Dynamic Predicate Logic (DPL) is a variant of Predicate Logic introduced by Groenendijk and Stokhof. One rationale behind the introduction of DPL is that it is closer to Natural Language than ordinary Predicate Logic in the way it treats scope.In this paper I develop some variants of DPL that can more easily approximate Natural Language in some further aspects. Specifically I add flexibility in the treatment of polarity and and some further flexibility in the treatment of scope.I develop a framework (...) that is intended to encourage further experimentation with alternative variants of DPL. In this framework the new meanings are, roughly,indexed sets of old meanings. The indices can be viewed as "files'' or "storage devices.''Each such file supports a separate "information stream.''The interaction of the new meanings is "programmed'' with the help of certain monoids acting on the indices. The construction of the new meanings can be viewed as an application of the Grothendieck Construction to monoids. (shrink)

A symmetric monoidal category naturally arises as the mathematical structure that organizes physical systems, processes, and composition thereof, both sequentially and in parallel. This structure admits a purely graphical calculus. This paper is concerned with the encoding of a fixed causal structure within a symmetric monoidal category: causal dependencies will correspond to topological connectedness in the graphical language. We show that correlations, either classical or quantum, force terminality of the tensor unit. We also show that well-definedness of the (...) concept of a global state forces the monoidal product to be only partially defined, which in turn results in a relativistic covariance theorem. Except for these assumptions, at no stage do we assume anything more than purely compositional symmetric-monoidal categorical structure. We cast these two structural results in terms of a mathematical entity, which we call a causal category . We provide methods of constructing causal categories, and we study the consequences of these methods for the general framework of categorical quantum mechanics. (shrink)

The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on sequential and parallel decomposability of processes in the framework of monoidal categories: We will give a precise definition, what it means for processes to be decomposable. Moreover, through examples, we argue that viewing parallel processes as coupled in this framework can be seen as (...) a category mistake or a misinterpretation. We highlight the suitability of category theory for a structuralistic interpretation of mathematical modelling and argue that for appliers of mathematics, such as engineers, there is a pragmatic advantage from this. (shrink)

Local deterministic string-to-string transductions arise in natural language processing (NLP) tasks such as letter-to-sound translation or pronunciation modeling. This class of transductions is a simple generalization of morphisms of free monoids; learning local transductions is essentially the same as inference of certain monoid morphisms. However, learning even a highly restricted class of morphisms, the so-called fine morphisms, leads to intractable problems: deciding whether a hypothesized fine morphism is consistent with observations is an NP-complete problem; and maximizing classification accuracy of (...) the even smaller class of alphabetic substitution morphisms is APX-hard. These theoretical results provide some justification for using the kinds of heuristics that are commonly used for this learning task. (shrink)

There is currently much interest in bringing together the tradition of categorial grammar, and especially the Lambek calculus, with the recent paradigm of linear logic to which it has strong ties. One active research area is designing non-commutative versions of linear logic (Abrusci, 1995; Retoré, 1993) which can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic (Dalrymple et al., 1995). Some connections between the Lambek calculus and computations in groups have long been (...) known (van Benthem, 1986) but no serious attempt has been made to base a theory of linguistic processing solely on group structure. This paper presents such a model, and demonstrates the connection between linguistic processing and the classical algebraic notions of non-commutative free group, conjugacy, and group presentations. A grammar in this model, or G-grammar is a collection of lexical expressions which are products of logical forms, phonological forms, and inverses of those. Phrasal descriptions are obtained by forming products of lexical expressions and by cancelling contiguous elements which are inverses of each other. A G-grammar provides a symmetrical specification of the relation between a logical form and a phonological string that is neutral between parsing and generation modes. We show how the G-grammar can be oriented for each of the modes by reformulating the lexical expressions as rewriting rules adapted to parsing or generation, which then have strong decidability properties (inherent reversibility). We give examples showing the value of conjugacy for handling long-distance movement and quantifier scoping both in parsing and generation. The paper argues that by moving from the free monoid over a vocabulary V (standard in formal language theory) to the free group over V, deep affinities between linguistic phenomena and classical algebra come to the surface, and that the consequences of tapping the mathematical connections thus established can be considerable. (shrink)

