We investigate the join semilattice of modal operators on a Boolean algebra B. Furthermore, we consider pairs ⟨f,g⟩\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\langle f,g \rangle $$\end{document} of modal operators whose supremum is the unary discriminator on B, and study the associated bi-modal algebras.

This paper deals with axiomatization problems for varieties of residuated meet semilattice-ordered monoids. An internal characterization of the finitely subdirectly irreducible RSs is proved, and it is used to investigate the varieties of RSs within which the finitely based subvarieties are closed under finite joins. It is shown that a variety has this closure property if its finitely subdirectly irreducible members form an elementary class. A syntactic characterization of this hypothesis is proved, and examples are discussed.

Contact algebra is one of the main tools in region-based theory of space. In it is generalized by dropping the operation Boolean complement. Furthermore we can generalize contact algebra by dropping also the operation meet. Thus we obtain structures, called contact join-semilattices and structures, called distributive contact join-semilattices. We obtain a set-theoretical representation theorem for CJS and a relational representation theorem for DCJS. As corollaries we get also topological representation theorems. We prove that the universal theory (...) of CJS and of DCJS is the same and is decidable. (shrink)

Purpose This study aims to examine the long-term effects of an Israeli digital literacy government program for disadvantaged populations, as they are perceived by participants of the program one year after completing the course. Design/methodology/approach Participants in the program were interviewed about the effects of participating in the program, their experiences and satisfaction, in retrospect, a year after they completed the program. Findings The main reasons for joining the program included cognitive motivations, mainly interest to become familiar with internet applications, (...) followed by employment aspiration. Positive benefits from participation included accumulated knowledge, confidence in using technology, empowerment and enhanced sense of self-efficacy. Interviewees also reported that as they could not practice or communicate with instructors once they completed the program, a significant portion of the accumulated gains faded. Social implications Social and practical implications: Digital technologies constitute key infrastructure to facilitate public participation, as well as for gaining social, political and economic capital. Therefore, there is a significant social value in reducing digital inequality by increasing digital literacy of disadvantaged populations, i.e. citizens with low socioeconomic status and low digital literacy. This study sheds light on the benefits gained from such programs, as perceived by past participants. Originality/value While previous studies evaluating digital literacy programs focus on specific technical improvements and short-term gains, this study investigates the long-term effects and shortcomings of the program as perceived by participants. (shrink)

In this paper I address two important objections to the theory called ‘ Composition as Identity’ : the ‘wall-bricks-and-atoms problem’, and the claim that CAI entails mereological nihilism. I aim to argue that the best version of CAI capable of addressing both problems is the theory I will call ‘Atomic Composition as Identity’ which consists in taking the plural quantifier to range only over proper pluralities of mereological atoms and every non-atomic entity to be identical to the plurality (...) of atoms it fuses. I will proceed in three main steps. First, I will defend Sider’s Composition as identity. Oxford University Press, Oxford, pp 211–221, 2014) idea of weakening the comprehension principle for pluralities and I will show that :219–235, 2016a) it can ward off both the WaBrA problem and the threat of mereological nihilism. Second, I will argue that CAI-theorists should uphold an ‘atomic comprehension principle’ which, jointly with CAI, entails that there are only proper pluralities of mereological atoms. Finally, I will present a novel reading of the ‘one of’ relation that not only avoids the problems presented by Yi Composition as identity. Oxford University Press, Oxford, pp 169–191, 2014) and Calosi :429–443, 2016b, Am Philos Q 55:281–292, 2018) but can also help ACAI-theorists to make sense of the idea that a composite entity is both one and many. (shrink)

In this paper we show that the one-generated free three dimensional polyadic and substitutional algebras Fr1PA3 and Fr1SCA3 are not atomic. What is more, their corresponding logics have the Gödel’s incompleteness property. This provides a partial solution to a longstanding open problem of Németi and Maddux going back to Alfred Tarski via the book [12].

This is the first commentary on Lucretius' theory of atomic motion, one of the most difficult and technical parts of De rerum natura. The late Don Fowler sets new standards for Lucretian studies in his awesome command both of the ancient literary, philological, and philosophical background to this Latin Epicurean poem, and of the relevant modern scholarship.

