Related papers: Graded Semantics and Graded Logics for Eilenberg-M…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
We define a notion of Lambda-simulation for coalgebraic modal logics, parametric on the choice Lambda of predicate liftings for a functor T. We show this notion is adequate in several ways: i) it preserves truth of positive formulas, ii)…
We provide an effect system CatEff based on a category-graded extension of algebraic theories that correspond to category-graded monads. CatEff has category-graded operations and handlers. Effects in CatEff are graded by morphisms of the…
This paper presents equational-based logics for proving first order properties of programming languages involving effects. We propose two dual inference system patterns that can be instanciated with monads or comonads in order to be used…
We consider conditional transition systems, that model software product lines with upgrades, in a coalgebraic setting. By using Birkhoff's duality for distributive lattices, we derive two equivalent Kleisli categories in which these…
Profinite equations are an indispensable tool for the algebraic classification of formal languages. Reiterman's theorem states that they precisely specify pseudovarieties, i.e. classes of finite algebras closed under finite products,…
We introduce categorical modularity, a novel low-resource intrinsic metric to evaluate word embedding quality. Categorical modularity is a graph modularity metric based on the $k$-nearest neighbor graph constructed with embedding vectors of…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
The paper relates two variants of semantic models for natural language, logical functional models and compositional distributional vector space models, by transferring the logic and reasoning from the logical to the distributional models.…
We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…
We present an algorithm for deriving a spatial-behavioral type system from a formal presentation of a computational calculus. Given a 2-monad Calc: Catv$\to$ Cat for the free calculus on a category of terms and rewrites and a 2-monad…
We define a new logic-induced notion of bisimulation (called $\rho$-bisimulation) for coalgebraic modal logics given by a logical connection, and investigate its properties. We show that it is structural in the sense that it is defined only…
Distributional semantics provides multi-dimensional, graded, empirically induced word representations that successfully capture many aspects of meaning in natural languages, as shown in a large body of work in computational linguistics;…
Primary cohomology operations, i.e., elements of the Steenrod algebra, are given by homotopy classes of maps between Eilenberg--MacLane spectra. Such maps (before taking homotopy classes) form the topological version of the Steenrod…
In programming language semantics, it has proved to be fruitful to analyze context-dependent notions of computation, e.g., dataflow computation and attribute grammars, using comonads. We explore the viability and value of similar modeling…
Boolean spaces with internal semigroups generalize profinite semigroups and are pertinent for the recognition of not-necessarily regular languages. Via recognition, the study of existential quantification in logic on words amounts to the…
In this paper we propose a general approach to define a many-valued preferential interpretation of gradual argumentation semantics. The approach allows for conditional reasoning over arguments and boolean combination of arguments, with…
Natural logic offers a powerful relational conception of meaning that is a natural counterpart to distributed semantic representations, which have proven valuable in a wide range of sophisticated language tasks. However, it remains an open…
Combining abstract, symbolic reasoning with continuous neural reasoning is a grand challenge of representation learning. As a step in this direction, we propose a new architecture, called neural equivalence networks, for the problem of…
We provide graded extensions of algebraic theories and Lawvere theories that correspond to graded monads. We prove that graded algebraic theories, graded Lawvere theories, and finitary graded monads are equivalent via equivalence of…