In the categorical approach to the foundations of quantum theory, one begins with a symmetric monoidal category, the objects of which represent physical systems, and the morphisms of which represent physical processes. Usually, this category is taken to be at least compact closed, and more often, dagger compact, enforcing a certain self-duality, whereby preparation processes (roughly, states) are interconvertible with processes of registration (roughly, measurement outcomes). This is in contrast to the more concrete “operational” approach, in which the states (...) and measurement outcomes associated with a physical system are represented in terms of what we here call a convex operational model: a certain dual pair of ordered linear spaces–generally, not isomorphic to one another. On the other hand, state spaces for which there is such an isomorphism, which we term weakly self-dual, play an important role in reconstructions of various quantum-information theoretic protocols, including teleportation and ensemble steering. In this paper, we characterize compact closure of symmetric monoidal categories of convex operational models in two ways: as a statement about the existence of teleportation protocols, and as the principle that every process allowed by that theory can be realized as an instance of a remote evaluation protocol—hence, as a form of classical probabilistic conditioning. In a large class of cases, which includes both the classical and quantum cases, the relevant compact closed categories are degenerate, in the weak sense that every object is its own dual. We characterize the dagger-compactness of such a category (with respect to the natural adjoint) in terms of the existence, for each system, of a symmetric bipartite state, the associated conditioning map of which is an isomorphism. (shrink)

Each Girard quantale (i.e., commutative quantale with a selected dualizing element) provides a support for a semantics for linear propositional formulas (but not for linear derivations). Several constructions of Girard quantales are known. We give two more constructions, one using an arbitrary partially ordered monoid and one using a partially ordered group (both commutative). In both cases the semantics can be controlled be a relation between pairs of elements of the support and formulas. This gives us a neat way of (...) handling duality. (shrink)

Monoidal triangular norm logic MTL is the logic of left-continuous triangular norms. In the paper we present a relational formalization of the logic MTL and then we introduce relational dual tableau that can be used for verification of validity of MTL-formulas. We prove soundness and completeness of the system.

We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes...

The notion of a natural numbers object in a monoidal category is defined and it is shown that the theory of primitive recursive functions can be developed. This is done by considering the category of cocommutative comonoids which is cartesian, and where the theory of natural numbers objects is well developed. A number of examples illustrate the usefulness of the concept.

The variety DMM of De Morgan monoids has just four minimal subvarieties. The join-irreducible covers of these atoms in the subvariety lattice of DMM are investigated. One of the two atoms consisting of idempotent algebras has no such cover; the other has just one. The remaining two atoms lack nontrivial idempotent members. They are generated, respectively, by 4-element De Morgan monoids C4 and D4, where C4 is the only nontrivial 0-generated algebra onto which finitely subdirectly irreducible De Morgan monoids may (...) be mapped by noninjective homomorphisms. The homomorphic preimages of C4 within DMM constitute a proper quasivariety, which is shown to have a largest subvariety U. The covers of the variety within U are revealed here. There are just ten of them. In exactly six of these ten varieties, all nontrivial members have C4 as a retract. In the varietal join of those six classes, every subquasivariety is a variety—in fact, every finite subdirectly irreducible algebra is projective. Beyond U, all covers of [or of ] within DMM are discriminator varieties. Of these, we identify infinitely many that are finitely generated, and some that are not. We also prove that there are just 68 minimal quasivarieties of De Morgan monoids. (shrink)

