Through reading the early work of Walter Benjamin—up to and including the Trauerspiel, author Monad Rrenban elicits a cohesive conception of the wild, inforgettable form, philosophy, as inherent in everything. This book, distinct in its analysis and depth of analysis, elaborates the wild, unforgettable form—philosophy in relation to language, the discipline and the practice of philosophy, criticism, and the politics of death.

In On a Discovery, Kant depicts monads as simple beings that are thought in the idea as the ground of appearances. He argues that his account of monads is partially in line with both Leibniz's monadology and his own critical philosophy. However, in the Critique of Pure Reason, Kant appears to depart from the monadologies of his predecessors. In this article, I make sense of Kant's late subscription to a version of Leibniz's monadology by arguing that Kant considers (...) monads to be the objects represented through cosmological and psychological ideas posited by reason in its search for the unconditioned conditions of appearances. In particular, I point to what I take to be two instances of what Kant calls “objects in the idea” in the Critique of Pure Reason, namely (a) the substratum of matter qua ground of external appearances, and (b) the soul qua ground of internal appearances. Drawing on Kant's reply to Eberhard and the Transcendental Dialectic of the first Critique, I highlight the merely regulative—and yet fundamental—role that monads conceived as objects of reason play in Kant's critical philosophy. (shrink)

Many scholars hold that Leibniz's monads are not located in space at all, and some attribute situations to simple substances directly. A more nuanced position is that monads have a situation only indirectly, namely through the situation of their bodies. It has been objected, however, that this intermediate position is untenable since it involves a viciously circular argument. Leibniz is clear that the situation is the basis for the extension. But if a substance is situated only through its (...) own (extended) body, then the situation would appear to presuppose the extension of the body. Thus extension presupposes situation, but the situation would presuppose extension. In this paper (1) we present textual evidence that Leibniz did indeed hold that monads are situated via their own bodies; (2) we suggest that, even if what is properly speaking situated are (extended) bodies, there is no circularity in holding that the extension of a body results from the mutual situations of its parts: a non-vicious infinite regress of explanations in terms of extended parts is possible; and (3) we defend this solution against a possible objection. (shrink)

Cappelen and Hawthorne present a powerful critique of fashionable relativist accounts of truth, and the foundational ideas in semantics on which the new relativism draws. They argue compellingly that the contents of thought and talk are propositions that instantiate the fundamental monadic properties of truth and falsity.

Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. GMV-algebras are a non-commutative generalization of MV-algebras and are an algebraic counterpart of the non-commutative Łukasiewicz infinite valued logic. We introduce monadic GMV-algebras and describe their connections to certain couples of GMV-algebras and to left adjoint mappings of canonical embeddings of GMV-algebras. Furthermore, functional MGMV-algebras are studied and polyadic GMV-algebras are introduced and discussed.

Requirement specifications in software engineering involve developing a conceptual model of a target domain. The model is based on ontological exploration of things in reality. Many things in such a process closely tie to problems in metaphysics, the field of inquiry of what reality fundamentally is. According to some researchers, metaphysicians are trying to develop an account of the world that properly conceptualizes the way it is, and software design is similar. Notions such as classes, object orientation, properties, instantiation, algorithms, (...) etc. are metaphysical concepts developed many years ago. Exploring the metaphysics of such notions aims to establish quality assurance though some objective foundation not subject to misapprehensions and conventions. Much metaphysical work might best be understood as a model-building process. Here, a model is viewed as a hypothetical structure that we describe and investigate to understand more complex, real-world systems. The purpose of this paper is to enhance understanding of the metaphysical origins of conceptual modeling as exemplified by a specific proposed high-level model called thinging machines (TMs). The focus is on thimacs (things/machine) as a single category of TM modeling in the context of a two-phase world of staticity and dynamics. The general idea of this reality has been inspired by Deleuze’s ‘the virtual’ and related to the classical notions of Leibniz’s monads and Avicenna’s essence. The analysis of TMs leads to several interesting results about a thimac’s nature at the static and existence levels. (shrink)

