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Probabilistic programming provides a convenient lingua franca for writing succinct and rigorous descriptions of probabilistic models and inference tasks. Several probabilistic programming languages, including Anglican, Church or Hakaru,…
Language is typically modelled with discrete sequences. However, the most successful approaches to language modelling, namely neural networks, are continuous and smooth function approximators. In this work, we show that Transformer-based…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…
We study the algebraic theory of computable functions, which can be viewed as arising from possibly non-halting computer programs or algorithms, acting on some state space, equipped with operations of composition, {\em if-then-else} and…
A circular program creates a data structure whose computation depends upon itself or refers to itself. The technique is used to implement the classic data structures circular and doubly-linked lists, threaded trees and queues, in a…
Implementing a complex concept as an executable model in a strongly typed, purely functional language hits a sweet spot between mere simulation and formal specification. For research and education it is often desirable to enrich the…
Over the years, integer linear programs have been employed to model inference in many natural language processing problems. This survey is meant to guide the reader through the process of framing a new inference problem as an instance of an…
An FOL-program consists of a background theory in a decidable fragment of first-order logic and a collection of rules possibly containing first-order formulas. The formalism stems from recent approaches to tight integrations of ASP with…
Extensions of Answer Set Programming with language constructs from temporal logics, such as temporal equilibrium logic over finite traces (TELf), provide an expressive computational framework for modeling dynamic applications. In this…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
Representing and reasoning about qualitative temporal information is an essential part of many artificial intelligence tasks. Lots of models have been proposed in the litterature for representing such temporal information. All derive from a…
Theoretical foundations of compositional reasoning about heaps in imperative programming languages are investigated. We introduce a novel concept of compositional symbolic memory and its relevant properties. We utilize these formal…
Human beings possess the most sophisticated computational machinery in the known universe. We can understand language of rich descriptive power, and communicate in the same environment with astonishing clarity. Two of the many contributors…
We present the first formalization and metatheory of language soundness for a user-schedulable language, the widely used array processing language Halide. User-schedulable languages strike a balance between abstraction and control in…
Language sciences rely less and less on formal syntax as their base. The reason is probably its lack of psychological reality, knowingly avoided. Philosophers of science call for a paradigm shift in which explanations are by mechanisms, as…
Many recent analyses for conventional imperative programs begin by transforming programs into logic programs, capitalising on existing LP analyses and simple LP semantics. We propose using logic programs as an intermediate program…
In this paper, we introduce methods of encoding propositional logic programs in vector spaces. Interpretations are represented by vectors and programs are represented by matrices. The least model of a definite program is computed by…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational…
We present the linear first-order intermediate language IL for verified compilers. IL is a functional language with calls to a nondeterministic environment. We give IL terms a second, imperative semantic interpretation and obtain a register…
Tool-integrated reasoning (TIR) has emerged as a dominant paradigm for mathematical problem solving in language models, combining natural language (NL) reasoning with code execution. However, this interleaved setup has three key…