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A better understanding of the emergent computation and problem-solving capabilities of recent large language models is of paramount importance to further improve them and broaden their applicability. This work investigates how a language…
In order to reason about the behaviour of programs described in a programming language, a mathematically rigorous definition of that language is needed. In this paper, we present a machine-checked formalisation of concurrent Core Erlang (a…
A longstanding question in cognitive science concerns the learning mechanisms underlying compositionality in human cognition. Humans can infer the structured relationships (e.g., grammatical rules) implicit in their sensory observations…
Compositionality is thought to be a key component of language, and various compositional benchmarks have been developed to empirically probe the compositional generalization of existing sequence processing models. These benchmarks often…
We compare two recent extensions of the answer set (stable model) semantics of logic programs. One of them, due to Lifschitz, Tang and Turner, allows the bodies and heads of rules to contain nested expressions. The other, due to Niemela and…
We investigate language interpretations of two extensions of the Lambek calculus: with additive conjunction and disjunction and with additive conjunction and the unit constant. For extensions with additive connectives, we show that…
It is well-known that Abstract State Machines (ASMs) can simulate "step-by-step" any type of machines (Turing machines, RAMs, etc.). We aim to overcome two facts: 1) simulation is not identification, 2) the ASMs simulating machines of some…
It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<, +1]) when interpreted over timed words; this remains true even when the time domain is bounded a priori.…
The standard operational semantics of the sequential composition operator gives rise to unbounded branching and forgetfulness when transparent process expressions are put in sequence. Due to transparency, the correspondence between…
We are entering a new era in which software systems are becoming more and more complex and larger. So, the composition of such systems is becoming infeasible by manual means. To address this challenge, self-organising software models…
Language models now provide an interface to express and often solve general problems in natural language, yet their ultimate computational capabilities remain a major topic of scientific debate. Unlike a formal computer, a language model is…
We analyse the expressiveness of the two-valued semantics of abstract argumentation frameworks, normal logic programs and abstract dialectical frameworks. By expressiveness we mean the ability to encode a desired set of two-valued…
The evolution of grammatical systems of syntactic and semantic composition is modeled here with a novel application of reinforcement learning theory. To test the functionalist thesis that speakers' expressive purposes shape their language,…
In combinatorics on words, a classical topic of study is the number of specific patterns appearing in infinite sequences. For instance, many works have been dedicated to studying the so-called factor complexity of infinite sequences, which…
Affine continuous logic is extended to affine integration logic. Affine compactness theorem is proved by both the ultramean construction and Henkin's method. Also, a proof system and a completeness theorem are given. An appropriate variant…
Despite the success of neural models in solving reasoning tasks, their compositional generalization capabilities remain unclear. In this work, we propose a new setting of the structured explanation generation task to facilitate…
Transformers trained on huge text corpora exhibit a remarkable set of capabilities, e.g., performing basic arithmetic. Given the inherent compositional nature of language, one can expect the model to learn to compose these capabilities,…
Compositional generalization is a basic mechanism in human language learning, but current neural networks lack such ability. In this paper, we conduct fundamental research for encoding compositionality in neural networks. Conventional…
Natural language is compositional; the meaning of a sentence is a function of the meaning of its parts. This property allows humans to create and interpret novel sentences, generalizing robustly outside their prior experience. Neural…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…