Monadic Approach Research Articles

TAG2G: A Diffusion-Based Approach to Interlocutor-Aware Co-Speech Gesture Generation

Extended reality (XR) systems are about to be integrated into our daily lives and will provide support in a variety of fields such as education and coaching. Enhancing user experience demands agents that are capable of displaying realistic affective and social behaviors within these systems, and, as a prerequisite, with the capability of understanding their interaction partner and responding appropriately. Based on our literature review of recent works published in the field of co-speech gesture generation, researchers have developed complex models capable of generating gestures characterized by a high level of human-likeness and speaker appropriateness. Nevertheless, this is only true in settings where the agent has an active status (i.e., the agent acts as the speaker), or it is delivering a monologue in a non-interactive setting. However, as illustrated in multiple works and competitions like the GENEA Challenge, these models remain inadequate in generating interlocutor-aware gestures. We consider interlocutor-aware gesture generation the process of displaying gestures that take into account the conversation partner’s behavior. Moreover, in settings where the agent is the listener, generated gestures lack the level of naturalness that we expect from a face-to-face conversation. To overcome these issues, we have designed a pipeline, called TAG2G, composed of a diffusion model, which was demonstrated to be a stable and powerful tool in gesture generation, and a vector-quantized variational auto-encoder (VQVAE), widely employed to produce meaningful gesture embeddings. Refocusing from monadic to dyadic multimodal input settings (i.e., taking into account text, audio, and previous gestures of both participants of a conversation) allows us to explore and infer the complex interaction mechanisms that lie in a balanced two-sided conversation. As per our results, a multi-agent conversational input setup improves the generated gestures’ appropriateness with respect to the conversational counterparts. Conversely, when the agent is speaking, a monadic approach performs better in terms of the generated gestures’ appropriateness in relation to the speech.

Abstract Interpreters: A Monadic Approach to Modular Verification

We argue that monadic interpreters built as layers of interpretations stacked atop the free monad constitute a promising way to implement and verify abstract interpreters in dependently-typed theories such as the one underlying the Coq proof assistant. The approach enables modular proofs of soundness of the resulting interpreters. We provide generic abstract control flow combinators proven correct once and for all against their concrete counterpart. We demonstrate how to relate concrete handlers implementing effects to abstract variants of these handlers, essentially capturing the traditional soundness of transfer functions in the context of monadic interpreters. Finally, we provide generic results to lift soundness statements via the interpretation of stateful and failure effects. We formalize all the aforementioned combinators and theories in Coq, and demonstrate their benefits by implementing and proving correct two illustrative abstract interpreters for a structured imperative language and a toy assembly.

From semantics to types: The case of the imperative λ-calculus

We study the logical semantics of an untyped λ-calculus equipped with operators representing read and write operations from and to a global store. Such a logic consists of an intersection type assignment system, which we derive from the denotational semantics of the calculus, based on the monadic approach to model computational λ-calculi.The system is obtained by constructing a filter model in the category of ω-algebraic lattices, such that the typing rules can be recovered out of the term interpretation. By construction, the so-obtained type system satisfies the “type-semantics” property and completeness.

Detection of river flow slow-down through sensing system and quasi-real time imaging

Flow slow-down in rivers and artificial canals is a basic aspect to be monitored and kept strictly under control. Flow slow-downs can become a major concern in the event of extreme phenomena. The paper illustrates an advanced image processing method that uses particle tracking velocimetry in conjunction with a monadic approach to better characterize water flow in the presence of waste or debris that block normal water flow within a river. An high-speed camera installed beneath a bridge takes periodic images of the water flow. The measured water level and the images taken by the camera are sent to a central system in real-time. Results demonstrate the capability of the proposed method to accurately detect the presence of debris from the measured water flow.

Monad Theory of Structural Synthesis of Mechanisms

Structural synthesis creates a structural scheme according to the given structural characteristics - the degree of abnormality of the structure S and the degree of its irrationality s. Structural scheme is created at the first stage of synthesis, containing only rotational kinematic pairs and corresponds to a given degree of abnormality, which is ensured by the ratio of structural units – plus monads, minus monads and null monads. At the second stage, the independence of structural characteristics makes it possible to bring the obtained scheme to a given degree of irrationality by downgrading the class of kinematic pairs. The proposed algorithm makes it possible to synthesize structural schemes of both normal structure and adaptive (with redundant motions), as well as indifferent (with redundant links). Monadic approach to structure research allows to formalize the structural features of the circuit and to create a knowledge base for automated design of structural circuits with given structural properties.

