Related papers: Symbolic Computation and Automated Reasoning for P…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
We extend first-order logic to include variadic function symbols, and prove a substitution lemma. Two applications are given: one to bounded quantifier elimination and one to the definability of certain Borel sets.
We present a new methodology for utilising machine learning technology in symbolic computation research. We explain how a well known human-designed heuristic to make the choice of variable ordering in cylindrical algebraic decomposition may…
This paper presents the development of a software tool that enables the translation of first-order predicate logic with at most three variables into relation algebra. The tool was developed using the Z3 theorem prover, leveraging its…
Argumentation problems are concerned with determining the acceptability of a set of arguments from their relational structure. When the available information is uncertain, probabilistic argumentation frameworks provide modelling tools to…
Symbolic mathematical computing systems have served as a canary in the coal mine of software systems for more than sixty years. They have introduced or have been early adopters of programming language ideas such ideas as dynamic memory…
First-order iterative optimization methods play a fundamental role in large scale optimization and machine learning. This paper presents control interpretations for such optimization methods. First, we give loop-shaping interpretations for…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
First-order optimization methods have attracted a lot of attention due to their practical success in many applications, including in machine learning. Obtaining convergence guarantees and worst-case performance certificates for first-order…
We propose a presentation of classical propositional tableaux elaborated by application of methods that are noteworthy in program design, namely program derivation with separation of concerns. We start by deriving from a straightforward…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Deep learning techniques lie at the heart of several significant AI advances in recent years including object recognition and detection, image captioning, machine translation, speech recognition and synthesis, and playing the game of Go.…
We introduce SMProbLog, a generalization of the probabilistic logic programming language ProbLog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly…
In this work we propose a multi-valued extension of logic programs under the stable models semantics where each true atom in a model is associated with a set of justifications, in a similar spirit than a set of proof trees. The main…
Automated reasoners, such as SAT/SMT solvers and first-order provers, are becoming the backbones of rigorous systems engineering, being used for example in applications of system verification, program synthesis, and cybersecurity.…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…