Assume T is stable, small and Φ(x) is a formula of L(T). We study the impact on $T\lceil\Phi$ of naming finitely many elements of a model of T. We consider the cases of $T\lceil\Phi$ which is ω-stable or superstable of finite rank. In these cases we prove that if T has $ countable models and Q = Φ(M) is countable and atomic or saturated, then any good type in S(Q) is τ-stable. If $T\lceil\Phi$ is ω-stable and (bounded, 1-based or (...) of finite rank) with $I(T, \aleph_0) , then we prove that every good p ∈ S(Q) is τ-stable for any countable Q. The proofs of these results lead to several new properties of small stable theories, particularly of types of finite weight in such theories. (shrink)

Introduction -- Light and life -- Biology and atomic physics -- Natural philosophy and human cultures -- Discussion with Einstein on epistemological problems in atomic physics -- Unity of knowledge -- Atoms and human knowledge -- Physical science and the problem of life.

According to a common belief concerning the Mach-Boltzmann debate on atoms, the new experiments performed in microphysics at the turn of the 19th and 20th centuries confirmed Boltzmann's atomic hypothesis and disproved Mach's anti-atomic view. This paper intends to show that this belief is partially unjustified. Mach's view on atoms consists in fact of different kinds of arguments. While the new experiments in microphysics refute indeed his scientific arguments against the atomic hypothesis, his epistemological arguments are unaffected. (...) In this regard, Mach's epistemological approach remains relevant for today's discussion on the status of the notion of atom. (shrink)

According to a common belief concerning the Mach-Boltzmann debate on atoms, the new experiments performed in microphysics at the turn of the 19th and 20th centuries confirmed Boltzmann’s atomic hypothesis and disproved Mach’s anti-atomic view. This paper intends to show that this belief is partially unjustified. Mach’s view on atoms consists in fact of different kinds of arguments. While the new experiments in microphysics refute indeed his scientific arguments against the atomic hypothesis, his epistemological arguments are unaffected. (...) In this regard, Mach’s epistemological approach remains relevant for today’s discussion on the status of the notion of atom. (shrink)

and in Sect. 5 should be reformulated as follows.

. In this paper we propose a new definition of entailment and construct a system S of predicate calculus based on this entailment. It is also shown that all well-known set theories can be based on the system S.

RésuméLe gros de la recherche orientaliste consacrée à la littérature théologique islamique a négligé les idées théologiques Ibāḍī à portée cosmologique, ce qui a conduit à une compréhension incomplète de la théologie islamique et à un manque considérable dans la recherche occidentale. L'omission de ce mouvement important de l'Islam est compréhensible étant donné que les textes Ibāḍī ne sont accessibles, publiés, diffusés et traduits que de façon très partielle. Cette étude vise donc à combler certaines de ces lacunes dans la (...) recherche sur la première théologie islamique. Les objectifs de cet article sont de: 1) caractériser la littérature Ibāḍī classique portant sur la théorie atomiste de la substance et de l'accident; 2) examiner les textes d'auteurs Ibāḍī duiiie/ixesiècle dialoguant et discutant avec d'autres écoles théologiques islamiques, à savoir les Muʿtazilites pré-Bahshamiyya (Abū Hāshim al-Jubbāʾī, d. 321/933) et les Ashʿarites (Abū al-Ḥasan al-Ashʿarī, d. 324/936), en lien avec la théorie atomiste de la substance et de l'accident; 3) passer en revue le grand nombre d'opinions soutenues parmi les premiers théologiens Ibāḍī, et examiner les sources et les thèmes spécifiques susceptibles d'avoir influencé cette école de pensée diversifiée. Cet article cherche aussi à identifier des traits communs dans l'approche Ibāḍī durant la période de formation de la théologie islamique, et à explorer les voies grâce auxquelles ces premiers théologiens ont pu avoir accès à des thèmes cosmologiques antérieurs à l'Islam. (shrink)