Dynamical systems are mathematical structures whose aim is to describe the evolution of an arbitrary deterministic system through time, which is typically modeled as (a subset of) the integers or the real numbers. We show that it is possible to generalize the standard notion of a dynamical system, so that its time dimension is only required to possess the algebraic structure of a monoid: first, we endow any dynamical system with an associated graph and, second, we prove that such a (...) graph is a category if and only if the time model of the dynamical system is a monoid. In addition, we show that the general notion of a dynamical system allows us not only to define a family of meaningful dynamical concepts, but also to distinguish among a cluster of otherwise tangled notions of reversibility, whose logical relationships are finally analyzed. (shrink)

Monoidal logics were introduced as a foundational framework to analyse the proof theory of deontic logic. Building on Lambek’s work in categorical logic, logical systems are defined as deductive systems, that is, as collections of equivalence classes of proofs satisfying specific rules and axiom schemata. This approach enables the classification of deductive systems with respect to their categorical structure. When looking at their proof theory, however, one can see that there are similarities between monoidal and substructural logics. The (...) purpose of the present paper is to address this issue and highlight the differences between these two approaches. We argue that monoidal logics provide a more flexible foundational framework that enables a finer analysis of the relationship between negation and other logical connectives. We show that the elimination of double negation is independent from the de Morgan dualities, that monoidal deductive systems are not necessarily weakly distributive and that deduc... (shrink)

This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of Eilenberg-Moore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. A part of the so-called Gelfand–Naimark–Segal (GNS) construction is identified as an isomorphism of categories, relating states on involutive monoids and inner products. This correspondence exists in arbritrary involutive symmetric monoidal (...) categories. (shrink)

It is proved that all the isomorphisms in the cartesian category freely generated by a set of objects (i.e., a graph without arrows) can be written in terms of arrows from the symmetric monoidal category freely generated by the same set of objects. This proof yields an algorithm for deciding whether an arrow in this free cartesian category is an isomorphism.

We study the monoid of primitive recursive functions and investigate a onestep construction of a kind of exact completion, which resembles that of the familiar category of modest sets, except that the partial equivalence relations which serve as objects are recursively enumerable. As usual, these constructions involve the splitting of symmetric idempotents.

ABSTRACTMonoidal logics were introduced as a foundational framework to analyze the proof theory of logical systems. Inspired by Lambek's seminal work in categorical logic, the objective is to defin...

The monoidal t-norm based logic MTL is obtained from Hájek''s Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and (...) rational completeness (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. (shrink)

We show how to reconstruct the topology on the monoid of endomorphisms of the rational numbers under the strict or reflexive order relation, and the polymorphism clone of the rational numbers under the reflexive relation. In addition we show how automatic homeomorphicity results can be lifted to polymorphism clones generated by monoids.

It is shown that given any finite system of monoid identities, it is decidable if the class of locally finite monoids that satisfy the system is a variety. This answers an open problem of Mark V. Sapir.

Let l be a commutative field; Bauval [1] showed that the theory of the ring l[X1,...,Xm] is the same as the weak second-order theory of the field l. Now, l[X1,...,Xm] is the ring of the monoid m, so it may be asked what properties of m we can deduce from the theory of l[;m], that is, if l[m] is elementarily equivalent to the ring of monoid k[G], with k, a field and G, a monoid, what do we know not only (...) about the first-order theory of G but also about more properties of G. We prove that in this case G is isomorphic to m.Bauval [1, Theorem V.2.1] proved that if a factorial ring A is elementarily equivalent to l[;X1,...,Xm], then A is isomorphic to F[X1,...,Xm], with F being the field of invertible elements of A.Our result is different from this property because, a priori, the field k is not the field of invertible elements . Furthermore, k[G]; is not always factorial or Neotherian: if G is isomorphic to the cartesian product ∏i<ω, then the number of irreducible elements that divide elements that divide X is infinite, and the ideal generated by the monomials X is not finitely generated.We recall that to be factorial of Neotherian are not elementary properties. (shrink)

