Countable homogeneous relational structures have been studied by many people. One area of focus is the Ramsey theory of such structures. After a review of background material, a partition theorem of Laflamme, Sauer, and Vuksanovic for countable homogeneous binary relational structures is discussed with a focus on the size of the set of unavoidable colors.

The properties of antisymmetry and linearity are easily seen to be sufficient for a recursively enumerable binary relation to be recursively isomorphic to a recursive relation. Removing either condition allows for the existence of a structure where no recursive isomorph exists, and natural examples of such structures are surveyed.

Let S be a signature of operations and relations definable in relation algebra, let R be the class of all S-structures isomorphic to concrete algebras of binary relations with concrete interpretations for symbols in S, and let F be the class of S-structures isomorphic to concrete algebras of binary relations over a finite base. To prove that membership of R or F for finite S-structures is undecidable, we reduce from a known undecidable problem—here we use the tiling problem, (...) the partial group embedding problem and the partial group finite embedding problem to prove undecidability of finite membership of R or F for various signatures S. It follows that the equational theory of R is undecidable whenever S includes the boolean operators and composition. We give an exposition of the reduction from the tiling problem and the reduction from the group embedding problem, and summarize what we know about the undecidability of finite membership of R and of F for different signatures S. (shrink)

We study partitions of Fraïssé limits of classes of finite relational structures where the partitions are encoded by infinite binary strings which are random in the sense of Kolmogorov-Chaitin.

We study those relational structures S with the property that each partition of S contains a block isomorphic to S. We show that the Fraïsse limits of parametric classes K. have property ; over a binary language, every countable structure in K satisfying along with a condition on 1-extensions must be isomorphic to this limit.

The topological structures imposed on the collection of binary relations on a given set by the symmetric difference metric and the Hausdorff metric provide opportunities for learning about how collections of binary relations with various properties fit into the collection of all binary relations. For example, there is some agreement and some disagreement between conclusions drawn about the rarity of certain properties of binary relations using first the symmetric difference metric and then the Hausdorff metric.

The aim of this paper is to provide a contribution to the natural logic program which explores logics in natural language. The paper offers two logics called \ \) and \ \) for dealing with inference involving simple sentences with transitive verbs and ditransitive verbs and quantified noun phrases in subject and object position. With this purpose, the relational logics are introduced and a model-theoretic proof of decidability for they are presented. In the present paper we develop algebraic semantics (...) of the logics using congruence theory. (shrink)

Traditionally the study of chemical elements has been limited to well-known concepts like the periodic properties and chemical families. However, current information shows a new and rich language that allows us to observe relations in the elements that are not limited to their positions in the table. These relations are evident when reactions are represented through networks, as in the case of similar reactivity of organic compounds sharing functional groups. For the past two decades, it has been argued that network (...) reactions may be considered the core of chemistry. This network, which constitutes the basic set of chemical knowledge, provides the basis for classification and delivers routes to obtain new and known substances. In order to provide an example, we constructed and analyzed a network of chemical elements from the formation of stoichiometric binary compounds, providing to the chemistry, a formal structure of extracting the chemical knowledge. Thus, we explored all possible presence of relationships among elements. Concepts like degree centrality and centralization, the relationships among metals, semimetal and nonmetal classes, blocks, and chemical families were analyzed. We observed that the network structure had a small core set of elements of high reactivity and also a peripheral set of elements of low reactivity. The classes, blocks and families show the following increasing order of reactivity: nonmetals > semimetals > metals; p > s > d > f; and families: boron, carbon, pnictogens, chalcogens, halogens, lanthanoids > other families. This example shows, from the network perspective, that the elements and their classifications exhibit properties such as the reactivity, order, and similarity. (shrink)

We investigate the partial orderings of the form 〈P(X),⊂〉\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle \mathbb{P}(\mathbb{X}), \subset \rangle}$$\end{document}, where X=〈X,ρ〉\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X} =\langle X, \rho \rangle }$$\end{document} is a countable binary relational structure and P(X)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{P} (\mathbb{X})}$$\end{document} the set of the domains of its isomorphic substructures and show that if the components of X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} (...) \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} are maximally embeddable and satisfy an additional condition related to connectivity, then the poset 〈P(X),⊂〉\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle \mathbb{P} (\mathbb{X}), \subset \rangle }$$\end{document} is forcing equivalent to a finite power of (P(ω)/ Fin)+, or to the poset (P(ω × ω)/(fin × Fin))+, or to the product (P(Δ)/EDfin)+×((P(ω)/Fin)+)n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${(P(\Delta )/\fancyscript{e}\fancyscript{d}_{\rm fin})^+ \times ((P(\omega )/{\rm Fin})^+)^n}$$\end{document}, for some n∈ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${n \in \omega}$$\end{document}. In particular we obtain forcing equivalents of the posets of copies of countable equivalence relations, disconnected ultrahomogeneous graphs and some partial orderings. (shrink)

Logics of binary relations corresponding, among others, to the class RRA of representable relation algebras and the class FRA of full relation algebras are presented together with the proof systems in the style of dual tableaux. Next, the logics are extended with relational constants interpreted as point relations. Applications of these logics to reasoning in non-classical logics are recalled. An example is given of a dual tableau proof of an equation which is RRA-valid, while not RA-valid.

