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Answer Set Programming (ASP) is a prominent problem-modeling and solving framework, whose solutions are called answer sets. Epistemic logic programs (ELP) extend ASP to reason about all or some answer sets. Solutions to an ELP can be seen…
Sentences that present a complex syntax act as a major stumbling block for downstream Natural Language Processing applications whose predictive quality deteriorates with sentence length and complexity. The task of Text Simplification (TS)…
Given a first-order theory $T$ formulated in the usual language of first-order arithmetic, we say that $T$ is of *restricted complexity* if there is some natural number $n$ and some set $\mathcal A$ of $\Sigma_n$-sentences such that $T$ can…
Text generation rarely considers the control of lexical complexity, which limits its more comprehensive practical application. We introduce a novel task of lexical complexity controlled sentence generation, which aims at keywords to…
The theory of regular cost functions is a quantitative extension to the classical notion of regularity. A cost function associates to each input a non-negative integer value (or infinity), as opposed to languages which only associate to…
This chapter presents a brief review of complexity research in mathematics education. We argue how research on complexity, as it pertains to mathematics education, can be viewed as an epistemological discourse, an historical discourse, a…
While large language models (LLMs) equipped with techniques like chain-of-thought prompting have demonstrated impressive capabilities, they still fall short in their ability to reason robustly in complex settings. However, evaluating LLM…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
How can non-classical logic contribute to the analysis of complexity in computer science? In this paper, we give a step towards this question, taking a logical model-theoretic approach to the analysis of complexity in fuzzy constraint…
When programmers want to prove strong program invariants, they are usually faced with a choice between using theorem provers and using traditional programming languages. The former requires them to provide program proofs, which, for many…
The Winograd Schema Challenge is both a commonsense reasoning and natural language understanding challenge, introduced as an alternative to the Turing test. A Winograd schema is a pair of sentences differing in one or two words with a…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
Epistemic logic programs (ELPs) are a popular generalization of standard Answer Set Programming (ASP) providing means for reasoning over answer sets within the language. This richer formalism comes at the price of higher computational…
The \emph{index set} of a computable structure $\mathcal{A}$ is the set of indices for computable copies of $\mathcal{A}$. We determine the complexity of the index sets of various mathematically interesting structures, including arbitrary…
Classical first-order logic is in many ways central to work in mathematics, linguistics, computer science and artificial intelligence, so it is worthwhile to define it in full detail. We present soundness and completeness proofs of a…
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…
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…
Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…
As is the case of many signals produced by complex systems, language presents a statistical structure that is balanced between order and disorder. Here we review and extend recent results from quantitative characterisations of the degree of…
Semantic matching of natural language sentences or identifying the relationship between two sentences is a core research problem underlying many natural language tasks. Depending on whether training data is available, prior research has…