In a previous paper we investigated the extraction of proof-theoretic properties of natural deduction derivations from their impredicative translation into System F. Our key idea was to introduce an extended equational theory for System F codifying at a syntactic level some properties found in parametric models of polymorphic type theory. A different approach to extract proof-theoretic properties of natural deduction derivations was proposed in a recent series of papers on the basis of an embedding of intuitionistic propositional logic into a (...) predicative fragment of System F, called atomic System F. In this paper we show that this approach finds a general explanation within our equational study of second-order natural deduction, and a clear semantic justification in terms of parametricity. (shrink)

In the last decade, the notion of triad was reintroduced by Eric Scerri, who suggested it as a possible categorical criterion to represent chemical periodicity. In particular, he reformulated the notion of triad in terms of atomic number instead of atomic weights; in this way, the value of the intermediate term of the triad became the exact average of the values of the two extremes. Following the inspiration of Scerri’s work, the main purpose of this article is to (...) obtain a representation where all the relations among the chemical elements that form the groups of the periodic system can be reconstructed on the basis of triads, without using electronic configurations. (shrink)

The first known statements of the deduction theorems for the first-order predicate calculus and the classical sentential logic are due to Herbrand [8] and Tarski [14], respectively. The present paper contains an analysis of closure spaces associated with those sentential logics which admit various deduction theorems. For purely algebraic reasons it is convenient to view deduction theorems in a more general form: given a sentential logic C (identified with a structural consequence operation) in a sentential language I, a quite arbitrary (...) set P of formulas of I built up with at most two distinct sentential variables p and q is called a uniform deduction theorem scheme for C if it satisfies the following condition: for every set X of formulas of I and for any formulas and , C(X{{a}}) iff P(, ) AC(X). [P(, ) denotes the set of formulas which result by the simultaneous substitution of for p and for q in all formulas in P]. The above definition encompasses many particular formulations of theorems considered in the literature to be deduction theorems. Theorem 1.3 gives necessary and sufficient conditions for a logic to have a uniform deduction theorem scheme. Then, given a sentential logic C with a uniform deduction theorem scheme, the lattices of deductive filters on the algebras A similar to the language of C are investigated. It is shown that the join-semilattice of finitely generated (= compact) deductive filters on each algebra A is dually Brouwerian. (shrink)

The semilattice relevant logics ∪R, ∪T, ∪RW, and ∪TW are defined by semilattice models in which conjunction and disjunction are interpreted in a natural way. For each of them, there is a cut-free labelled sequent calculus with plural succedents . We prove that these systems are equivalent, with respect to provable formulas, to the restricted systems with single succedents . Moreover, using this equivalence, we give a new Hilbert-style axiomatizations for ∪R and ∪T and prove equivalence between two semantics for (...) the contractionless logics ∪RW and ∪TW. (shrink)

J. Robert Oppenheimer was one of the outstanding physicists of his generation. He was also an immensely gifted writer and speaker, who thought deeply about the way that scientific discoveries have changed the way people live and think. Displaying his subtlety of thought and expression as do few other documents, this book of his lectures discusses the moral and cultural implications of developments in modern physics.

Hilbert algebras provide the equivalent algebraic semantics in the sense of Blok and Pigozzi to the implication fragment of intuitionistic logic. They are closely related to implicative semilattices. Porta proved that every Hilbert algebra has a free implicative semilattice extension. In this paper we introduce the notion of an optimal deductive filter of a Hilbert algebra and use it to provide a different proof of the existence of the free implicative semilattice extension of a Hilbert algebra as well as (...) a simplified characterization of it. The optimal deductive filters turn out to be the traces in the Hilbert algebra of the prime filters of the distributive lattice free extension of the free implicative semilattice extension of the Hilbert algebra. To define the concept of optimal deductive filter we need to introduce the concept of a strong Frink ideal for Hilbert algebras which generalizes the concept of a Frink ideal for posets. (shrink)

John Dewey's political and educational ideas can offer some guidance in arbitrating the online literacy debate.