We build a collection of topological Ramsey spaces of trees giving rise to universal inverse limit structures, extending Zheng’s work for the profinite graph to the setting of Fraïssé classes of finite ordered binary relational structures with the Ramsey property. This work is based on the Halpern-Läuchli theorem, but different from the Milliken space of strong subtrees. Based on these topological Ramsey spaces and the work of Huber-Geschke-Kojman on inverse limits of finite ordered graphs, we prove that for (...) each such Fraïssé class, its universal inverse limit structure has finite big Ramsey degrees under finite Baire-measurable colorings. For such Fraïssé classes satisfying free amalgamation as well as finite ordered tournaments and finite partial orders with a linear extension, we characterize the exact big Ramsey degrees. (shrink)

This study addresses the problem of Arrovian preference aggregation. Social rationality plays a crucial role in the standard Arrovian framework. However, no assumptions on social rationality are imposed here. Social preferences are allowed to be any binary relation (possibly incomplete and intransitive). We introduce the axiom of hybrid invariance, which requires that if social preferences under two preference profiles make the same judgment, then a social preference under a “hybrid” of the two profiles must extend the original judgment in (...) a certain way. Then, we characterize the structure of decisive coalitions under hybrid invariance. (shrink)

We study the structure of algebraic -closed subsets of an algebraic lattice L, where is some Browerian binary relation on L, in the special case when the lattice of such subsets is an atomistic lattice. This gives an approach to investigate the atomistic lattices of congruence-Noetherian quasivarieties.

We study the structure of algebraic τ-closed subsets of an algebraic lattice L, where τ is some Browerian binary relation on L, in the special case when the lattice of such subsets is an atomistic lattice. This gives an approach to investigate the atomistic lattices of congruence-Noetherian quasivarieties.

Physicalism about colour is the thesis that colours are identical with response-independent, physical properties of objects. I endorse the Argument from Structure against Physicalism about colour. The argument states that Physicalism cannot accommodate certain obvious facts about colour structure: for instance, that red is a unitary colour while purple is a binary colour, and that blue resembles purple more than green. I provide a detailed formulation of the argument. According to the most popular response to the argument, (...) the Physicalist can accommodate colour structure by explaining it in terms of colour experience. I argue that this response fails. Along the way, I examine other interesting issues in the philosophy of colour and colour perception, for instance the relational structure of colour experience and the description theory of how colour names refer. (shrink)

Fix an integer $r \ge 3$. We consider metric spaces on n points such that the distance between any two points lies in $\left\{ {1, \ldots,r} \right\}$. Our main result describes their approximate structure for large n. As a consequence, we show that the number of these metric spaces is $\left\lceil {{{r + 1} \over 2}} \right\rceil ^{\left + o\left}.$Related results in the continuous setting have recently been proved by Kozma, Meyerovitch, Peled, and Samotij [34]. When r is even, (...) our structural characterization is more precise and implies that almost all such metric spaces have all distances at least $r/2$. As an easy consequence, when r is even, we improve the error term above from $o\left$ to $o\left$, and also show a labeled first-order 0-1 law in the language ${\cal L}_r $, consisting of r binary relations, one for each element of $[r]$. In particular, we show the almost sure theory T is the theory of the Fraïssé limit of the class of all finite simple complete edge-colored graphs with edge colors in $\left\{ {r/2, \ldots,r} \right\}$.Our work can be viewed as an extension of a long line of research in extremal combinatorics to the colored setting, as well as an addition to the collection of known structures that admit logical 0-1 laws. (shrink)

-/- This unique book develops an operational approach to preference and rationality as the author employs operators over binary relations to capture the concept of rationality. -/- A preference is a basis of individual behavior and social judgment and is mathematically regarded as a binary relation on the set of alternatives. Traditionally, an individual/social preference is assumed to satisfy completeness and transitivity. However, each of the two conditions is often considered to be too demanding; and then, weaker rationality (...) conditions are introduced by researchers. This book argues that the preference rationality conditions can be captured mathematically by “operators,” which are mappings from the set of operators to itself. This operational approach nests traditional concepts in individual/social decision theory and clarifies the underlying formal structure of preference rationality. -/- The author also applies his approach to welfare economics. The core problem of ‘new welfare economics,’ developed by Kaldor, Hicks, and Samuelson, is the rationality of social preference. In this book the author translates the social criteria proposed by those three economists into operational forms, which provide new insights into welfare economics extending beyond ‘new welfare economics.’ . (shrink)