The untyped computational λ-calculus and its intersection type discipline

We study a Curry style type assignment system for untyped λ-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational λ-calculus based on Wadler's variant, without let, and with unit and bind operators. We define a notion of reduction for the calculus and prove it confluent.We then introduce an intersection type system inspired by Barendregt, Coppo and Dezani system for ordinary untyped λ-calculus, establishing type invariance under conversion.Finally, we introduce a notion of convergence, which is precisely related to reduction, and characterize convergent terms via their types.

Regions in International Politics: a Framework for Integrating Systemic, Regional, Dyadic, and Monadic Approaches

The article proposes the framework of further analysis of regional political processes. The authors believe that the significant amount of activities is occurring on the regional level. Thus, the moderate aim of the article is to link different levels of analysis and to present measurable variable to explore regional political developments in this context. The basic assumption of the article is that there are more hierarchical relationships on the regional level than on the global one. Regional powers objective try to create security and stability in their regional areas which increases the overall stability. However, some regions are lacking conditions for durable hierarchy, which is a structural reason for instability and conflicts. The problem the latter regions face is their limited chance of creating durable structures of cooperation, because hierarchy implies some structural violence that helps to realize interests and understand policy limitations. The article presents comparative framework that assesses features of regional powers such as strength or weakness, absence of rivals or their presence. The framework also includes state’s policies that may disregard the regional context in order to seek more promising opportunities. The “hierarchy and interest”- based analysis demonstrates that some regions have strong spatial appearance while the others are only in search of their spatial identity. This allows elaborating on the dependent variables such as territorial disputes, cooperation of rivals, political regime performance. The authors conclude that the presented framework can be useful for further analysis and enriches potential for testing hypotheses of regional political behavior of state actors.

Milton’s Italy: Anglo-Italian Literature, Travel, and Religion in Seventeenth-Century England. Catherine Gimelli Martin. New York: Routledge, 2017. Pp. xv+318.

<i>Milton’s Italy: Anglo-Italian Literature, Travel, and Religion in Seventeenth-Century England</i>. Catherine Gimelli Martin. New York: Routledge, 2017. Pp. xv+318.

On lifting of biadjoints and lax algebras

Given a pseudomonad $mathcal{T} $ on a $2$-category $mathfrak{B} $, if a right biadjoint $mathfrak{A}tomathfrak{B} $ has a lifting to the pseudoalgebras $mathfrak{A}tomathsf{Ps}textrm{-}mathcal{T}textrm{-}mathsf{Alg} $ then this lifting is also right biadjoint provided that $mathfrak{A} $ has codescent objects. In this paper, we give general results on lifting of biadjoints. As a consequence, we get a biadjoint triangle theorem which, in particular, allows us to study triangles involving the $2$-category of lax algebras, proving analogues of the result described above. In the context of lax algebras, denoting by $ell :mathsf{Lax}textrm{-}mathcal{T}textrm{-}mathsf{Alg} tomathsf{Lax}textrm{-}mathcal{T}textrm{-}mathsf{Alg} _ell $ the inclusion, if $R: mathfrak{A}tomathfrak{B} $ is right biadjoint and has a lifting $J: mathfrak{A}to mathsf{Lax}textrm{-}mathcal{T}textrm{-}mathsf{Alg} $, then $ellcirc J$ is right biadjoint as well provided that $mathfrak{A} $ has some needed weighted bicolimits. In order to prove such result, we study descent objects and lax descent objects. At the last section, we study direct consequences of our theorems in the context of the $2$-monadic approach to coherence.

A precise monadic dynamic slicing method

Dynamic program slicing is useful in software debugging, testing and maintenance, because it can extract more precise results than those obtained by static slicing. In this paper, we propose a precise approach for dynamic program slicing, monadic dynamic slicing, which is based on modular monadic semantics. Firstly, we abstract the computation of dynamic slicing as an object of independent language, dynamic slice-monad transformer. Then we discuss and illustrate a modular monadic dynamic slice algorithm in detail. In this monadic algorithm, dynamic slices are computed on abstract syntax directly, without the need to explicitly construct intermediate structures such as dependence graphs, or to record an execution history. Finally, we address the implementation and complexity analysis of this algorithm. We conclude that the monadic approach has excellent flexibility, combinability and parallelizability properties.

