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Rewriting is a formalism widely used in computer science and mathematical logic. The classical formalism has been extended, in the context of functional languages, with an order over the rules and, in the context of rewrite based languages,…
For many decades, advances in static verification have focused on linear integer arithmetic (LIA) programs. Many real-world programs are, however, written with non-linear integer arithmetic (NLA) expressions, such as programs that model…
This paper proposes algorithms for learning two-level Boolean rules in Conjunctive Normal Form (CNF, i.e. AND-of-ORs) or Disjunctive Normal Form (DNF, i.e. OR-of-ANDs) as a type of human-interpretable classification model, aiming for a…
A formal context consists of objects, properties, and the incidence relation between them. Various notions of concepts defined with respect to formal contexts and their associated algebraic structures have been studied extensively,…
String diagrams provide a convenient graphical framework which may be used for equational reasoning about morphisms of monoidal categories. However, unlike term rewriting, rewriting string diagrams results in shorter equational proofs,…
We introduce the notion of multipass automata as a generalization of pushdown automata and study the classes of languages accepted by such machines. The class of languages accepted by deterministic multipass automata is exactly the Boolean…
Partial correctness of imperative or functional programming divides in logic programming into two notions. Correctness means that all answers of the program are compatible with the specification. Completeness means that the program produces…
Common algorithms for sentence and word-alignment allow the automatic identification of word translations from parallel texts. This study suggests that the identification of word translations should also be possible with non-parallel and…
In this paper, we propose a model-agnostic cost-effective approach to developing bilingual base large language models (LLMs) to support English and any target language. The method includes vocabulary expansion, initialization of new…
When a bilingual student learns to solve word problems in math, we expect the student to be able to solve these problem in both languages the student is fluent in,even if the math lessons were only taught in one language. However, current…
Boolean matching is an important problem in logic synthesis and verification. Despite being well-studied for conventional Boolean circuits, its treatment for reversible logic circuits remains largely, if not completely, missing. This work…
Multilingual Large Language Models (LLMs) exhibit remarkable cross-lingual abilities, yet often exhibit a systematic bias toward the representations from other languages, resulting in semantic interference when generating content in…
Refusal behavior in large language models (LLMs) enables them to decline responding to harmful, unethical, or inappropriate prompts, ensuring alignment with ethical standards. This paper investigates refusal behavior across six LLMs from…
We contemplate a higher-level bipolar abstract argumentation for non-elementary arguments such as: X argues against Ys sincerity with the fact that Y has presented his argument to draw a conclusion C, by omitting other facts which would not…
This paper aims at providing a comprehensive solution to the archaic open problem: how to define semantics of three-valued modal logic with vivid intuitive picture, convincing philosophical justification as well as versatile practical…
We introduce a simple approach that uses a large language model (LLM) to automatically implement a fully interpretable rule-based data-to-text system in pure Python. Experimental evaluation on the WebNLG dataset showed that such a…
Natural language generation (NLG) systems are commonly evaluated using n-gram overlap measures (e.g. BLEU, ROUGE). These measures do not directly capture semantics or speaker intentions, and so they often turn out to be misaligned with our…
Although large language models (LLMs) have been touted for their ability to generate natural-sounding text, there are growing concerns around possible negative effects of LLMs such as data memorization, bias, and inappropriate language.…
This note presents a method of interpreting the tree adjoining languages as the natural third step in a hierarchy that starts with the regular and the context-free languages. The central notion in this account is that of a higher-order…
The model checking problem for multi-agent systems against Strategy Logic specifications is known to be non-elementary. On this logic several fragments have been defined to tackle this issue but at the expense of expressiveness. In this…