In this paper, we explore the relation between an agent’s doxastic attitude and her arguments in support of a given claim. Our main contribution is the design of a logical setting that allows us reason about binary arguments which are either in favour or against a certain claim. This is a setting in which arguments and propositions are the basic building blocks so that the concept of argument-based belief emerges in a straightforward way. We work against the background of (...) Dung’s abstract argumentation framework, extending it to a new setting in which we can study the formal properties of binary arguments as well as the larger structures they establish. This paper introduces a formal ‘two-dimensional’ language to talk about propositions and arguments, for which a sound and complete axiom system is provided. (shrink)

We consider the expressive power of second - order generalized quantifiers on finite structures, especially with respect to the types of the quantifiers. We show that on finite structures with at most binary relations, there are very powerful second - order generalized quantifiers, even of the simplest possible type. More precisely, if a logic is countable and satisfies some weak closure conditions, then there is a generalized second - order quantifier which is monadic, unary and simple, and a uniformly (...) obtained sublogic of which is equivalent to. We show some other results of the above kind, relating other classes of quantifiers to other classes of structures. For example, if the quantifiers are of the simplest non-monadic type, then the result extends to finite structures of any arity. We further show that there are second - order generalized quantifiers which do not increase expressive power of first- order logic but do increase the power significantly when added to stronger logics. (shrink)

We consider the structure $IT_S$ of all labeled trees, called also infinite terms, in the first order language ${\cal L}$ with function symbols in a recursive signature $S$ of cardinality at least two and at least a symbol of arity two, with equality and a binary relation symbol $\sqsubseteq$ which is interpreted to be the subtree relation. The existential theory over ${\cal L}$ of this structure is decidable, but more complex fragments of the theory are undecidable. We (...) prove that the $ \exists\Delta$ theory of the structure is in $\Sigma^1_1$, where $ \exists\Delta$ formulas are those in prenex form consisting of a string of unbounded existential quantifiers followed by a string of arbitrary quantifiers all bounded with respect to $\sqsubseteq$. Since the fragment of the theory was already known to be $\Sigma^1_1$-hard, it is now established to be $\Sigma^1_1$-complete. (shrink)

Any dynamic decision model should be based on conditional objects and must refer to (not necessarily structured) domains containing only the elements and the information of interest. We characterize binary relations, defined on an arbitrary set of conditional events, which are representable by a coherent generalized decomposable conditional measure and we study, in particular, the case of binary relations representable by a coherent conditional probability.

Goguen categories extend the relational calculus and its categorical formalization to the fuzzy world. Starting from the fundamental concepts of sets, binary relations and lattices, this book introduces several categorical formulations of an abstract theory of relations such as allegories, Dedekind categories and related structures. It is shown that neither theory is sufficiently rich to describe basic operations on fuzzy relations.

We consider the structure of all labeled trees, called also infinite terms, in the first order language with function symbols in a recursive signature of cardinality at least two and at least a symbol of arity two, with equality and a binary relation symbol which is interpreted to be the subtree relation. The existential theory over of this structure is decidable (see Tulipani [9]), but more complex fragments of the theory are undecidable. We prove that the theory (...) of the structure is in , where formulas are those in prenex form consisting of a string of unbounded existential quantifiers followed by a string of arbitrary quantifiers all bounded with respect to . Since the fragment of the theory was already known to be -hard (see Marongiu and Tulipani [5]), it is now established to be -complete. (shrink)

This paper deals with the problematic aspect of the reconstruction of binary relations: it includes all the questions raising the possibility or impossibility to determine a structure by gathering given substructures. It is the continuation of three studies: the first made by G. Lopez [9] in 1972 about the determination of a binary relation through the types of isomorphism of its restrictions, the second made by K. B. Reid and C. Thomassen [15] in 1976 about the strongly (...) self-complementary tournaments , the third made by C. Thomassen [16] in 1989 about the cycle space of a tournament. In the second section, we use the notion of class of difference to extend a study made in [16] to binary relations. Then, in the third section, we improve the result of this last study in the case of the tournaments. After noticing that the result of [15] inferred itself naturally from the approach developed in [9], we extend, in the fourth section, the study made in [15] to binary relations. (shrink)