The Shuffle Quasimonad and Modules with Differentiation and Integration

Differential linear logic and the corresponding categorical structure, differential categories, introduced the idea of differential structure associated to a (co)monad. Typically in settings such as algebraic geometry, one expresses differential structure for an algebra by having a module with a derivation, i.e. a map satisfying the Leibniz rule. In the monadic approach, we are able to continue to work with algebras and derivations, but the additional structure allows us to define other rules of the differential calculus for such modules; in particular one can define a monadic version of the chain rule as well as other basic identities.In attempting to develop a similar theory of integral linear logic, we were led to consider the shuffle multiplication. This was shown by Guo and Keigher to be fundamental in the construction of the free Rota-Baxter algebra, the Rota-Baxter equation being the integral analogue of the Leibniz rule. This shuffle multiplication induces a quasimonad on the category of vector spaces. The notion of quasimonad, called r-unital monad by Wisbauer, is slightly weaker than that of monad, but is still sufficient to define a sensible notion of module with differentiation and integration.In this paper, we demonstrate this quasimonad structure, show that its free modules have both differential and integral operators satisfying the Leibniz and Rota-Baxter rules and satisfy the fundamental theorems of calculus.

Contrary-to-Duty Reasoning: A Categorical Approach

This paper provides an analysis of contrary-to-duty reasoning from the proof-theoretical perspective of category theory. While Chisholm’s paradox hints at the need of dyadic deontic logic by showing that monadic deontic logics are not able to adequately model conditional obligations and contrary-to-duties, other arguments can be objected to dyadic approaches in favor of non-monotonic foundations. We show that all these objections can be answered at one fell swoop by modeling conditional obligations within a deductive system defined as an instance of a symmetric monoidal closed category. Using category theory as a foundational framework for logic, we show that it is possible to model conditional normative reasoning and conflicting obligations within a monadic approach without adding further operators or considering deontic conditionals as primitive.

Where Do We Go from Here? Conceptual, Theoretical, and Methodological Gaps in the Large-N Civil War Research Program1

Since the early 1990s, the large-N civil war research program has been a vibrant one but has reached an analytical plateau because methodological issues have obscured fundamental conceptual and theoretical concerns. The existing ground-clearing work has shed light on macro- and micro-level determinants of internal conflict onset, duration, and termination, but has left the field theoretically impoverished. This article discusses remaining gaps in the quantitative civil war literature, and proposes conceptual, theoretical, and methodological remedies. Five main lacunae are identified. First, civil war may be a longer process, with several waves of escalation and de-escalation, than generally described in the extant literature. Second, existing theories conflate civil conflict with violence—war onset and violence may be conceptually distinct. Third, we have few systemic-level theories of civil war onset and duration. Fourth, we need better theories that allow us to determine whether civil wars are different from other types of wars. Finally, we need to go beyond state-centric monadic approaches, and be more rigorous when building our models for explaining civil war onset, duration, or termination.

A monadic approach to automated reasoning for Bluespec SystemVerilog

We embed a non-trivial subset of Bluespec SystemVerilog (BSV) in the higher order logic of the PVS theorem prover. Owing to the clean semantics of BSV, application of monadic techniques leads to a ...

A deontic logic framework allowing for factual detachment

Since our ethical and behavioral norms have a conditional form, it is of great importance that deontic logics give an account of deontic commitments such as “ A commits you to do/bring about B”. It is commonly agreed that monadic approaches are suboptimal for this task due to several shortcomings, for instance their falling short of giving a satisfactory account of “Strengthening the Antecedent” or their difficulties in dealing with contrary-to-duty paradoxes. While dyadic logics are more promising in these respects, they have been criticized for not being able to model “detachment”: A and the commitment under A to do B implies the actual obligation to do B. “We seem to feel that detachment should be possible after all. But we cannot have things both ways, can we? This is the dilemma on commitment and detachment.” (Lennart Åqvis. Deontic logic. In D. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, p. 199, Kluwer, Dordrecht, 2002). In this paper I answer Åqvist's question with “Yes, we can”. I propose a general method to turn dyadic deontic logics in adaptive logics allowing for a defeasible factual detachment while paying special attention to specificity and contrary-to-duty cases. I show that a lot of controversy about detachment can be resolved by analysing different notions of unconditional obligations. The logical modeling of detachment is paradigmatically realized on basis of one of Lou Goble's conflict tolerant CDPM logics.

