Related papers: ABox Abduction via Forgetting in ALC (Long Version…
Large Language Models (LLMs) often produce fluent but factually incorrect responses, a phenomenon known as hallucination. Abstention, where the model chooses not to answer and instead outputs phrases such as "I don't know", is a common…
The aim of this paper is to introduce a new framework for defining abductive reasoning operators based on a notion of retraction in arbitrary logics defined as satisfaction systems. We show how this framework leads to the design of…
An extension of Transformers is proposed that enables explicit relational reasoning through a novel module called the Abstractor. At the core of the Abstractor is a variant of attention called relational cross-attention. The approach is…
Abductive explanations (AXp's) are widely used for understanding decisions of classifiers. Existing definitions are suitable when features are independent. However, we show that ignoring constraints when they exist between features may lead…
Abductive logic programming offers a formalism to declaratively express and solve problems in areas such as diagnosis, planning, belief revision and hypothetical reasoning. Tabled logic programming offers a computational mechanism that…
In order to meet usability requirements, most logic-based applications provide explanation facilities for reasoning services. This holds also for Description Logics, where research has focused on the explanation of both TBox reasoning and,…
Hypothetical Datalog is based on an intuitionistic semantics rather than on a classical logic semantics, and embedded implications are allowed in rule bodies. While the usual implication (i.e., the neck of a Horn clause) stands for…
Most existing computational tools for assumption-based argumentation (ABA) focus on so-called flat frameworks, disregarding the more general case. In this paper, we study an instantiation-based approach for reasoning in possibly non-flat…
Non-deductive reasoning, encompassing inductive and abductive reasoning, is essential in addressing complex real-world questions. One key feature of inductive and abductive reasoning is that there are many valid hypotheses; the simplest…
Deduction is the one of the major forms of inferences and commonly used in formal logic. This kind of inference has the feature of monotonicity, which can be problematic. There are different types of inferences that are not monotonic, e.g.…
Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense world knowledge,…
Uncertain information is being taken into account in an increasing number of application fields. In the meantime, abduction has been proved a powerful tool for handling hypothetical reasoning and incomplete knowledge. Probabilistic logical…
Abstraction is a powerful idea widely used in science, to model, reason and explain the behavior of systems in a more tractable search space, by omitting irrelevant details. While notions of abstraction have matured for deterministic…
The vital role of analogical reasoning in human cognition allows us to grasp novel concepts by linking them with familiar ones through shared relational structures. Despite the attention previous research has given to word analogies, this…
Category theory can be used to state formulas in First-Order Logic without using set membership. Several notable results in logic such as proof of the continuum hypothesis can be elegantly rewritten in category theory. We propose in this…
While inference-time scaling enables LLMs to carry out increasingly long and capable reasoning traces, the patterns and insights uncovered during these traces are immediately discarded once the context window is reset for a new query.…
This study evaluates the GPT-4 Large Language Model's abductive reasoning in complex fields like medical diagnostics, criminology, and cosmology. Using an interactive interview format, the AI assistant demonstrated reliability in generating…
We present a consequence-based calculus for concept subsumption and classification in the description logic ALCHOIQ, which extends ALC with role hierarchies, inverse roles, number restrictions, and nominals. By using standard…
Description logics (DL) are a family of formal languages for representing and reasoning about structured knowledge in terms of concepts and their relationships. A central reasoning problem in DL is concept subsumption. Although this problem…
In this paper we explore a unifying approach --- that of hypotheses assumption --- as a means to provide a semantics for all Normal Logic Programs (NLPs), the Minimal Hypotheses (MH) semantics. This semantics takes a positive hypotheses…