This thesis proposes and presents two new models for belief representation and belief revision. The first model is the B-structures model which relies on a notion of partial language splitting and tolerates some amount of inconsistency while retaining classical logic. The model preserves an agent's ability to answer queries in a coherent way using Belnap's four-valued logic. Axioms analogous to the AGM axioms hold for this new model. The distinction between implicit and explicit beliefs is represented and psychologically plausible, computationally (...) tractable procedures for query answering and belief base revision are obtained. ;The second model presents a method for relevance sensitive non-monotonic inference from belief sequences which incorporates insights pertaining to prioritized inference and relevance sensitive, inconsistency tolerant belief revision. Our model uses a finite, logically open sequence of propositional formulas as a representation for beliefs and defines a notion of inference from maxiconsistent subsets of formulas guided by two orderings: a temporal sequencing and an ordering based on relevance relations between the conclusion and formulas in the sequence. The relevance relations are ternary as opposed to standard binary axiomatizations. The inference operation thus defined easily handles iterated revision by maintaining a revision history, blocks the derivation of inconsistent answers from a possibly inconsistent sequence and maintains the distinction between explicit and implicit beliefs. In doing so, it provides a finitely representable formalism and a plausible model of reasoning for automated agents. (shrink)

roots In the Lexicon of Malagasy we include an entry whose string part is vidy ('buy'). Its category is 'RT [AG, TH) ', indicating that it is a root and is associated with a two element set of theta roles, AGFNT and THEME. Semantically this entry is interpreted as a binary relation (= a two participant event), noted VIDY'.

Real causal systems are complicated. Despite this, causal learning research has traditionally emphasized how causal relations can be induced on the basis of idealized events, i.e. those that have been mapped to binary variables and abstracted from time. For example, participants may be asked to assess the efficacy of a headache-relief pill on the basis of multiple patients who take the pill (or not) and find their headache relieved (or not). In contrast, the current study examines learning via interactions (...) with continuous dynamic systems, systems that include continuous variables that interact over time (and that can be continuously observed in real time by the learner). To explore such systems, we develop a new framework that represents a causal system as a network of stationary Gauss--Markov (``\OU'') processes and show how such \textit{OU networks} can express complex dynamic phenomena such as feedback loops and oscillations. To assess adult's abilities to learn such systems, we conducted an experiment in which participants were asked to identify the causal relationships of a number of OU networks, potentially carrying out multiple, temporally-extended interventions. We compared their judgments to a normative model for learning OU networks as well as a range of alternative and heuristic learning models from the literature. We found that, although participants exhibited substantial learning of such systems, they committed certain systematic errors. These successes and failures were best accounted for by a model that describes people as focusing on pairs of variables, rather than evaluating the evidence with respect to the full space of possible structural models. We argue that our approach provides both a principled framework for exploring the space of dynamic learning environments as well as new algorithmic insights into how people interact successfully with a continuous causal world. (shrink)

We establish that the isomorphism problem for the classes of computable nilpotent rings, distributive lattices, nilpotent groups, and nilpotent semigroups is \-complete, which is as complicated as possible. The method we use is based on uniform effective interpretations of computable binary relations into computable structures from the corresponding algebraic classes.

We describe punctual categoricity in several natural classes, including binary relational structures and mono-unary functional structures. We prove that every punctually categorical structure in a finite unary language is${\text {PA}}(0')$-categorical, and we show that this upper bound is tight. We also construct an example of a punctually categorical structure whose degree of categoricity is$0''$. We also prove that, with a bit of work, the latter result can be pushed beyond$\Delta ^1_1$, thus showing that punctually categorical structures (...) can possess arbitrarily complex automorphism orbits.As a consequence, it follows that binary relational structures and unary structures are not universal with respect to primitive recursive interpretations; equivalently, in these classes every rich enough interpretation technique must necessarily involve unbounded existential quantification or infinite disjunction. In contrast, it is well-known that both classes are universal for Turing computability. (shrink)

We explore a non-classical, universal set theory, based on a purely 'structural' conception of sets. A set is a transfinite process of unfolding of an arbitrary binary structure, with identity of sets given by the observational equivalence between such processes. We formalize these notions using infinitary modal logic, which provides partial descriptions for set structures up to observational equivalence. We describe the comprehension and topological properties of the resulting set-theory, and we use it to give non-classical solutions to (...) classical paradoxes, to prove fixed-point theorems that relate recursion and corecursion, to formalize 'super-large', reflexive categories and 'super-large' circular modes, and to provide 'natural' solutions for domain equations. (shrink)