Adding fuzziness to terms and powerobjects using a monadic approach

Fuzzy mathematics often starts by taking a piece of classical mathematics and introducing fuzziness to existing mathematical concepts, and then proceeds to a more essential adoption of a fuzzy perspective. This paper explores this progression for two important monads: the powerset monad and its generalizations to fuzzy powerobjects, and the term monad and its generalization to using fuzzy sets of operators. This brings together two lines of research previously discussed at the Linz seminars. The powerset and its fuzzy analogs are important in the development of topology in a fuzzy world and the term monad and its fuzzy analogs are vital in understanding fuzzy computer science.

Aristotle on the Category of Relation (review)

Reviewed by: Aristotle on the Category of Relation Roderick T. Long Pamela M. Hood . Aristotle on the Category of Relation. Lanham, MD: University Press of America, 2004. Pp. xi + 154. Paper, $28.00. It is often assumed that Aristotle cannot have an adequate understanding of relations, and in particular that "his substance-accident ontology and his reduction of propositions to the logical structure of subject-predicate form" (3) compel him to treat relations as monadic properties of the relata. But as Hood shows in this book, Aristotle's theory does indeed make room for dyadic (and generally polyadic) predicates—meaning not just that he employs such predicates in practice (that by itself would be no surprise), but that he does so in self-conscious connection with his theory of relatives. Moreover, Hood argues persuasively that Aristotle's characterization of relatives as holding "somehow" toward their correlatives suggests that he recognizes not only relational properties but relations as well. Along the way, she usefully distinguishes her interpretation from those of other commentators; especially helpful is Hood's diagnosis and critique of Morales's interpretation that relatives cease to be relatives when their correlatives are specified. At first Hood seems to want to show that Aristotle's account of relations is not only adequate, but also consistent with his placing individual substances at the center of his ontology. Given the importance of this ontological orientation to Aristotle's overall philosophic project, it would indeed be valuable to be able to show that Aristotle can acknowledge dyadic relations without sacrificing his ontological commitments. But Hood's remark that Aristotle's relational theory transcends "the limitations of his other philosophical positions" (142) suggests instead that she doubts Aristotle's consistency, and perhaps dismisses his substance-based ontology as well-lost. [End Page 149] Similarly, while Aristotle's claim that the actualization of an agent affecting a patient is something located in the patient has sometimes been taken as symptomatic of Aristotle's confused assumption that predicates must have unitary subjects, Hood convincingly refutes this interpretation, showing that Aristotle explicitly describes the actualization as having both the agent and the patient as subjects (62). So far, so good. But one would then expect the moral to be that, when Aristotle speaks of the actualization's being located in the patient, he must mean something other than the actualization's having one subject rather than two. Hood concludes instead that Aristotle's "relational theory . . . may outstrip his causal theory" (63), as though the causal claim were embarrassingly indicative of a monadic approach to relatives after all. Left unconsidered is the possibility that Aristotle might have good reasons—unconnected with any confusion about relatives—for locating the actualization in the patient. Hood's oddest omission is the lack of a clear explanation of what she takes items in the category of relative to be: relations? relata? relational properties? Hood glosses Aristotle's observation that "a man is not called 'someone's man' [but rather] 'someone's property'" (Cat. 8a22–24) as a distinction "between a specimen from the species and the species itself" (38); but I do not think that that can be right. For if Aristotle's reason for rejecting the expression 'someone's man' were that it would imply that someone owns the human species, then Aristotle's approval of the expression 'someone's property' would correspondingly imply that someone owns the species property. Surely what Aristotle actually means is that it is not qua man, but rather qua property, that a man belongs to someone; the distinction is not between specimen and species, but rather between a subject qua specimen of one species and the same subject qua specimen of a different species. Now Hood does see that it is not Peggy's slavehood, but Peggy qua slave, that is supposed to be the relative. But it is unclear whether Hood thinks Peggy qua slave is just Peggy, or instead some complex (a "kooky object"?) constituted by Peggy together with her slavehood. She calls relatives "Complex Predicative Entities," for example, and writes that, while "Peggy's fundamental existence is as a primary substance, not as a relative," because Peggy is "the underlying...

