Related papers: From Interpolating Formulas to Separating Language…
When LLMs judge moral dilemmas, do they reach different conclusions in different languages, and if so, why? Two factors could drive such differences: the language of the dilemma itself, or the language in which the model reasons. Standard…
For those of us who generally live in the world of syntax, semantic proof techniques such as reducibility, realizability or logical relations seem somewhat magical despite -- or perhaps due to -- their seemingly unreasonable effectiveness.…
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)}…
An interesting line of research in natural language processing (NLP) aims to incorporate linguistic typology to bridge linguistic diversity and assist the research of low-resource languages. While most works construct linguistic similarity…
Morphological analysis involves predicting the syntactic traits of a word (e.g. {POS: Noun, Case: Acc, Gender: Fem}). Previous work in morphological tagging improves performance for low-resource languages (LRLs) through cross-lingual…
Causal inference has been a pivotal challenge across diverse domains such as medicine and economics, demanding a complicated integration of human knowledge, mathematical reasoning, and data mining capabilities. Recent advancements in…
We investigate the polynomial closure operation (C -> Pol(C)) defined on classes of regular languages. We present an interesting and useful connection relating the separation problem for the class C and the membership problem for it…
Recent reports claim that Large Language Models (LLMs) have achieved the ability to derive new science and exhibit human-level general intelligence. We argue that such claims are not rigorous scientific claims, as they do not satisfy…
Logical reasoning is central to human cognition and intelligence. It includes deductive, inductive, and abductive reasoning. Past research of logical reasoning within AI uses formal language as knowledge representation and symbolic…
We construct Lagrange interpolating polynomials for a set of points and values belonging to the algebra of real quaternions $H\simeq R_{0,2}$, or to the real Clifford algebra $R_{0,3}$. In the quaternionic case, the approach by means of…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
The paper presents a solution to the long-standing question about the decidability of the two-variable fragment of the superintuitionistic predicate logic $\mathbf{QLC}$ defined by the class of linear Kripke frames, which is also the…
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…
We consider the problem of automatically inferring specifications in the branching-time logic, Computation Tree Logic (CTL), from a given system. Designing functional and usable specifications has always been one of the biggest challenges…
This paper is a reflexion on the computability of natural language semantics. It does not contain a new model or new results in the formal semantics of natural language: it is rather a computational analysis of the logical models and…
CLP(H) is an instantiation of the general constraint logic programming scheme with the constraint domain of hedges. Hedges are finite sequences of unranked terms, built over variadic function symbols and three kinds of variables: for terms,…
We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates…
With the technology of the time, Kowalski's seminal 1974 paper {\em Predicate Logic as a Programming Language} was a breakthrough for the use of logic in computer science. It introduced two fundamental ideas: on the declarative side, the…
Ordinary infinitary languages L_{lambda, kappa} satisfy the Interpolation Theorem only in the case lambda <= {aleph_1}, kappa = {aleph_0}, this include first order logic of course. There are also some pairs of such logics satifying…
A regular realizability (RR) problem is testing nonemptiness of intersection of some fixed language (filter) with given regular language. We study here complexity of RR problems. It appears that for any language L there exists RR problem…