We study the partial orderings of the form ⟨P,⊂⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle \mathbb{P}, \subset\rangle}$$\end{document}, where X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} is a binary relational structure with the connectivity components isomorphic to a strongly connected structure Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Y}}$$\end{document} and P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{P} }$$\end{document} is the set of substructures of X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} (...) \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {X}}$$\end{document} isomorphic to X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document}. We show that, for example, for a countable X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document}, the poset ⟨P,⊂⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\langle \mathbb {P}, \subset\rangle}$$\end{document} is either isomorphic to a finite power of P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{P} }$$\end{document} or forcing equivalent to a separative atomless σ-closed poset and, consistently, to P/fin. In particular, this holds for each ultrahomogeneous structure X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} such that X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}}$$\end{document} or Xc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{X}^{c}}$$\end{document} is a disconnected structure and in this case Y\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Y}}$$\end{document} can be replaced by an ultrahomogeneous connected digraph. (shrink)

In this paper we investigate several extensions of the first order-language with finitely many binary relations. The most interesting of the studied extensions appears to be the monadic second-order one. We show that the extended languages have the same expressive power as the first-order language over the class of all relational structures of equivalence relations in local agreement by providing appropriate translation of formulae. The decidability of the considered extensions over the above mentioned class of structures is also (...) shown. (shrink)

In this paper, I argue that Marx's central concern, consistent throughout his works, is to challenge and overcome hierarchical oppositions, which he considers as the core of modern, capitalist societies and the cause of alienation. The young Marx critiques the hierarchical idealism/materialism opposition. In this opposition, idealism abstracts from and reduces all material elements to the mind (or spirit), and materialism abstracts from and reduces all mental abstractions to the body (or matter). The mature Marx sophisticates this critique with his (...) theory of the commodity fetish. The commodity fetish abstracts the exchange-value (the mind) from the commodity's use-value (the body). Although Marx aims to challenge capitalism by abolishing the hierarchical relation among binary oppositions, I show that in his early and later writings on the working-class woman, he reinforces hierarchical binaries, pointing at the gendered unconscious structure of capitalism. (shrink)

This article explores the influence of textual structures on the acquisition of knowledge in popularization discourses related to biopesticides. Following a terminological insight into the linguistic and cognitive complexities of the notion, we proceed to a semantic analysis of press articles in major Anglo-Saxon newspapers, focusing on the explanation strategies used by the media to simplify their presentation. We show that in the mediation process, biopesticides are systematically described as being environmentally friendly, and opposed to chemical pesticides, consistently shown to (...) be detrimental to the environment. We hypothesize that this simplistic binary framing is exploited by journalists as it is easy to understand in a context of agroecological transition and commonly shared distrust for chemical pesticides. In that respect, it proves to be adequate for purposes of explanation and simplification. However, by outlining this discursive process based on duality, we aim to draw attention to the potential misconceptions of plant protection issues in general, and biopesticides in particular. We ultimately demonstrate that when adopting other perspectives, this dual framing proves to be inadequate for the construction of knowledge by any non-expert press reader. (shrink)

We consider successor-invariant first-order logic (FO + succ)inv, consisting of sentences Φ involving an “auxiliary” binary relation S such that (.

In this paper it is analyzed from the informational perspective the relation between mind and body, an ancient philosophic issue defined as a problem, which still did not receive up to date an adequate solution. By introducing/using the concept of information, it is shown that this concept includes two facets, one of them referring to the common communications and another one referring to a hidden/structuring matter-related information, effectively acting in the human body and in the living systems, which determines the (...) dynamic inter-change of information between specific structures of the organism by electric/electronic/chemical agents and genetic/epigenetic processes. It is shown that the maintenance of body, permanently and obligatory depending on the external matter (foods, air, water) resources, needed to provide both the structuring/restructuring basic material and energy, determines the necessary existence of an info-managing system, administrating the internal mechano-chemical/physical processes. As a natural consequence, such a system should organize and assure own survival by an effective informational operability to detect the external food resources, to select the appropriate interest information and to decide as a function of circumstances. One important component in such an informational system is memory, allowing to dispose of the reference informational data for analysis/comparison and the selection between good and bad binary possible decisions. The memory receives and stores therefore signals from external reality and from the body itself, referring to the emotional reaction, digestion status, creation, and inherited predilections, within specific info-neural communication circuits between the brain and body execution/sensitive organs, the human body appearing as an integrated info-matter self-managed dynamic system. The specific body components memorize information with different degrees of info-integration: short/long-term integration, emotive/action reaction, info-abilities, culminating with the integration in the chromosomal structures by epigenetic processes. The new acquired information is transgenerationally transmissible, and is manifested as new traits, showing the adaptation capability of the human and close relation between mind and body. Analyzing the results of such a mind-body informational model in comparison with the earlier assumed/proposed/asserted archaic, Greek and Occidental philosophies, which represent only partial aspects of this relation, it is shown that this informational model, elaborated in terms of information on the basis of scientific reasons and arguments, constitutes a general, realist, and coherent model of the mind-body relation, able to integrate and/or explain most of the others. (shrink)

We prove that each ∀1 free amalgamation class K over a finite relational language L admits a countable generic structure M isometrically embedding all countable structuresin K relative to a fixed metric. We expand L by infinitely many binary predicates expressingdistance, and prove that the resulting expansion of K has a model companion axiomatizedby the first-order theory of M. The model companion is non-finitely axiomatizable, evenover a strong form of the axiom scheme of infinity.