The variety MBA of monadic bounded algebras consists of Boolean algebras with a distinguished element E, thought of as an existence predicate, and an operator ∃ reflecting the properties of the existential quantifier in free logic. This variety is generated by a certain class FMBA of algebras isomorphic to ones whose elements are propositional functions. We show that FMBA is characterised by the disjunction of the equations ∃E = 1 and ∃E = 0. We also define a weaker notion of (...) "relatively functional" algebra, and show that every member of MBA is isomorphic to a relatively functional one. (shrink)

One of the main obstacles for panpsychism, the view that consciousness is fundamental and ubiquitous, is the difficulty of explaining how simple subjects could combine to form complex subjects. Known as the subject combination problem, it poses a possibly insurmountable challenge to the view. In this paper, I will assume that this challenge cannot be overcome and instead present a version of panpsychism that completely avoids talk of combination. Inspired by Gottfried Wilhelm Leibniz’s metaphysics of monads, I will focus (...) on a relational explanation of how simple subjects could constitute complex experiences, without them having to combine in virtue of their subjectivity. I call this view monadic panpsychism. Additionally, my proposal will not rely on emergence and so it will circumvent problems commonly faced by emergentist accounts. As I will argue, monadic panpsychism is preferable to combinatory and emergentist panpsychism because it faces a significantly less worrisome set of objections. Apart from being unaffected by the seemingly insuperable issue of subject combination, I will demonstrate that monadic panpsychism also has tools to address other kinds of the combination problem. That alone justifies the need for a new formulation of panpsychism, one which faces unique difficulties but also offers unique solutions. (shrink)

Aiming for applications in monadic second-order model theory, we study first-order theories without definable pairing functions. Our main results concern forking-properties of sequences of indiscernibles. These turn out to be very well-behaved for the theories under consideration.

In this paper we extend Mundici’s functor Γ to the category of monadic MV-algebras. More precisely, we define monadic ℓ -groups and we establish a natural equivalence between the category of monadic MV-algebras and the category of monadic ℓ -groups with strong unit. Some applications are given thereof.

The problem at the center of this essay is how one can reconcile the continuity of space with a monadological theory of matter, according to which matter is ultimately composed of simple elements, a problem that greatly exercised Leibniz, the Wolffians, and Kant. The underlying purpose of this essay is to illustrate my reading of Kant’s philosophical development, and of his relation to the Wolffians and Leibniz, according to which, (a), this development was fueled by ‘home-grown’ problems that arose within (...) the framework of the Wolffian philosophy from which Kant started out, and, (b), on his journey to critical idealism, Kant gradually moved away from Wolffianism, but closer to Leibniz, which, however, he came to realize only some years after the publication of the Critique of Pure Reason. This reading is illustrated by showing that the problem of how to reconcile the continuity of space with a monadological theory of matter is a problem that Kant inherits from Leibniz and the Wolffians, in whose thinking it already plays an important role, that Leibniz’s mature solution to the problem differs markedly from the Wolffian solution, and that Kant’s early, pre-critical solution is largely Wolffian, while his later critical solution is largely Leibnizian, as he himself notes with gleeful satisfaction. The discussion also reveals that this problem is one of the key problems that fueled Kant’s philosophical development and, eventually, led him to the discovery of transcendental idealism. (shrink)

This chapter offers a novel account of how to understand Leibniz’s views on compossibility when applied to infinite worlds constituted by unextended, immaterial substances or ‘monads’. The first section sets the stage by taking up some essential questions about the relationship between monads and space. The second section argues that—with a better understanding of that relationship—it is possible to see how the so-called ‘packing strategy’ can be applied quite directly, even intuitively, to monadic worlds and substances. The third (...) section argues that thinking through the application of the packing strategy to monadic worlds highlights an important, neglected Leibnizian commitment and reveals surprising affinities between the packing strategy and recent cosmological interpretations. (shrink)