A propositional logic has the variable sharing property if φ → ψ is a theorem only if φ and ψ share some propositional variable. In this note, I prove that positive semilattice relevance logic and its extension with an involution negation have the variable sharing property. Typical proofs of the variable sharing property rely on ad hoc, if clever, matrices. However, in this note, I exploit the properties of rather more intuitive arithmetical structures to establish the variable sharing property for (...) the systems discussed. (shrink)

We devise exact conditions under which a join semilattice with a weak contact relation can be semilattice embedded into a Boolean algebra with an overlap contact relation, equivalently, into a distributive lattice with additive contact relation. A similar characterization is proved with respect to Boolean algebras and distributive lattices with weak contact, not necessarily additive, nor overlap.

We present here, without proofs, some results from a paper which will appear in Latvijskij Matematiˇceckij Ezegodnik.

The central thesis of this paper is that Epicurus held that swerves of the constituent atoms of agents' minds cause the agents' volitions from the bottom up. "De Rerum Natura" 2.216-93 is examined at length, and Lucretius is found to be making the following claims: both atoms and macroscopic bodies sometimes swerve as they fall, but so minimally that they are undetectable. Swerves are oblique deviations, not right-angled turns. Swerves must be posited to account both for cosmogonic collisions quite generally (...) and for every "free volition," including those of animals. All volitions are fresh starts of macroscopic motion, caused by that "something in our chests" which later philosophers would call 'the faculty of will.' Since nothing can come to be from nothing, volitions must be caused from the bottom up by swerves, fresh starts in the mind's atoms motions caused by the atoms' inherent swerviness. This is what Lucretius is saying, and what Epicurus had to say in order to defend both libertarianism and atomism. Modern scholars are wrong, then, in rejecting the interpretation of Guissani and Bailey, which was crudely stated, but substantively correct. The rival interpretations of Furley, Fowler, and Englert do not do justice to Epicurus' libertarianism, and that of Sedley does not do justice to his atomism, which entails universal bottom-up causation. Epicurus did not himself draw much attention to his positive doctrine of the swerve, preferring to emphasize the untenability of the deterministic alternative. The notoriety of the doctrine in Cicero's day is due primarily to Chrysippus, who insisted that swerves cannot occur, since they would be 'uncaused' motions, and secondarily to Carneades and Zeno of Sidon. (shrink)

Mereological atomism is the thesis that everything is ultimately composed of atomic parts, i.e., parts lacking proper parts. Standardly, this thesis is characterized by an axiom that says, more simply, that everything has atomic parts. Anthony Shiver has argued that this characterization is satisfied by models that are not atomistic, and is therefore inadequate. I argue that Shiver’s conclusion can and ought to be resisted, for the models in question are atomistic in the intended sense, and even though (...) the standard characterization does not say that everything is composed of atoms, it implies so. If there is a sense in which the relevant models are problematic, it lies elsewhere. (shrink)

After observing that the truth conditions of connectives of non–classical logics are generally defined in terms of formulas of first–order logic, we introduce ‘protologics’, a class of logics whose connectives are defined by arbitrary first–order formulas. Then, we introduce atomic and molecular logics, which are two subclasses of protologics that generalize our gaggle logics and which behave particularly well from a theoretical point of view. We also study and introduce a notion of equi-expressivity between two logics based on different (...) classes of models. We prove that, according to that notion, every pure predicate logic with \ variables and constants is as expressive as a predicate atomic logic, some sort of atomic logic. Then, we prove that the class of protologics is equally expressive as the class of molecular logics. That formally supports our claim that atomic and molecular logics are somehow ‘universal’. Finally, we identify a subclass of molecular logics that we call predicate molecular logics and which constitutes its representative core: every molecular logic is as expressive as a predicate molecular logic. (shrink)

An atom is confined to a box in its ground state. An attempt is made to observe it in the left half of the box by scattering photons out of a photon wave packet passing through this half of the box. If no photons are scattered, the atom is missing. It is located on the right side of the box and its wave function is changed. The expectation value of the combined atom and photon energy is increased. For the other (...) alternative, that the atom is found on the left side, the expectation value is decreased. By including both alternatives, it is shown that the mean energy is conserved. (shrink)