Colours appear to instantiate a number of structural properties: for instance, they stand in distinctive relations of similarity and difference, and admit of a fundamental distinction into unique and binary. Accounting for these structural properties is often taken to present a serious problem for physicalist theories of colour. This paper argues that a prominent attempt by Byrne and Hilbert to account for the structural properties of the colours, consistent with the claim that colours are types of surface spectral reflectance, (...) is unsuccessful. Instead, it is suggested that a better account of the structural properties of the colours is provided by a form of non-reductive physicalism about colour: a naïve realist theory of colour, according to which colours are superficial mind-independent properties. (shrink)

This thesis provides a comparative analysis of the different ways Hegel and Sartre understand that consciousness can be alienated. Because understanding the various ways Hegel and Sartre hold that consciousness can be alienated is not possible without first understanding what each thinker understands by consciousness, I first identify and outline the different ways Hegel and Sartre conceptualise consciousness’s ontological structure before identifying the various ways each thinker understands that consciousness can be alienated. The general argument developed shows that while (...) Hegel and Sartre agree that alienation is a constitutive aspect of consciousness’s existence and are, therefore, allies in the battle against it, Sartre’s analysis of consciousness’s ontological structure is unable to provide the same depth of analysis as Hegel’s. Put differently, I believe it is Hegel’s analysis of consciousness’s ontological structure that provides an analysis of alienation that is more nuanced, subtle, complex, and multi-dimensional than the account Sartre’s provides. To support my argument, I first explore Sartre’s understanding of consciousness’s ontological structure. This discloses that, because Sartre defines consciousness as ontologically nothing, he holds that consciousness is defined in strict ontological opposition to objectivity. Consciousness’s ontological nothingness leads Sartre to hold that consciousness is free to choose its mode of being. This leads me to identify what Sartre holds to be constitutive of authentic and inauthentic modes of being. But while Sartre distinguishes between the ontological structure of consciousness and its experiences, I argue that Hegel: 1) does not introduce a distinction between consciousness’s ontological structure and its mode of being, but holds that consciousness’s self-understanding and ontological structure develop through its experiences; and 2) holds that consciousness is not ontologically opposed to objectivity, but is a spiritual synthesis of subjectivity and objectivity. I show that because Hegel holds that consciousness’s intentional object is an aspect of its ontological structure, rather than something simply opposed to itself, and because he recognises that consciousness must learn what it is ontologically by experiencing numerous different relations with its object, he is able to show that while the subject/object binary opposition of Sartre’s analysis of consciousness’s ontological structure describes one potential ontological relation consciousness can have to its object, it is not the only one. Indeed, Hegel’s analysis of consciousness’s ontological structure insists that consciousness will only truly understand its ontological structure if it learns to not think of itself in terms of the subject/object dichotomy and, instead, realises that it is a spiritual synthesis of subjectivity and objectivity. To show how this fundamental difference manifests itself throughout their thought, I identify and compare what each thinker’s understanding of consciousness’s ontological structure means in terms of consciousness’s relation to the world, alienation, authenticity, ethics, self-transformation, and social relations. (shrink)

