Related papers: Initial Semantics for Strengthened Signatures
Quantitative algebras are algebras enriched in the category $\mathsf{Met}$ of metric spaces so that all operations are nonexpanding. Mardare, Plotkin and Panangaden introduced varieties (aka $1$-basic varieties) as classes of quantitative…
In this paper we provide a (negative) solution to a problem posed by Stanis{\l}aw Krajewski. Consider a recursively enumerable theory U and a finite expansion of the signature of U that contains at least one predicate symbol of arity $\ge$…
Both algebraic and computational approaches for dealing with similarity spaces are well known in generalized rough set theory. However, these studies may be said to have been confined to particular perspectives of distinguishability in the…
We introduce a novel scheme for parsing a piece of text into its Abstract Meaning Representation (AMR): Graph Spanning based Parsing (GSP). One novel characteristic of GSP is that it constructs a parse graph incrementally in a top-down…
The assignment of weights to attacks in a classical Argumentation Framework allows to compute semantics by taking into account the different importance of each argument. We represent a Weighted Argumentation Framework by a non-binary…
There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and…
We give a new syntax independent definition of the notion of a generalized algebraic theory as an initial object in a category of categories with families (cwfs) with extra structure. To this end we define inductively how to build a valid…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We introduce a linear infinitary $\lambda$-calculus, called $\ell\Lambda_{\infty}$, in which two exponential modalities are available, the first one being the usual, finitary one, the other being the only construct interpreted…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…
Sign language translation (SLT) is typically trained with text in a single spoken language, which limits scalability and cross-language generalization. Earlier approaches have replaced gloss supervision with text-based sentence embeddings,…
In previous work ("From signatures to monads in UniMath"), we described a category-theoretic construction of abstract syntax from a signature, mechanized in the UniMath library based on the Coq proof assistant. In the present work, we…
The Unified Modelling Language is emerging as a de-facto standard for modelling object-oriented systems. However, the semantics document that a part of the standard definition primarily provides a description of the language's syntax and…
Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to…
Textual content around us is growing on a daily basis. Numerous articles are being written as we speak on online newspapers, blogs, or social media. Similarly, recent advances in the AI field, like language models or traditional classic AI…
Spurious ambiguity is the phenomenon whereby distinct derivations in grammar may assign the same structural reading, resulting in redundancy in the parse search space and inefficiency in parsing. Understanding the problem depends on…
Accounts of semantic phenomena often involve extending types of meanings and revising composition rules at the same time. The concept of monads allows many such accounts -- for intensionality, variable binding, quantification and focus --…
Lexical ambiguity is a challenging and pervasive problem in machine translation (\mt). We introduce a simple and scalable approach to resolve translation ambiguity by incorporating a small amount of extra-sentential context in neural \mt.…
Operations of arbitrary arity expressible via addition modulo 2^n and bitwise addition modulo 2 admit a simple description. The identities connecting these two additions have finite basis. Moreover, the universal algebra with these two…