ABSTRACT This essay analyzes the controversy that attended the prize essay question on monads proposed by the Berlin Academy of Sciences in 1746. The controversy was first touched off by an anonymous pamphlet published by the mathematician Leonhard Euler, the academy's most well known member, that attacked the doctrine of monads. It peaked with the awarding of the prize to Johann Heinrich Gottlob Justi, whose winning essay closely followed Euler's arguments. This essay discusses the controversy as one instance (...) in a broader quarrel in the German academic community over the suitability of Christian Wolff's philosophy as the foundation for a broad range of academic disciplines, including natural philosophy. It also analyzes the controversy as displaying the central role of the periodical press in the emergent German public sphere. (shrink)

In this new work, Richard T. W. Arthur offers a fresh interpretation of Leibniz's theory of substance. He goes against a long trend of idealistic interpretations of Leibniz's thought by instead taking seriously Leibniz's claim of introducing monads to solve the problem of the composition of matter and motion.

We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in detail arbitrary tensor products of ultrafilters, as well as by characterising their combinatorial properties by means of their monads. This extends to arbitrary sets and properties methods previously used to study partition regular Diophantine equations on. Several applications are described by means of multiple examples.

_Explore the universe of Frank Herbert’s Dune in all its philosophical richness_ “He who controls the spice controls the universe.” Frank Herbert’s _Dune _saga is the epic story of Paul, son of Duke Leto Atreides, and heir to the massive fortune promised by the desert planet Arrakis and its vast reservoirs of a drug called “spice.” To control the spice, Paul and his mother Jessica, a devotee of the pseudo-religious Bene Gesserit order, must find their place in the culture of (...) the desert-dwelling Fremen of Arrakis. Paul must contend with both the devious rival House Harkonnen and the gargantuan desert sandworms—the source of the spice. The future of the Imperium depends upon one young man who will need to lead a new jihad to control the universe. _Dune and Philosophy _recruits 23 philosophers to sift wisdom from Frank Herbert’s Duniverse_, _including the first of an expected series of films following Paul “Muad’Dib” Atreides and his descendants, captivatingly brought to the big screen by Denis Villeneuve in 2021. Part of the New Wave of science fiction of the 60s and 70s, _Dune _is characterized by literary experimentation with shifting styles, differing narrative points of view, and with the “psychedelic” culture of the period. In _Dune_, the long-term strategies and intricate plots of warring Great Houses are driven not just by Heighliner spacecraft and lasguns, but also by mind-expanding drugs, psychic powers, dystopian themes, race memories, and martial arts allowing control of the mind and the body. Substantial yet accessible chapters address philosophical questions including: Is it morally right to create a savior? Would interplanetary travel change human nature? What is the deeper meaning of desert ecologies? In conflict, how can you stay light years ahead of your opponents? Are there some drugs we would want to be addicted to? Does history repeat itself? Tens of thousands of years into an intergalactic future, can humans endure or will we sacrifice what is most important in our humanity for power, glory, religion and of course, the control of the spice? _Dune and Philosophy _sets an intellectual course through sand and stars to find out. (shrink)

In this paper we extend Mundici's functor? to the category of monadic MV- algebras. More precisely, we define monadic?- groups and we establish a natural equivalence between the category of monadic MV- algebras and the category of monadic?- groups with strong unit. Some applications are given thereof.

In our paper, monadic modal pseudocomplemented De Morgan algebras are considered following Halmos’ studies on monadic Boolean algebras. Hence, their topological representation theory is used successfully. Lattice congruences of an mmpM is characterized and the variety of mmpMs is proven semisimple via topological representation. Furthermore and among other things, the poset of principal congruences is investigated and proven to be a Boolean algebra; therefore, every principal congruence is a Boolean congruence. All these conclusions contrast sharply with known results for monadic (...) De Morgan algebras. Finally, we show that the above results for mmpM are verified for monadic tetravalent modal algebras. (shrink)

