Related papers: Languages with Decidable Learning: A Meta-theorem

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…

It is widely acknowledged that function symbols are an important feature in answer set programming, as they make modeling easier, increase the expressive power, and allow us to deal with infinite domains. The main issue with their…

We present a novel approach to construction of a formal semantics for a programming language. Our approach, using a parametric denotational semantics, allows the semantics to be easily extended to support new language features, and…

In language learning in the limit, the most common type of hypothesis is to give an enumerator for a language. This so-called $W$-index allows for naming arbitrary computably enumerable languages, with the drawback that even the membership…

We identify a decidable synthesis problem for a class of programs of unbounded size with conditionals and iteration that work over infinite data domains. The programs in our class use uninterpreted functions and relations, and abide by a…

By algorithmic metatheorems for a model checking problem P over infinite-state systems we mean generic results that can be used to infer decidability (possibly complexity) of P not only over a specific class of infinite systems, but over a…

We introduce a new application for inductive logic programming: learning the semantics of programming languages from example evaluations. In this short paper, we explored a simplified task in this domain using the Metagol meta-interpretive…

We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…

We study the question of whether a given regular language of finite trees can be defined in first-order logic. We develop an algebraic approach to address this question and we use it to derive several necessary and sufficient conditions for…

Making a linguistic theory is like making a programming language: one typically devises a type system to delineate the acceptable utterances and a denotational semantics to explain observations on their behavior. Via this connection, the…

We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…

We study the problem of learning differentiable functions expressed as programs in a domain-specific language. Such programmatic models can offer benefits such as composability and interpretability; however, learning them requires…

Large language models (LLMs) are increasingly evaluated on reasoning tasks, yet their logical abilities remain contested. To address this, we study LLMs' reasoning in a well-defined fragment of logic: syllogistic reasoning. We cast the…

Sets with atoms serve as an alternative to ZFC foundations for mathematics, where some infinite, though highly symmetric sets, behave in a finitistic way. Therefore, one can try to carry over analysis of the classical algorithms from finite…

We prove that all standard subregular language classes are linearly separable when represented by their deciding predicates. This establishes finite observability and guarantees learnability with simple linear models. Synthetic experiments…

It is well known that for a regular tree language it is decidable whether or not it can be recognized by a deterministic top-down tree automaton (DTA). However, the computational complexity of this problem has not been studied. We show that…

Recognizable languages of finite words are part of every computer science cursus, and they are routinely described as a cornerstone for applications and for theory. We would like to briefly explore why that is, and how this word-related…

There are many types of automata and grammar models that have been studied in the literature, and for these models, it is common to determine whether certain problems are decidable. One problem that has been difficult to answer throughout…

Programming with logic for sophisticated applications must deal with recursion and negation, which together have created significant challenges in logic, leading to many different, conflicting semantics of rules. This paper describes a…

The class of Boolean combinations of tree languages recognized by deterministic top-down tree automata (also known as deterministic root-to-frontier automata) is studied. The problem of determining for a given regular tree language whether…