Related papers: PIE -- Proving, Interpolating and Eliminating on t…
Autoepistemic logic extends propositional logic by the modal operator L. A formula that is preceded by an L is said to be "believed". The logic was introduced by Moore 1985 for modeling an ideally rational agent's behavior and reasoning…
This text discusses several popular explanatory methods that go beyond the error measurements and plots traditionally used to assess machine learning models. Some of the explanatory methods are accepted tools of the trade while others are…
First-order logic is the basis for many knowledge representation formalisms and methods. Providing technological support for learning to write first-order formulas for natural language specifications requires methods to test formulas for…
Idiomatic expressions like `out of the woods' and `up the ante' present a range of difficulties for natural language processing applications. We present work on the annotation and extraction of what we term potentially idiomatic expressions…
Inductive Logic Programming (ILP) approaches like Meta \-/ Interpretive Learning (MIL) can learn, from few examples, recursive logic programs with invented predicates that generalise well to unseen instances. This ability relies on a…
First-order logic (FOL) has proved to be a versatile and expressive tool as the basis of abstract modeling languages. Used to verify complex systems with unbounded domains, such as heap-manipulating programs and distributed protocols, FOL,…
We provide an overall description of the Ciao multiparadigm programming system emphasizing some of the novel aspects and motivations behind its design and implementation. An important aspect of Ciao is that, in addition to supporting logic…
To support reasoning about properties of programs operating with boolean values one needs theorem provers to be able to natively deal with the boolean sort. This way, program properties can be translated to first-order logic and theorem…
Learning and logic are distinct and remarkable approaches to prediction. Machine learning has experienced a surge in popularity because it is robust to noise and achieves high performance; however, ML experiences many issues with knowledge…
Pragmatic reasoning, inferring intended meaning beyond literal semantics, underpins everyday communication yet remains difficult for large language models. We present the Contextual Emotional Inference (CEI) Benchmark: 300 human-validated…
When working on intelligent tutor systems designed for mathematics education and its specificities, an interesting objective is to provide relevant help to the students by anticipating their next steps. This can only be done by knowing,…
This paper develops a general methodology to connect propositional and first-order interpolation. In fact, the existence of suitable skolemizations and of Herbrand expansions together with a propositional interpolant suffice to construct a…
Pre-trained language models (PLMs) leverage chains-of-thought (CoT) to simulate human reasoning and inference processes, achieving proficient performance in multi-hop QA. However, a gap persists between PLMs' reasoning abilities and those…
This paper discusses the representation of ontologies in the first-order logical environment {\ttfamily FOLE}. An ontology defines the primitives with which to model the knowledge resources for a community of discourse. These primitives…
Natural language understanding applications such as interactive planning and face-to-face translation require extensive inferencing. Many of these inferences are based on the meaning of particular open class words. Providing a…
We derive a Prolog theorem prover for an Intuitionistic Epistemic Logic by starting from the sequent calculus {\bf G4IP} that we extend with operator definitions providing an embedding in intuitionistic propositional logic ({\bf IPC}). With…
HolPy is an interactive theorem proving system implemented in Python. It uses higher-order logic as the logical foundation. Its main features include a pervasive use of macros in producing, checking, and storing proofs, a JSON-based format…
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;…
Grounding is the task of reducing a first-order theory and finite domain to an equivalent propositional theory. It is used as preprocessing phase in many logic-based reasoning systems. Such systems provide a rich first-order input language…
The vast amounts of on-line text now available have led to renewed interest in information extraction (IE) systems that analyze unrestricted text, producing a structured representation of selected information from the text. This paper…