In this paper I argue that Kant’s investigation of the nature of bodies, although it was largely based on Newtonian science, was more dependent on notions and debates in German logic and metaphysics. In section 1, I introduce the role of material substance in the Metaphysical Foundations of Natural Science, arguing that the systematic framework of Kant’s “metaphysics of corporeal nature” cannot be described as a “foundation of Newtonian philosophy” and is best understood in the context of the reception of (...) Newton’s physics in Wolffian metaphysics. In section 2, I analyze the crucial role of monads, monadology and materialism in the development of Kant’s dynamics. In section I3, I address Kant’s “continuum” theory of matter in the Metaphysical Foundations, pointing out that it depended on non-Newtonian (or post-Newtonian) models. In section 4, I examine the methodological background of Kant’s critique of the “solidity” of bodies, tracing it back to Kant’s earlier debate on the method of science and metaphysics with Johann Heinrich Lambert. (shrink)

This paper is a discussion of the treatment of Leibniz's conception of substance in Heidegger's The Metaphysical Foundations of Logic. I explain Heidegger's account, consider its relation to recent interpretations of Leibniz in the Anglophone secondary literature, and reflect on the ways in which Heidegger's methodology may illuminate what it is to read Leibniz and other figures in the history of philosophy.

This paper examines a widely accepted reading of monads as the most fundamental elements of reality. Garber [Leibniz – Body, Substance, Monad, Oxford: Oxford University Press, 2009] argues that simple monads – seen as mind-like atoms without parts and extension – replace the corporeal substance of Leibniz’s middle period. Phemister [Leibniz and the Natural World – Activity, Passivity and Corporeal Substances in Leibniz’s Philosophy, Dordrecht: Springer, 2005] argues that monads figure also at the top as complete corporeal (...) substances. Building on Fichant [‘L’invention métaphysique’ in G.W. Leibniz, Discours de métaphysique suivi de Monadologie et autres textes, edited by Michel Fichant, Paris: Gallimard, 2004], I argue that, for Leibniz, monads function not only as building blocks at the bottom level of composition but also at the top, as grounding the unity and hence the being of complete substances and organic unities. Since organic unities or living beings are seen by Leibniz as natural machines with a nested structure, and since monads are likened to living beings, this would imply that the use of the concept ‘monad’ holds not only at the bottom, and not only at the top, but all over the range between them. (shrink)

This article discusses the final development of Gottfried Wilhelm Leibniz’s metaphysics: the theory of monads. It examines Leibniz’s arguments for monads as mindlike “simple substances,” his description of the properties of monads, and the distinction he draws among different types of monads. The remainder of the article focuses on two problems that attend Leibniz’s claim that reality ultimately consists solely of monads and their internal states (perceptions and appetitions). The first problem is whether a relation (...) among monads can account for the supposed unity of a living body or corporeal substance; the second is whether the metaphysics of monads supports a plausible explanation of the reality of matter. With regard to the second problem, the article explores Leibniz’s thesis that monads are, in two senses, “requisites” of matter. It concludes with reflections on the limits of his attempt to explain the physical world in terms of monads alone. (shrink)

In this paper, we introduce the variety of algebras, which we call monadic k×j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\times j$$\end{document}-rough Heyting algebras. These algebras constitute an extension of monadic Heyting algebras and in 3×2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$3\times 2$$\end{document} case they coincide with monadic 3-valued Łukasiewicz–Moisil algebras. Our main interest is the characterization of simple and subdirectly irreducible monadic k×j\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\times j$$\end{document}-rough Heyting algebras. (...) In order to this, an Esakia-style duality for these algebras is developed. (shrink)

The main purpose of this work is to introduce the class of the monadic dynamic algebras (dynamic algebras with one quantifier). Similarly to a theorem of Kozen we establish that every separable monadic dynamic algebra is isomorphic to a monadic (possibly non‐standard) Kripke structure. We also classify the simple (monadic) dynamic algebras. Moreover, in the dynamic duality theory, we analyze the conditions under which a hemimorphism of a dynamic algebra into itself defines a quantifier. (© 2006 WILEY‐VCH Verlag GmbH & (...) Co. KGaA, Weinheim). (shrink)

We define and study monadic MV-algebras as pairs of MV-algebras one of which is a special case of relatively complete subalgebra named m-relatively complete. An m-relatively complete subalgebra determines a unique monadic operator. A necessary and sufficient condition is given for a subalgebra to be m-relatively complete. A description of the free cyclic monadic MV-algebra is also given.