The endomorphism monoid of a model-theoretic structure carries two interesting topologies: on the one hand, the topology of pointwise convergence induced externally by the action of the endomorphisms on the domain via evaluation; on the other hand, the Zariski topology induced within the monoid by (non-)solutions to equations. For all concrete endomorphism monoids of $\omega $ -categorical structures on which the Zariski topology has been analysed thus far, the two topologies were shown to coincide, in turn yielding that the pointwise (...) topology is the coarsest Hausdorff semigroup topology on those endomorphism monoids. We establish two systematic reasons for the two topologies to agree, formulated in terms of the model-complete core of the structure. Further, we give an example of an $\omega $ -categorical structure on whose endomorphism monoid the topology of pointwise convergence and the Zariski topology differ, answering a question of Elliott, Jonušas, Mitchell, Péresse, and Pinsker. (shrink)

The global dispersal of prehistoric ancient humans from Africa to North America, and the existence of artistic innovation evidenced in the Late Pleistocene are, by now, parts of a familiar and fascinating story. But the explanation of how our human career was possible cries out for clarification. In this chapter, I argue that dual process theory can provide the needed explanation. My claim will be that the advent of System-2 reasoning running offline, aided by executive cognitive control and language, and (...) facilitated by neural plasticity, made possible the remarkable human dispersal from Africa to North America by way of the Middle East and Asia. System-1 modular adaptations, together with System-2 reasoning, gave rise to the flexible, culturally-informed, mental operations that were essential to shape the psychologically modern mind. The result was, inter alia, the surprising Late Pleistocene dispersal of ancient humans to North America. (shrink)

A construction is described of a cartesian closed category A with exactly two elements out of a C-monoid such that can be recovered from A without reference to the construction.

The paper deals with involutive FLe-monoids, that is, commutative residuated, partially-ordered monoids with an involutive negation. Involutive FLe-monoids over lattices are exactly involutive FLe-algebras, the algebraic counterparts of the substructural logic IUL. A cone representation is given for conic involutive FLe-monoids, along with a new construction method, called twin-rotation. Some classes of finite involutive FLe-chains are classified by using the notion of rank of involutive FLe-chains, and a kind of duality is developed between positive and non-positive rank algebras. As a (...) side effect, it is shown that the substructural logic IUL plus t ↔ f does not have the finite model property. (shrink)

Dual-process and dual-system theories in both cognitive and social psychology have been subjected to a number of recently published criticisms. However, they have been attacked as a category, incorrectly assuming there is a generic version that applies to all. We identify and respond to 5 main lines of argument made by such critics. We agree that some of these arguments have force against some of the theories in the literature but believe them to be overstated. We argue that the dual- (...) class='Hi'>processing distinction is supported by much recent evidence in cognitive science. Our preferred theoretical approach is one in which rapid autonomous processes are assumed to yield default responses unless intervened on by distinctive higher order reasoning processes. What defines the difference is that Type 2 processing supports hypothetical thinking and load heavily on working memory. (shrink)

Every transformation monoid comes equipped with a canonical topology, the topology of pointwise convergence. For some structures, the topology of the endomorphism monoid can be reconstructed from its underlying abstract monoid. This phenomenon is called automatic homeomorphicity. In this paper we show that whenever the automorphism group of a countable saturated structure has automatic homeomorphicity and a trivial center, then the monoid of elementary self-embeddings has automatic homeomorphicity, too. As a second result we strengthen a result by Lascar by showing (...) that whenever \ is a countable \-categorical G-finite structure whose automorphism group has a trivial center and if \ is any other countable structure, then every isomorphism between the monoids of elementary self-embeddings is a homeomorphism. (shrink)

We use a new version of the Definability Theorem of Beth in order to unify classical theorems of Yuri Matiyasevich and Jan Denef in one structural statement. We give similar forms for other important definability results from Arithmetic and Number Theory.

