Modal Type of Weak Intuitionistic Fuzzy Implications Generated by the Operation Δ

In 2020 L. Atanassova has been introduced the new operation Δ over intuitionistic fuzzy sets and over intuitionistic fuzzy pairs. Some of its properties have been studied in 2021 from L. Atanassova and P. Dworniczak. In 2021 L. Atanassova and P. Dworniczak generated an intuitionistic fuzzy implication by the operation Δ, and it has been introduced and some of its basic properties have been described. Here, eight modal type of intuitionistic fuzzy implications are generated by the first one and some of their properties are discussed.

Contextual modal types for algebraic effects and handlers

Programming languages with algebraic effects often track the computations’ effects using type-and-effect systems. In this paper, we propose to view an algebraic effect theory of a computation as a variable context; consequently, we propose to track algebraic effects of a computation with contextual modal types . We develop ECMTT, a novel calculus which tracks algebraic effects by a contextualized variant of the modal □ (necessity) operator, that it inherits from Contextual Modal Type Theory (CMTT). Whereas type-and-effect systems add effect annotations on top of a prior programming language, the effect annotations in ECMTT are inherent to the language, as they are managed by programming constructs corresponding to the logical introduction and elimination forms for the □ modality. Thus, the type-and-effect system of ECMTT is actually just a type system. Our design obtains the properties of local soundness and completeness, and determines the operational semantics solely by β-reduction, as customary in other logic-based calculi. In this view, effect handlers arise naturally as a witness that one context (i.e., algebraic theory) can be reached from another, generalizing explicit substitutions from CMTT. To the best of our knowledge, ECMTT is the first system to relate algebraic effects to modal types. We also see it as a step towards providing a correspondence in the style of Curry and Howard that may transfer a number of results from the fields of modal logic and modal type theory to that of algebraic effects.

Multimodal Dependent Type Theory

We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode theory allow us to use the same type theory to compute and reason in many modal situations, including guarded recursion, axiomatic cohesion, and parametric quantification. We reproduce examples from prior work in guarded recursion and axiomatic cohesion, thereby demonstrating that MTT constitutes a simple and usable syntax whose instantiations intuitively correspond to previous handcrafted modal type theories. In some cases, instantiating MTT to a particular situation unearths a previously unknown type theory that improves upon prior systems. Finally, we investigate the metatheory of MTT. We prove the consistency of MTT and establish canonicity through an extension of recent type-theoretic gluing techniques. These results hold irrespective of the choice of mode theory, and thus apply to a wide variety of modal situations.

SIBERIAN SPATIAL IDENTITY AND MENTALITY

The article discusses some theoretical problems of the concept of spatial identity. The problem is revealed by the example of the Siberian macro-region, which is distinguished by a special mentality of society. Attempts are being made to analyze the category “Siberian” as a modal type that has peculiar value orientations associated with natural landscape, historical and cultural components, as well as specific behavioral strategies and practices of Siberians.

Seeing Like an Area Specialist

In this chapter, the author argues that the ubiquitous and often polemical distinction between ‘area studies’ and history as idiographic disciplines and ‘social science’ as a nomothetic discipline is false, and that the best scholarship has now moved towards an integration of history and the ‘areas’ into a theoretically-informed American intellectual agenda that is considerably more advanced than the modal type of inquiry in American social science, which remains wedded to an obsolescent model of how people do their work in the so-called ‘hard’ sciences.

Semantical Analysis of Contextual Types

We describe a category-theoretic semantics for a simply typed variant of Cocon, a contextual modal type theory where the box modality mediates between the weak function space that is used to represent higher-order abstract syntax (HOAS) trees and the strong function space that describes (recursive) computations about them. What makes Cocon different from standard type theories is the presence of first-class contexts and contextual objects to describe syntax trees that are closed with respect to a given context of assumptions. Following M. Hofmann’s work, we use a presheaf model to characterise HOAS trees. Surprisingly, this model already provides the necessary structure to also model Cocon. In particular, we can capture the contextual objects of Cocon using a comonad $$\flat $$ ♭ that restricts presheaves to their closed elements. This gives a simple semantic characterisation of the invariants of contextual types (e.g. substitution invariance) and identifies Cocon as a type-theoretic syntax of presheaf models. We express our category-theoretic constructions by using a modal internal type theory that is implemented in Agda-Flat.

The on-line emergence of Hebrew insubordinate she- (‘that/which/who’) clauses

This study examines the on-line emergence of insubordinate clauses in Hebrew conversation as constrained by local interactional contingencies, questioning traditional notions of grammatical ‘subordination’ and contributing to conceptions of grammar as a locally sensitive, temporally unfolding resource for social interaction. The clauses examined are syntactically unintegrated (unembedded in any matrix clause), or loosely-integrated (cannot be viewed unambiguously as constituting a relative, complement, or adverbial clause), yet they all begin with she- – the general ‘subordinating conjunction’ in traditional Modern Hebrew grammar. All 102 insubordinate she- clauses found throughout a 5.5 hour audio-recorded corpus were classified according to their discourse function: modal, elaborative, or evaluative/epistemic. Leaving aside the modal type, the remaining insubordinate she- clauses (N = 70, 69%) are shown to emerge on-line while speakers are busy performing a variety of tasks and responding to local interactional contingencies. In all of these cases she- functions as a generic ‘wildcard’ tying back to immediately prior discourse and projecting an elaboration/evaluation of it, in either same- or other-speaker talk. The findings concerning insubordinate clauses suggest a usage-based perspective also on canonical subordinate clauses, positioning canonical and syntactically unintegrated clauses at two ends of a continuum.