This paper reconstructs Stanisław Ignacy Witkiewicz’s understanding of logic, accentuating the differences in his evaluation of logic and systems of ‘logistics’. Leśniewski’s theory of collective sets (mereology) exemplifies logistics as understood by Witkiewicz. I present an outline of Leśniewski’s nominalism, which entails a belief in a non-abstract nature of sets. I focus on these features of mereology that could have led Witkiewicz to interpreting it as an ontological system. Witkacy (Witkiewicz’s penname) was skeptical of the usefulness of formal systems (or (...) logistics), and of mereology in particular, for the purposes of designing a unified ontological system describing essential properties of objects (the world). According to Witkiewicz, such formal systems assumed the role of ontology but severely lacked in philosophical justification. I argue that regardless of his nominalism and corporeal conception of individuals, mereology cannot be considered a formal theory of Witkiewicz’s monads. (shrink)

In this paper, we are concerned with the development of a general set theory using the single axiom version of Leśniewski’s mereology. The specification of mereology, and further of Tarski’s geometry of solids will rely on the Calculus of Inductive Constructions (CIC). In the first part, we provide a specification of Leśniewski’s mereology as a model for an atomless Boolean algebra using Clay’s ideas. In the second part, we interpret Leśniewski’s mereology in monadic second-order logic using names and develop a (...) full version of mereology referred to as CIC-based Monadic Mereology (λ-MM) allowing an expressive theory while involving only two axioms. In the third part, we propose a modeling of Tarski’s solid geometry relying on λ-MM. It is intended to serve as a basis for spatial reasoning. All parts have been proved using a translation in type theory. (shrink)

We introduce the equational notion of a monadic bounded algebra (MBA), intended to capture algebraic properties of bounded quantification. The variety of all MBA's is shown to be generated by certain algebras of two-valued propositional functions that correspond to models of monadic free logic with an existence predicate. Every MBA is a subdirect product of such functional algebras, a fact that can be seen as an algebraic counterpart to semantic completeness for monadic free logic. The analysis involves the representation of (...) MBA's as powerset algebras of certain directed graphs with a set of "marked" points. It is shown that there are only countably many varieties of MBA's, all are generated by their finite members, and all have finite equational axiomatisations classifying them into fourteen kinds of variety. The universal theory of each variety is decidable. Finitely generated MBA's are shown to be finite, with the free algebra on r generators having exactly $2^{3.2^{r.} } ^{2^{{\rm{2}}^{{\rm{r - 1}}} } } $ elements. An explicit procedure is given for constructing this freely generated algebra as the powerset algebra of a certain marked graph determined by the number r. (shrink)

This chapter concerns the question as to considers why monads play such a negligible role in Leibniz’s _Theodicy_. Against those who argue that the _Theodicy_ is an exoteric text and thus not an appropriate place for Leibniz to present his esoteric doctrines, the chapter argues that Leibniz did not include his esoteric doctrines in the Theodicy them simply because they are not directly relevant to the main theme: of the _Theodicy_, the problem of evil. More generally, it is argued (...) that even though Leibniz’s philosophy is unified and systematic, Leibniz quite self-consciously sought to present his thought in a way that it could be communicated in discrete units, absorbed piece by piece, without having to absorb the entire system at once. In this sense it is modular. This explains why Leibniz’s preferred form is the short essay or note, and why most of his publications were in learned journals. Finally, it is argued that at the time of the _Theodicy_ (1710), the monadological metaphysics was still a somewhat amorphous and incompletely digested collection of doctrines, nothing that could easily have been inserted into the book, even if Leibniz had judged it appropriate. The monadological metaphysics is not fully formulated until the _Principles of Nature and Grace_ and the _Monadology_, both of 1714, it is claimed. (shrink)

