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Large Language Models (LLMs) are known to acquire reasoning capabilities through shared inference patterns in pre-training data, which are further elicited via Chain-of-Thought (CoT) practices. However, whether fundamental reasoning…
In this paper we investigate the complexity of abduction, a fundamental and important form of non-monotonic reasoning. Given a knowledge base explaining the world's behavior it aims at finding an explanation for some observed manifestation.…
In order to formulate mathematical conjectures likely to be true, a number of base cases must be determined. However, many combinatorial problems are NP-hard and the computational complexity makes this research approach difficult using a…
Investigating the reasoning abilities of transformer models, and discovering new challenging tasks for them, has been a topic of much interest. Recent studies have found these models to be surprisingly strong at performing deductive…
We lift the SCL calculus for first-order logic without equality to the SCL(T) calculus for first-order logic without equality modulo a background theory. In a nutshell, the SCL(T) calculus describes a new way to guide hierarchic resolution…
Transformer large language models (LLMs) have sparked admiration for their exceptional performance on tasks that demand intricate multi-step reasoning. Yet, these models simultaneously show failures on surprisingly trivial problems. This…
Previous work has shown that reasoning with real-time temporal logics is often simpler when restricted to models with bounded variability---where no more than v events may occur every V time units, for given v, V. When reasoning about…
In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…
Conflict and dependency analysis is an important static analysis tool that provides an overview of the potential interactions of (graph) transformation rules. This analysis is based on critical pairs and initial conflicts, which represent…
Practically all programming languages allow the programmer to split a program into several modules which brings along several advantages in software development. In this paper, we are interested in the area of answer-set programming where…
Description Logics (DLs) are a family of knowledge representation formalisms mainly characterised by constructors to build complex concepts and roles from atomic ones. Expressive role constructors are important in many applications, but can…
Partial label learning (PLL) is a significant weakly supervised learning framework, where each training example corresponds to a set of candidate labels and only one label is the ground-truth label. For the first time, this paper…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there is constraint logic programming which computes a solution as an answer substitution to a query containing the…
We study the complexity of computational problems arising from existence theorems in extremal combinatorics. For some of these problems, a solution is guaranteed to exist based on an iterated application of the Pigeonhole Principle. This…
We recently described a formalism for reasoning with if-then rules that re expressed with different levels of firmness [18]. The formalism interprets these rules as extreme conditional probability statements, specifying orders of magnitude…
Multimodal large language models (MLLMs) must resolve conflicts when different modalities provide contradictory information, a process we term modality following. Prior work measured this behavior only with coarse dataset-level statistics,…
We investigate the decidability of the definability problem for fragments of first order logic over finite words enriched with modular predicates. Our approach aims toward the most generic statements that we could achieve, which…
The paper analizes a set of issues related to analogy and analogical reasoning, namely: 1) The problem of analogy and its duplicity; 2) The role of analogy in demonstrative reasoning; 3) The role of analogy in non-demonstrative reasoning;…
These notes pose a "proof challenge": a proof, or disproof, of the proposition that "For any given body of information, I, expressed as a one-dimensional sequence of atomic symbols, a multiple alignment concept, described in the document,…
We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…