_Process Philosophy_ surveys the basic issues and controversies surrounding the philosophical approach known as “process philosophy.” Process philosophy views temporality, activity, and change as the cardinal factors for our understanding of the real—process has priority over product, both ontologically and epistemically. Rescher examines the movement’s historical origins, reflecting a major line of thought in the work of such philosophers as Heracleitus, Leibniz, Bergson, Peirce, William James, and especially A. N. Whitehead. Reacting against the tendency to associate process philosophy too closely (...) with this last-named thinker, Rescher writes, “Indeed, one cardinal task for the partisans of process at this particular juncture of philosophical history is to prevent the idea of ‘process philosophy’ from being marginalized through a limitation of its bearing to the work and influence of any one single individual or group.” This book will appeal to both students and professors of philosophy. Those teachers who have not been trained in process philosophy will welcome this new text by one one of North America’s foremost philosophers as a perspicuous and informative introduction. (shrink)

Process theism has been in the limelight for the past few decades for its controversial and refreshing conception of God. One aspect of process theism that has received increasing attention is process theodicy. However, in regard to this problem, it must be said that none of the process philosophers had devoted more attention to it than Charles Hartshorne. This paper reviews Hartshorne's strategy for a process solution of physical evil. The conclusion is that Hartshorne's attempt to collapse the problem of (...) physical evil into the problem of moral evil via the free-will defence and pan-psychism is bogged down by a serious hitch. (shrink)

This volume constitutes the first collection of essays exploring the implications of process philosophy for social thought. Process philosophy is a product of the twentieth century, but its Platonic roots relate it to one of the prime initiators of Western philosophical thinking. Alfred North Whitehead originated the style of thinking that subsequently has been termed "process philosophy.".

_Intersubjective Processes and the Unconscious _looks at how the minds of the therapist and the patient interact with each other in a profound and unconscious way: a concept first described by Freud. This book expands Freud’s ideas further and examines how these have been greatly elaborated by contributions from the Kleinian School as well as from the work of Bion. It explores how, together, patient and therapist co-create a narrative through these unconscious intersubjective processes. Topics of discussion include: the unconscious (...) dimensions of intersubjective processes an historical overview of Freudian, Kleinian and Bionian contributions an integrated theory of the nature of unconscious intersubjective processes the central importance of dreaming in intersubjective processes the clinical implications of this intersubjective model The author offers in-depth clinical examples and case vignettes to illustrate the application of these principles when working with trauma, countertransference dreams and supervision. As such, this book will be invaluable to all psychoanalysts and psychotherapists interested in the topic of intersubjectivity as well as those who want to learn more about the interactional dimensions of Freud, Klein and Bion. (shrink)

Identity Processing Style and Defense Mechanisms To investigate relationships between identity processing styles and patterns of defense mechanisms, 213 participants completed measures of defense-mechanism clusters and styles of negotiating identity conflicts and threats. A self-exploratory, informational identity style was associated with defense mechanisms that control anxiety and threats via internal cognitive maneuvers. In contrast, a diffuse-avoidant identity style was found to be related to maladaptive defensive maneuvers including turning against others and turning aggression inward against oneself, which is (...) related to depressive reactions. A foreclosing, normative identity style was associated with defenses that limit awareness of threatening ideas and information by denial, distortion, and negation. None of these relationships was qualified by age or gender. The findings are discussed in terms of a process model of identity development that emphasizes social-cognitive differences in how individuals construct, maintain, and reconstruct their self-identity. (shrink)

Bodies as conceived in macroscopic theories are loosely spoken of as participating in processes. But are there any systematic reasons for regarding processes as part of the ontology of macroscopic theory? The present paper suggests that suitable motivation can be found within a project of describing a phenomenological, macroscopic ontology for equilibrium thermodynamics, and outlines some aspects of the interrelation between continuant bodies and processes.

Mental Processes in the Human Brain provides an integrative overview of the rapid advances and future challenges in understanding the neurobiological basis of mental processes that are characteristically human. With chapters from leading figures in the brain sciences, it will be essential for all those in the cognitive and brain sciences.

