some challenging questions concerning artifacts which arise for both hylomorphic and other approaches to the metaphysics of concrete particular objects. Section V concludes by summarizing why, as contemporary metaphysicians, we should prefer a hylomorphic theory over its competitors as an analysis of concrete particular objects that is compatible with our current scientific understanding of the world. (shrink)

Reclaiming Fuller -- Before the debate -- The 1958 debate -- The morality of law -- The reply to critics -- Resituating Fuller I : Raz -- Resituating Fuller II : Dworkin -- Three conversations.

In Aristotle's account of change, lacking a form is called privation (Physics I.7 191a14). For example, someone takes on the form of being musical only from previously having the privation of being unmusical. However, he also states that “shape and nature are spoken of in two ways, for the privation too is in a way form” (Physics II.1 193b19). I will demonstrate that these seemingly contradictory statements are not actually in tension. Since all perceptible matter must be (...) enformed, we would have trouble discussing things that have yet to undergo generation, like menstrual fluid, and things that have undergone corruption, like corpses, if we did not cite the privation as a sort of form. I will argue that, given his commitment to hylomorphism, Aristotle is committed to privation being a form in a qualified sense. It cannot be a form in an unqualified sense because privation often spoils the matter such that it can no longer be reformed. The fact of the matter is we cannot draw a bright line between privation and form because the two are contraries and can be said to hold to different degrees at different points on a spectrum. (shrink)

Formal thought disorder (FTD) is a clinical mental condition that is typically diagnosable by the speech productions of patients. However, this has been a vexing condition for the clinical community, as it is not at all easy to determine what “formal” means in the plethora of symptoms exhibited. We present a logic-based model for the syntax–semantics interface in semantic networking that can not only explain, but also diagnose, FTD. Our model is based on description logic (DL), which is well known (...) for its adequacy to model terminological knowledge. More specifically, we show how faulty logical form as defined in DL-based Conception Language (CL) impacts the semantic content of linguistic productions that are characteristic of FTD. We accordingly call this the dyssyntax model. (shrink)