A potential challenge in bridging Husserl’s egological approach to Leibniz’ monadological metaphysics, itself a promising project for various reasons as discussed throughout this collection, is the so-called world-boundedness of monads. If any monad is bounded to a possible world, then there hardly would be a room for transcendental monads. In other words, the view that the transcendental intersubjectivity is to constitute the world is in tension with the view that any transcendental subject, while considered as a monad, is (...) already bounded to a world. However, all this arise when Leibinz’s monadology verily implies world-boundedness of all monads. In this chapter, I wish to show first that a well-known argument attributed to Leibniz which rejects the trans-world identity of individuals is invalid. Second, I argue that Leibnizian metaphysics indeed involves the trans-world identity of certain monads, namely, the self-conscious monads, and it offers a criterion for such an identity. Therefore, in this regard, there is no real tension between transcendental phenomenology and monadological metaphysics. (shrink)

In spite of their materialist aspirations, both classical and neoclassical economic theories rely on non-material notions of value to explain market activity. André Orléan calls this commitment of orthodox economics "the substance hypothesis." In this essay, I show how the substance hypothesis mirrors Gottfried Wilhelm Leibniz's account of monads, which he called the "true atoms of nature." I argue that value is the atom of economic nature in orthodox economic theories. Like monads, it is a fantasy. The atom (...) of economic nature that governs our actual, material lives, I argue, is money. (shrink)

Assume ZFC is consistent then for everyB⫅ω there is a generic extension of the ground world whereB is recursive in the monadic theory ofω 2.

I shall proceed in the following way. In parts II and III of this paper, I shall discuss the strengths and weaknesses of the interpretation put forward by Robert Merrihew Adams in his recent book, and I shall expand upon this account, discussing a crucial but hitherto unexamined aspect of the relation between dominant and subordinate monads, reconstructed from Leibniz's letters to Des Bosses and his essays of 1714, _Principles of Nature and Grace and Monadology. In part IV of (...) this paper, I shall examine various difficulties that arise both for my interpretation and, more generally, for Leibniz's account of the relation of domination and subordination. (edited). (shrink)

Most interpreters think that for Leibniz, teleology is goodness-directedness. Explaining a monadic action teleologically, according to them, simply means explaining it in terms of the goodness of the state at which the agent aims. On some interpretations, the goodness at issue is always apparent goodness: an action is end-directed iff it aims at what appears good to the agent. On other interpretations, the goodness at issue is only sometimes apparent goodness and at other times merely objective goodness: some actions do (...) not aim at what appears good to the agent, but merely at what is objectively good—that is, at what God knows to be good—and that is sufficient for teleology. My paper, on the other hand, argues that both of these interpretations are mistaken. Monadic teleology, I contend, does not have to consist in striving for the good; neither goodness nor God is required to make monadic actions teleological. (shrink)

Many concepts, which can be constituents of thoughts, are somehow indicated with words that can be constituents of sentences. But this assumption is compatible with many hypotheses about the concepts lexicalized, linguistic meanings, and the relevant forms of composition. The lexical items simply label the concepts they lexicalize, and that composition of lexical meanings mirrors composition of the labeled concepts, which exhibit diverse adicities. If a phrase must be understood as an instruction to conjoin monadic concepts that correspond to the (...) constituents, lexicalization must be a process in which non-monadic concepts are used to introduce monadic analogues. But given such analogues, along with some thematic concepts, conjunctions can mimic the effect of saturating polyadic concepts. The lexical items efface conceptual adicity distinctions, making it possible to treat a recursive combination of expressions as a sign of monadic predicate conjunction. (shrink)

We show that monadic intuitionistic quantifiers admit the following temporal interpretation: “always in the future” (for$\forall $) and “sometime in the past” (for$\exists $). It is well known that Prior’s intuitionistic modal logic${\sf MIPC}$axiomatizes the monadic fragment of the intuitionistic predicate logic, and that${\sf MIPC}$is translated fully and faithfully into the monadic fragment${\sf MS4}$of the predicate${\sf S4}$via the Gödel translation. To realize the temporal interpretation mentioned above, we introduce a new tense extension${\sf TS4}$of${\sf S4}$and provide a full and faithful translation (...) of${\sf MIPC}$into${\sf TS4}$. We compare this new translation of${\sf MIPC}$with the Gödel translation by showing that both${\sf TS4}$and${\sf MS4}$can be translated fully and faithfully into a tense extension of${\sf MS4}$, which we denote by${\sf MS4.t}$. This is done by utilizing the relational semantics for these logics. As a result, we arrive at the diagram of full and faithful translations shown in Figure 1 which is commutative up to logical equivalence. We prove the finite model property (fmp) for${\sf MS4.t}$using algebraic semantics, and show that the fmp for the other logics involved can be derived as a consequence of the fullness and faithfulness of the translations considered. (shrink)

Monads, Composition, and Force: Ariadnean Threads through Leibniz’s Labyrinth, by ArthurRichard. Oxford: Oxford University Press, 2018. Pp. ix + 329.