An integral subresiduated lattice ordered commutative monoid (or integral srl-monoid for short) is a pair $({\textbf {A}},Q)$ where ${\textbf {A}}=(A,\wedge,\vee,\cdot,1)$ is a lattice ordered commutative monoid, 1 is the greatest element of the lattice $(A,\wedge,\vee )$ and _Q_ is a subalgebra of _A_ such that for each $a,b\in A$ the set $\{q \in Q: a \cdot q \le b\}$ has maximum, which will be denoted by $a\rightarrow b$. The integral srl-monoids can be regarded as algebras $(A,\wedge,\vee,\cdot,\rightarrow,1)$ of type (2, 2, (...) 2, 2, 0). Furthermore, this class of algebras is a variety which properly contains the varieties of integral commutative residuated lattices and subresiduated lattices respectively. In this paper we study the quasivariety of $\{\wedge,\cdot,\rightarrow,1\}$ -subreducts of integral srl-monoids, which will be denoted by $\mathsf {SR^s}$. In particular, we show that $\mathsf {SR^s}$ is a variety. We also characterize simple and subdirectly irreducible algebras of $\mathsf {SR^s}$ respectively. Finally, through a Hilbert style system, we present a logic which has as algebraic semantics the variety $\mathsf {SR^s}$ and we apply this result in order to present an expansion of the previous logic which has as algebraic semantics the variety of integral srl-monoids. (shrink)

The influence of Aśvaghoṣa on the later tradition of kāvya was largely passed over in the South Asian tradition, even though the debt to his influence is clear in processional scenes developed by Kālidāsa and the attempted seduction of Arjuna developed by Bhāravi in his Kirātārjunīyam. We know from the testimony of the Chinese pilgrim Yijing that the Buddhacarita was a revered object of study in the Sumatran capital Śrībhoga near the close of the seventh century CE. It thus perhaps (...) comes as no surprise that three tropes or themes developed by Aśvaghoṣa were developed by several important composers of kakawin, the Old Javanese literary genre comparable to the kāvya of South Asia. This paper looks at the development of the themes of processions, divine battles and attempted seductions in a long history beginning with Aśvaghoṣa and closing with the work of the Javanese author Mpu Tantular, who completed the Buddhist kakawin Sutasoma c. 1365–1389 CE. This paper is partly based on a revised perspective on the history of the Shailendra and Sañjaya dynasties of central Java developed by examining the role of the “Shailendra royal preceptors” in bringing Sanskrit learning to Central Java in the period 778–847 CE. (shrink)

PROCESS THOUGHT Edited by Nicholas Rescher • Johanna Seibt • Michel Weber Advisory Board Mark Bickhard • Jaime Nubiola • Roberto Poli Volume 14 ...

(1996). Business process change: A systems thinking perspective. World Futures: Vol. 47, Unity and Diversity in Contemporary Systems Tinking: Systematic Pictures at an Exhibition, pp. 69-77.

Computation and information processing are among the most fundamental notions in cognitive science. They are also among the most imprecisely discussed. Many cognitive scientists take it for granted that cognition involves computation, information processing, or both – although others disagree vehemently. Yet different cognitive scientists use ‘computation’ and ‘information processing’ to mean different things, sometimes without realizing that they do. In addition, computation and information processing are surrounded by several myths; first and foremost, that they are (...) the same thing. In this paper, we address this unsatisfactory state of affairs by presenting a general and theory-neutral account of computation and information processing. We also apply our framework by analyzing the relations between computation and information processing on one hand and classicism and connectionism on the other. We defend the relevance to cognitive science of both computation, in a generic sense that we fully articulate for the first time, and information processing, in three important senses of the term. Our account advances some foundational debates in cognitive science by untangling some of their conceptual knots in a theory-neutral way. By leveling the playing field, we pave the way for the future resolution of the debates’ empirical aspects. (shrink)