I claim that the revisions John Rawls made to his theory of justice—as seen in his political conception of justice as fairness in the revised edition of Political Liberalism and Justice as Fairness: A Restatement—result in him being able to secure justice for all persons even in their private lives. Thus, I defend his theory against common communitarian and feminist criticisms, viz the lack of moral community and inability to secure justice for individuals in the private domain. I demonstrate that (...) justice is secured from the categorical requirement that all associational life and moral doctrines must adhere to the constraints of justice, by (what Rawls terms) the indirect application of the first principle of justice. The implications of and necessity for this indirect application are precisely what I interrogate in this thesis. I suggest that this indirect application requires unconditional acknowledgement and internalisation of the values of liberty and equality (political values of the first principle) into all aspects of civil society. I claim that Rawls realised this necessity for the congruence between the moral powers of persons, the spheres of society, and the right and the good and, as such, developed a complementary relation between these three features. Coherence between these three aspects is essential; without coherence, citizens would have a split moral personality, the public and the non-public spheres would be in conflict, and the political values and the moral doctrines of individuals would undermine one another. The significance of this strict coherence is that it can ensure the adequate development of individuals’ capacity for citizenship during the three stages of moral development. This results in citizens being able to form bonds of civic friendship necessary for justice as reciprocity to be realised. Thus, in this thesis, I position my argument against theorists such as Nancy Rosenblum, who argue for a more relaxed congruence between political institutions and civil society, as according to her illiberal forms of associational life can help form the necessary bonds of love and care needed for mutual cooperation in a liberal society. In opposition to this, I claim that strict congruence is necessary; without it, a stable liberal society is not possible as the citizens would not be able to able to respect one another on free, equal, and mutually beneficial terms. I rely on Hochschild’s sociological evidence to demonstrate that civic friendship has not been developed, due to a lack of reciprocity, impacting the negative development of one’s sense of justice. I then illustrate how this lack of reciprocity is amplified by digital and artificial intelligence (AI) technologies. The significance of this thesis is that I claim, firstly, Rawls’s last revisions and works before his death demonstrate that justice is a collective non-comprehensive good that results by constraining individuals’ associational life and their partial comprehensive doctrines to Rawlsian demands of justice. Thus, Rawls takes seriously the feminist and communitarian critiques he received. Secondly, I claim that this interpretation of Rawls’s theory of justice cannot be conceptualised in terms of a binary presentation of the priority of the right versus the good debate and, instead, I argue for a reconceptualisation of the priority of the right versus the good as ranges on a continuum of structural relations between the right and the good. (shrink)

This paper concerns the semantic difference between strong and weak neces-sity modals. First we identify a number of explananda: their well-known in-tuitive difference in strength between ‘must’ and ‘ought’ as well as differ-ences in connections to probabilistic considerations and acts of requiring and recommending. Here we argue that important extant analyses of the se-mantic differences, though tailored to account for some of these aspects, fail to account for all. We proceed to suggest that the difference between ’ought’ and ’must’ lies (...) in how they relate to scalar and binary standards. Briefly put, must(φ) says that among the relevant alternatives, φ is selected by the relevant binary standard, whereas ought(φ) says that among the relevant al-ternatives, φ is selected by the relevant scale. Given independently plausi-ble assumptions about how standards are provided by context, this ex-plains the relevant differences discussed. (shrink)

Colours appear to instantiate a number of structural properties: for instance, they stand in distinctive relations of similarity and difference, and admit of a fundamental distinction into unique and binary. Accounting for these structural properties is often taken to present a serious problem for physicalist theories of colour. This paper argues that a prominent attempt by Byrne and Hilbert to account for the structural properties of the colours, consistent with the claim that colours are types of surface spectral reflectance, (...) is unsuccessful. Instead, it is suggested that a better account of the structural properties of the colours is provided by a form of non-reductive physicalism about colour: a naïve realist theory of colour, according to which colours are superficial mind-independent properties. (shrink)

We study effectively inseparable prelattices $\wedge, \vee$ are binary computable operations; ${ \le _L}$ is a computably enumerable preordering relation, with $0{ \le _L}x{ \le _L}1$ for every x; the equivalence relation ${ \equiv _L}$ originated by ${ \le _L}$ is a congruence on L such that the corresponding quotient structure is a nontrivial bounded lattice; the ${ \equiv _L}$ -equivalence classes of 0 and 1 form an effectively inseparable pair of sets). Solving a problem in we show, (...) that if L is an e.i. prelattice then ${ \le _L}$ is universal with respect to all c.e. preordering relations, i.e., for every c.e. preordering relation R there exists a computable function f reducing R to ${ \le _L}$, i.e., $xRy$ if and only if $f\left{ \le _L}f\left$, for all $x,y$. In fact ${ \le _L}$ is locally universal, i.e., for every pair $a{ < _L}b$ and every c.e. preordering relation R one can find a reducing function f from R to ${ \le _L}$ such that the range of f is contained in the interval $\left\{ {x:a{ \le _L}x{ \le _L}b} \right\}$. Also ${ \le _L}$ is uniformly dense, i.e., there exists a computable function f such that for every $a,b$ if $a{ < _L}b$ then $a{ < _L}f\left{ < _L}b$, and if $a{ \equiv _L}a\prime$ and $b{ \equiv _L}b\prime$ then $f\left{ \equiv _L}f\left$. Some consequences and applications of these results are discussed: in particular for $n \ge 1$ the c.e. preordering relation on ${{\rm{\Sigma }}_n}$ sentences yielded by the relation of provable implication of any c.e. consistent extension of Robinson’s system R or Q is locally universal and uniformly dense; and the c.e. preordering relation yielded by provable implication of any c.e. consistent extension of Heyting Arithmetic is locally universal and uniformly dense. (shrink)