Representations of monadic MV -algebra, the characterization of locally finite monadic MV -algebras, with axiomatization of them, definability of non-trivial monadic operators on finitely generated free MV -algebras are given. Moreover, it is shown that finitely generated m-relatively complete subalgebra of finitely generated free MV -algebra is projective.

Epistemic monadic Boolean algebras are obtained by enriching monadic Boolean algebras with a knowledge operator. Epistemic monadic logic as the monadic fragment of first-order epistemic logic is introduced for talking about knowing things. A Halmos-style representation of epistemic monadic Boolean algebras is established. Relativizations of epistemic monadic algebras are given for modelling updates. These logics are semantically complete.

\ of monadic m-generalized Łukasiewicz algebras of order n -algebras), namely a generalization of monadic n-valued Łukasiewicz algebras. In this article, we determine the congruences and we characterized the subdirectly irreducible \-algebras. From this last result we proved that \ is a discriminator variety and as a consequence we characterized the principal congruences. In the last part of this paper we find an immersion of these algebras in a functional algebra and we proved that in the finite case they are (...) isomorphic. This last result allows to show a new functional representation for monadic n-valued Łukasiewicz algebras. Finally, we define the notions of \-algebra of fractions and maximal algebra of fractions and we prove the existence of a maximal \-algebra of fractions for an \-algebra. (shrink)

Two variants of monadic fuzzy predicate logic are analyzed and compared with the full fuzzy predicate logic with respect to finite model property (properties) and arithmetical complexity of sets of tautologies, satisfiable formulas and of analogous notion restricted to finite models.

In this paper, we investigate universal and existential quantifiers on NM-algebras. The resulting class of algebras will be called monadic NM-algebras. First, we show that the variety of monadic NM-algebras is algebraic semantics of the monadic NM-predicate logic. Moreover, we discuss the relationship among monadic NM-algebras, modal NM-algebras and rough approximation spaces. Second, we introduce and investigate monadic filters in monadic NM-algebras. Using them, we prove the subdirect representation theorem of monadic NM-algebras, and characterize simple and subdirectly irreducible monadic NM-algebras. (...) Finally, we present the monadic NM-logic and prove its completeness with respect to monadic NM-algebras. These results constitute a crucial first step for providing an algebraic foundation for the monadic NM-predicate logic. (shrink)

This paper deals with the varieties of monadic Heyting algebras, algebraic models of intuitionistic modal logic MIPC. We investigate semisimple, locally finite, finitely approximated and splitting varieties of monadic Heyting algebras as well as varieties with the disjunction and the existence properties. The investigation of monadic Heyting algebras clarifies the correspondence between intuitionistic modal logics over MIPC and superintuitionistic predicate logics and provides us with the solutions of several problems raised by Ono [35].

We prove that every monadic second-order property of the unfolding of a transition system is a monadic second-order property of the system itself. An unfolding is an instance of the general notion of graph covering. We consider two more instances of this notion. A similar result is possible for one of them but not for the other.

We investigate monadic fragments of Intuitionistic Control Logic, which is obtained from Intuitionistic Propositional Logic by extending language of IPL by a constant distinct from intuitionistic constants. In particular we present the complete description of purely negational fragment and show that most of monadic fragments are finite.

We investigate the monadic logic of trees with ω + 1 levels, the monadic topology of the product space ω λ and a strengthening of monadic logic for trees with ω levels.

Daniel Garber presents a study of Leibniz's conception of the physical world, elucidating his puzzling metaphysics of monads, mind-like simple substances.