Related papers: Anaphora and Ellipsis in Lambek Calculus with a Re…
We present new descriptive complexity characterisations of classes REG (regular languages), LCFL (linear context-free languages) and CFL (context-free languages) as restrictions on inference rules, size of formulae and permitted connectives…
Word embeddings are rich word representations, which in combination with deep neural networks, lead to large performance gains for many NLP tasks. However, word embeddings are represented by dense, real-valued vectors and they are therefore…
The Lambek calculus is a substructural logic known to be closely related to the formal language theory: on the one hand, it is used for generating formal languages by means of categorial grammars and, on the other hand, it has formal…
We develop the operational semantics of an untyped probabilistic lambda-calculus with continuous distributions, as a foundation for universal probabilistic programming languages such as Church, Anglican, and Venture. Our first contribution…
We explore the consequences of layering a Lambek proof system over an arbitrary (constraint) logic. A simple model-theoretic semantics for our hybrid language is provided for which a particularly simple combination of Lambek's and the proof…
In the first part we show that a vector-valued almost separably valued function $f$ is holomorphic (harmonic) if and only if it is dominated by an $L^1_\mathrm{loc}$ function and there exists a separating set $W\subset X'$ such that…
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.…
Morrill and Valentin in the paper "Computational coverage of TLG: Nonlinearity" considered an extension of the Lambek calculus enriched by a so-called "exponential" modality. This modality behaves in the "relevant" style, that is, it allows…
Large language models (LLMs) often encode word-form variation (e.g., walk vs. walked) as linear directions in the embedding space. However, standard tokenization algorithms treat such variants as distinct words with different vocabulary…
Language models (LMs) are trained on billions of tokens in an attempt to recover the true language distribution. Still, vanilla random sampling from LMs yields low quality generations. Decoding algorithms attempt to restrict the LM…
We designed a superposition calculus for a clausal fragment of extensional polymorphic higher-order logic that includes anonymous functions but excludes Booleans. The inference rules work on $\beta\eta$-equivalence classes of…
In this paper, we study logics of bounded distributive residuated lattices with modal operators considering $\Box$ and $\Diamond$ in a noncommutative setting. We introduce relational semantics for such substructural modal logics. We prove…
This paper proves a homomorphism between extensional formal semantics and distributional vector space semantics, demonstrating structural compatibility. Formal semantics models meaning as reference, using logical structures to map…
Capturing the semantic relations of words in a vector space contributes to many natural language processing tasks. One promising approach exploits lexico-syntactic patterns as features of word pairs. In this paper, we propose a novel model…
Pregroup grammars were developed in 1999 and stayed Lambek's preferred algebraic model of grammar. The set-theoretic semantics of pregroups, however, faces an ambiguity problem. In his latest book, Lambek suggests that this problem might be…
Large language models (LLMs) were invented for natural language tasks such as translation, but they have proved that they can perform highly complex functions across domains. Additionally, they have been thought to develop new skills…
In this paper we extend the research programme in algebraic proof theory from axiomatic extensions of the full Lambek calculus to logics algebraically captured by certain varieties of normal lattice expansions (normal LE-logics).…
Algebraic effects & handlers have become a standard approach for side-effects in functional programming. Their modular composition with other effects and clean separation of syntax and semantics make them attractive to a wide audience.…
We present Lilac, a separation logic for reasoning about probabilistic programs where separating conjunction captures probabilistic independence. Inspired by an analogy with mutable state where sampling corresponds to dynamic allocation, we…
In this paper, we discuss the question whether phrasal comparatives should be given a direct interpretation, or require an analysis as elliptic constructions, and answer it with Yes and No. The most adequate analysis of wide reading…