An efficient method of value assessment of a set of exchangeable alternatives A = a1,a2, ? ,an is presented. It particularly applies to situations where certain preferences may be easily evaluated or are already known, while other binary comparisons may not at once be available. Further applications are to ranking partial tournaments and the emergence and the characterisation of organisational hierarchy. By sequentially performing transitively efficient assessments of uncompared pairs, an initial weakly acyclical preference structure in A is (...) transformed into an ordering of A in echelons. We call these nicely surveyable preference structures echelon orders. Theoretical properties of echelon orders are investigated, including a characterisation and a numerical representation. (shrink)

It is argued that the `problem of time' in quantum gravity necessitates a refinement of the local inertial structure of the world, demanding a replacement of the usual Minkowski line element by a 4+2n dimensional pseudo-Euclidean line element, with the extra 2n being the number of internal phase space dimensions of the observed system. In the refined structure, the inverse of the Planck time takes over the role of observer-independent conversion factor usually played by the speed of light, (...) which now emerges as an invariant but derivative quantity. In the relativistic theory based on the refined structure, energies and momenta turn out to be invariantly bounded from above, and lengths and durations similarly bounded from below, by their respective Planck scale values. Along the external timelike world-lines, the theory naturally captures the `flow of time' as a genuinely structural attribute of the world. The theory also predicts expected deviations---suppressed quadratically by the Planck energy---from the dispersion relations for free fields in the vacuum. The deviations from the special relativistic Doppler shifts predicted by the theory are also suppressed quadratically by the Planck energy. Nonetheless, in order to estimate the precision required to distinguish the theory from special relativity, an experiment with a binary pulsar emitting TeV range gamma-rays is considered in the context of the predicted deviations from the second-order shifts. (shrink)

It is widely held that under ordinal utility, utility differences are ill-defined. Allegedly, for these to be well-defined (without turning to choice under risk or the like), one should adopt as a new kind of primitive quaternary relations, instead of the traditional binary relations underlying ordinal utility functions. Correlatively, it is also widely held that the key structural properties of quaternary relations are entirely arbitrary from an ordinal point of view. These properties would be, in a nutshell, the hallmark (...) of cardinal utility. While much is obviously true in these two tenets, this note explains why, as stated, they should be abandoned. Any ordinal utility function induces a rich quaternary relation. There is such a thing as ordinal utility differences. Furthermore, this induced quaternary relation respects, apart from completeness, the most standard structural properties of quaternary relations. These properties are, from an ordinal point of view, anything but arbitrary; from a quaternary perspective only completeness should be considered the hallmark—if any—of cardinal utility. These facts are explained to be especially relevant to the critical appreciation of the ordinalist methodology. (shrink)

If mysticism, as Coventry Patmore defines it, is 'the science of ultimates,' in what way would mysticism explain the possibility of a profound relationship between ultimate reality as infinite and proximate reality as finite ? This paper attempts to address that question through the lens of Evelyn Underhill’s philosophy of mysticism. The paper fundamentally works at framing two of Hegel’s triadic patterns of dialectic against the being-becoming binary as engaged by Underhill. This application helps unveil the relation of transcendence (...) with immanence, a relation that is crucial for a structuring of the infinite-finite mystical intimacy. (shrink)

How should a machine intelligence perform unsupervised structure discovery over streams of sensory input? One approach to this problem is to cast it as an apperception task [1]. Here, the task is to construct an explicit interpretable theory that both explains the sensory sequence and also satisfies a set of unity conditions, designed to ensure that the constituents of the theory are connected in a relational structure. However, the original formulation of the apperception task had one fundamental (...) limitation: it assumed the raw sensory input had already been parsed using a set of discrete categories, so that all the system had to do was receive this already-digested symbolic input, and make sense of it. But what if we don't have access to pre-parsed input? What if our sensory sequence is raw unprocessed information? The central contribution of this paper is a neuro-symbolic framework for distilling interpretable theories out of streams of raw, unprocessed sensory experience. First, we extend the definition of the apperception task to include ambiguous (but still symbolic) input: sequences of sets of disjunctions. Next, we use a neural network to map raw sensory input to disjunctive input. Our binary neural network is encoded as a logic program, so the weights of the network and the rules of the theory can be solved jointly as a single SAT problem. This way, we are able to jointly learn how to perceive (mapping raw sensory information to concepts) and apperceive (combining concepts into declarative rules). (shrink)