In this stimulating investigation, Gideon Freudenthal has linked social history with the history of science by formulating an interesting proposal: that the supposed influence of social theory may be seen as actual through its co herence with the process of formation of physical concepts. The reinterpre tation of the development of science in the seventeenth century, now widely influential, receives at Freudenthal's hand its most persuasive statement, most significantly because of his attention to the theoretical form which is charac teristic. (...) of classical Newtonian mechanics. He pursues the sources of the parallels that may be noted between that mechanics and the dominant philosophical systems and social theories of the time; and in a fascinating development Freudenthal shows how a quite precise method - as he descriptively labels it, the 'analytic-synthetic method' - which underlay the Newtonian form of theoretical argument, was due to certain interpretive premisses concerning particle mechanics. If he is right, these depend upon a particular stage of con ceptual achievement in the theories of both society and nature; further, that the conceptual was generalized philosophically; but, strikingly, Freudenthal shows that this concept-formation itself was linked to the specific social relations of the times of Newton and Hobbes. (shrink)

The article demonstrates that to describe the property of atomicity of transactions in database systems, we need a three-valued logic with propositional connective characterized in the same way as Blamey’s interjunction. However, the article explains that since Blamey’s partial logic with interjunction is a logic without tautologies, it does not satisfy some salient conditions of being a logic of atomic transactions. The article introduces a logic of the considered kind, and provides an example of the formal exposition of the (...) case of an atomic transaction. Finally, the article explains the philosophical significance of the introduced logic. (shrink)

We give an example of a countable theory $T$ such that for every cardinal $\lambda \geq \aleph_2$ there is a fully indiscernible set $A$ of power $\lambda$ such that the principal types are dense over $A$, yet there is no atomic model of $T$ over $A$. In particular, $T$ is a theory of size $\lambda$ where the principal types are dense, yet $T$ has no atomic model.

A possible atomic mechanism underlying the Re- and Ru-induced strengthening effects on the n - n ' interface in Ni-based single-crystal superalloys has been investigated using the DMol3 molecular orbital package based on density functional theory. The calculation of bonding properties has been performed on a cluster designed to model Re and Ru strengthening effects within the interface. The stronger Re--Ni bonds are formed mainly as a result of d- hybridization, while the Ni--Ni bonding become weaker accompanying the Re (...) substitution. The vertical and horizontal bond orders for a local environmental cluster are proposed and developed for the description of the strengthening effect on the n - n ' interface, with larger bond order values achieving better effect. Results show that both Re and Ru significantly strengthen the interface. It is also shown that the strengthening effect of Re is better than that of Ru, and this is explained in terms of the charge transfer of electrons between orbitals of Ru atom according to Mulliken population analysis. The calculation results provide a basis for understanding the atomic mechanism of Re- and Ru-induced n - n ' interfacial strengthening. (shrink)

This paper solves the special composition question for solid objects and discusses the properties of wholes in relation to the properties of their parts, including emergent properties. By considering the causal properties of solid objects, this paper argues that it is possible for objects that are undoubtedly ontological units (called atoms) to combine to form a whole that is also an ontological unit of the same standing. It begins by considering the various different kinds of property that a whole object (...) could possess and the ways in which those properties could be related to the properties of its atoms, where some of the properties of the whole could be called emergent properties. There are properties of the whole that are determinate relative to the properties of the atoms, where the atoms’ possessing certain properties, being arranged spatially in a certain way, and with certain forces connecting them determine the instantiation of a specific property of the whole. There are also properties of the whole that are merely determinate as to kind, where the properties of the atoms merely determine that some property belonging to a certain kind will be instantiated. Further distinctions are made between properties of the whole that cannot be possessed by the atoms and properties of the whole that can. These distinctions are illustrated by a few physical examples. A number of different arguments are then given to show that a whole object composed of atoms possesses monadic properties of its own that are causally significant. Next a “real boundary condition for solid objects” is proposed, where the appropriate sort of boundary is both a spatial and an energetic boundary, one having to do with energy states. The paper concludes with a simple example of a solid object that is used to show that the description of the action and motion of the whole cannot be reduced to the descriptions of the actions and motions of its atoms. (shrink)