Related papers: Knowledge of Uncertain Worlds: Programming with Lo…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
We present an approach to program reasoning which inserts between a program and its verification conditions an additional layer, the denotation of the program expressed in a declarative form. The program is first translated into its…
In large language models (LLMs), code and reasoning reinforce each other: code offers an abstract, modular, and logic-driven structure that supports reasoning, while reasoning translates high-level goals into smaller, executable steps that…
Providing explanations for the outputs of artificial neural networks (ANNs) is crucial in many contexts, such as critical systems, data protection laws and handling adversarial examples. Logic-based methods can offer explanations with…
The paper presents two equivalent definitions of answer sets for logic programs with aggregates. These definitions build on the notion of unfolding of aggregates, and they are aimed at creating methodologies to translate logic programs with…
Constraint propagation is one of the techniques central to the success of constraint programming. To reduce search, fast algorithms associated with each constraint prune the domains of variables. With global (or non-binary) constraints, the…
An uninterpreted program (UP) is a program whose semantics is defined over the theory of uninterpreted functions. This is a common abstraction used in equivalence checking, compiler optimization, and program verification. While simple, the…
Constraint logic programming emerged in the late 80's as a highly declarative class of programming languages based on first-order logic and theories with decidable constraint languages, thereby subsuming Prolog restricted to equality…
The quality of rationales is essential in the reasoning capabilities of language models. Rationales not only enhance reasoning performance in complex natural language tasks but also justify model decisions. However, obtaining impeccable…
Logic is playing an increasingly important role in the engineering of real-time, hybrid, and cyber-physical systems, but mostly in the form of posterior verification and high-level analysis. The core methodology in the design of real-world…
Answer Set Programming (ASP) is an important logic programming paradigm within the field of Knowledge Representation and Reasoning. As a concise, human-readable, declarative language, ASP is an excellent tool for developing trustworthy…
Artificial intelligence has recently experienced remarkable advances, fueled by large models, vast datasets, accelerated hardware, and, last but not least, the transformative power of differentiable programming. This new programming…
Extended multi-adjoint logic programming arises as an extension of multi-adjoint normal logic programming where constraints and a special type of aggregator operator have been included. The use of this general aggregator operator permits to…
Two major difficulties in using default logics are their intractability and the problem of selecting among multiple extensions. We propose an approach to these problems based on integrating nommonotonic reasoning with plausible reasoning…
Logic-based problems such as planning, theorem proving, or puzzles, typically involve combinatoric search and structured knowledge representation. Artificial neural networks are very successful statistical learners, however, for many years,…
One recurring problem in program development is that of understanding how to re-use code developed by a third party. In the context of (constraint) logic programming, part of this problem reduces to figuring out how to query a program. If…
While neural models show remarkable accuracy on individual predictions, their internal beliefs can be inconsistent across examples. In this paper, we formalize such inconsistency as a generalization of prediction error. We propose a…
The use of meta-rules in logic, i.e., rules whose content includes other rules, has recently gained attention in the setting of non-monotonic reasoning: a first logical formalisation and efficient algorithms to compute the (meta)-extensions…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
The recent efforts in automation of machine learning or data science has achieved success in various tasks such as hyper-parameter optimization or model selection. However, key areas such as utilizing domain knowledge and data semantics are…