Preface: Volume 69

This volume contains the proceedings of the 9th Conference on Category Theory and Computer Science (CTCS'02), which was held at the University of Ottawa from August 15-17, 2002. The purpose of this conference series is the advancement of the foundations of computing using the tools of category theory. Indeed, category theory provides one of the key tools in the analysis of the interaction between logic and the theory of computation. The extent to which category theory has influenced these areas can be seen from the following list of topics, which are typical of the interests of this conference: • coalgebras and computing • concurrent and distributed systems • constructive mathematics • declarative programming and term rewriting • domain theory and topology • foundations of computer security • linear logic • modal and temporal logics • models of computation • program logics, data refinement, and specification • programming language semantics • type theory The list is by no means exhaustive. The vitality of the field is well displayed by the extremely high quality and the diversity of the 18 papers in this volume. For the first time in the history of CTCS, this year's conference was preceded by a “Graduate Student Preconference”, which took place from August 12-14 and which offered introductory courses in areas of importance to the conference. The response to this preconference was extraordinary, with more than 50 students and interested others taking part. This certainly suggests that the field of research of this conference will be strong and active for many years to come. The preconference offered courses in: • Introductory category theory (Susan Niefield) • Categorical logic (Philip Scott) • Concurrency theory (Peter Selinger) • Coalgebraic methods (Jiri Adamek) • Game theory (Robin Cockett) • Linear logic (Rick Blute) To hold this preconference, we received substantial funding from the Centre de Recherches Mathematiques (CRM). We thank them and Jacques Hurtubise, the Director of CRM, for their kind support. Without the help of many individuals in many different capacities, this conference would not have been possible. The editors would especially like to thank the following people: • The organizing committee: ◦ E. Moggi, Chair, (Genova) ◦ S. Abramsky (Oxford) ◦ P. Dybjer (Chalmers) ◦ B. Jay (Sydney) ◦ A. Pitts (Cambridge) • Local organizers: ◦ Rick Blute ◦ Philip Scott • The programme committee: ◦ Rick Blute, Chair (Ottawa) ◦ Robin Cockett (Calgary) ◦ Thierry Coquand (Chalmers) ◦ Andrea Corradini (Pisa) ◦ Thomas Ehrhard (Luminy) ◦ Ryu Hasegawa (Tokyo) ◦ Martin Hofmann (Munich) ◦ Bart Jacobs (Nijmegen) ◦ Michael Johnson (Macquarie) ◦ Dusko Pavlovic (Kestrel Institute) ◦ Alex Simpson (Edinburgh) • Lecturers in the student preconference: ◦ Susan Niefield (Union) ◦ Philip Scott (Ottawa) ◦ Robin Cockett (Calgary) ◦ Rick Blute (Ottawa) ◦ Jiri Adamek (Braunschweig) ◦ Peter Selinger (Ottawa)

A monadic approach to polycategories

Polycategories form a rather natural generalization of multicategories. Besides the domains also the codomains of morphisms are allowed to be strings of objects. Small multicategories can be characterized elegantly as monads in a suitable bicategory of special spans with free monoids as domains. To find a similar description of small polycategories, we first investigate distributive laws in the sense of Beck between cartesian monads S and T on a category X with pullbacks as tools for constructing new bicategories of S-T-spans. We identify a class of “super-cartesian” distributive laws that indeed produce such bicategories in a straightforward manner.If we decompose the free monoid monad (_)∗ into the free semigroup monad and the exception monad, a relation on (_)∗∗ can be defined by means of three super-cartesian distributive laws such that the resulting bicategory of (_)∗-(_)∗-spans has precisely the small planar polycategories as monads. General polycategories require a different construction and a span instead of a relation. However, only the notion of planar polycategory can be generalized to 2-dimensional structures, where objects are replaced by typed 1-cells. “ fc-polycategories” have essentially the same characterization as planar polycategories, but over the base grph rather than set.One of the distributive laws used above, complementation on the free semigroup monad, seems to be new. We identify its algebras as associative double semi-groups.Then we address the question, which spans between TS and ST correctly generalize (super-cartesian) distributive laws and provide an associative composition for S-T-spans with canonical units. We obtain four simple sufficient conditions, best formulated in the fc-multicategory of spans and morphisms in [ X,X], that clarify the notion of super-cartesian distributive law and justify the added generality.Finally, we show how by first quotienting the bicategory X-spn the constructions outlined above can be used even for weakly cartesian monads, in particular the free commutative monoid monad, which fails to be cartesian.

Monads for incremental computing

This paper presents a monadic approach to incremental computation, suitable for purely functional languages such as Haskell. A program that uses incremental computation is able to perform an incremental amount of computation to accommodate for changes in input data. Recently, Acar, Blelloch and Harper presented a small Standard ML library that supports efficient, high-level incremental computations [1]. Here, we present a monadic variant of that library, written in Haskell extended with first-class references. By using monads, not only are we able to provide a purely functional interface to the library, the types also enforce "correct usage" without having to resort to any type-system extension. We also find optimization opportunities based on standard monadic combinators.This is an exercise in putting to work monad transformers with environments, references, and continuations.