In the process of creating our built environments, the threat of ecological crises often tempt us to focus on “fixes” of resource management and technological innovation. Yet if such approaches overwhelm the significance of place and our complex existential engagements within those places, then the earth becomes a mere collection of resources. Sustainability undertaken in such a categorical manner results in environments that are either nostalgic or alienating, and neither is sustainable. Sustainability becomes a holistic movement capable of coping with (...) both the specific and peculiar when it is undertaken as a recurring process of response. (shrink)

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

This paper presents the algebraic and Kripke modelsoundness and completeness ofa logic over Boolean monoids. An additional axiom added to thelogic will cause the resulting monoid models to be representable as monoidsof relations. A star operator, interpreted as reflexive, transitiveclosure, is conservatively added to the logic. The star operator isa relative modal operator, i.e., one that is defined in terms ofanother modal operator. A further example, relative possibility,of this type of operator is given. A separate axiom,antilogism, added to the logic (...) causes the Kripke models to support acollection of abstract topological uniformities which become concretewhen the Kripke models are dual to monoids of relations. The machineryfor the star operator is shownto be a recasting of Scott-Montague neighborhood models. An interpretationof the Kripke frames and properties thereof is presented in terms ofcertain CMOS transister networks and some circuit transformation equivalences.The worlds of the Kripke frame are wires and the Kripke relation is a specializedCMOS pass transistor network. (shrink)

We study the variety Var() of lattice-ordered monoids generated by the natural numbers. In particular, we show that it contains all 2-generated positively ordered lattice-ordered monoids satisfying appropriate distributive laws. Moreover, we establish that the cancellative totally ordered members of Var() are submonoids of ultrapowers of and can be embedded into ordered fields. In addition, the structure of ultrapowers relevant to the finitely generated case is analyzed. Finally, we provide a complete isomorphy invariant in the two-generated case.

This Article offers an integrated analysis of the combined effect of the presence of migration bans and the absence of BLAs in domestic work in the emigration regime of Nepal. It identifies, acknowledges, critiques, and contributes to the critical literature highlighting entrapment processes in labor relations and immigration regimes by demonstrating the presence of such in the emigration regime. Drawing on the empirical findings of a participatory action research project conducted in Nepal, the Article demonstrates how restrictive emigration policies and (...) practices entail entrapment processes constitutive of the existing historical, cultural, gendered, racialized, and classed constraints impacting the lives of Nepalese citizens. The Article contributes to the critical literature that seeks to advance migrants’ rights, arguing that experiencing, encountering and escaping entrapment processes in the emigration regime impacts their agency when navigating immigration regimes and labor relations. This contribution advances the existing efforts to establish oft-ignored emigration regimes as important epistemological sites of research, theorization, and intervention. (shrink)

Botanical illustration combines scientific knowledge and artistic technique. However, whereas illustrated botanical images record static visual qualities, such as form and color, written botanical narratives supply crucial sensory, ecological, historical, and cultural contexts that complement visual representation. Understanding the text-image interface—where images and words intersect—contributes to humanities-based analyses of botanical illustration and illustrators. More specifically, a process philosophy perspective reveals the extent to which botanical representations engage the temporality, cyclicality, and contextuality of the living plants being illustrated. This article takes (...) up these themes through a comparative theoretical study of three female Western Australian botanical illustrators, Georgiana Leake, Emily Pelloe, and Philippa Nikulinsky, whose lives together span the 183 year history of the Swan River Colony and the state of Western Australia. I apply a processist framework to examine the text-image interface of their works. All three illustrators use some form of textuality: marginalia, annotations, written accompaniments, introductory statements, and other narrative materials. In examining their written commentaries and traces, I identify the emergence of a process mode of botanical illustration that represents plants as ecological, historical, cultural, and temporal organisms. (shrink)