Related papers: Towards a Decidable LogicWeb via Length-Bounded De…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
The ease and speed of spreading misinformation and propaganda on the Web motivate the need to develop trustworthy technology for detecting fallacies in natural language arguments. However, state-of-the-art language modeling methods exhibit…
Defeasible rules are used in providing computable representations of legal documents and, more recently, have been suggested as a basis for explainable AI. Such applications draw attention to the scalability of implementations. The…
Recent deep-thinking large language models often reason extensively to improve performance, but such lengthy reasoning is not always desirable, as it incurs excessive inference costs with disproportionate performance gains. Controlling…
A logic program is an executable specification. For example, merge sort in pure Prolog is a logical formula, yet shows creditable performance on long linked lists. But such executable specifications are a compromise: the logic is distorted…
We establish decidability for the infinitely many axiomatic extensions of the commutative Full Lambek logic with weakening FLew (i.e. IMALLW) that have a cut-free hypersequent proof calculus (specifically: every analytic structural rule…
"To Appear in Theory and Practice of Logic Programming (TPLP)" This paper presents a technique for the optimization of bound queries over disjunctive deductive databases with constraints. The proposed approach is an extension of the…
We present a propositional logic to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and complete axiomatization…
Metric Temporal Logic, $\mtlfull$ is amongst the most studied real-time logics. It exhibits considerable diversity in expressiveness and decidability properties based on the permitted set of modalities and the nature of time interval…
The study of machine learning-based logical query answering enables reasoning with large-scale and incomplete knowledge graphs. This paper advances this area of research by addressing the uncertainty inherent in knowledge. While the…
Machine learning solutions for pattern classification problems are nowadays widely deployed in society and industry. However, the lack of transparency and accountability of most accurate models often hinders their safe use. Thus, there is a…
We present a proof-theoretic analysis of the logic NL$\lambda$ (Barker \& Shan 2014, Barker 2019). We notably introduce a novel calculus of proof nets and prove it is sound and complete with respect to the sequent calculus for the logic. We…
Linear Temporal Logic (LTL) interpreted on finite traces is a robust specification framework popular in formal verification. However, despite the high interest in the logic in recent years, the topic of their quantitative extensions is not…
This paper discusses the semantics and proof theory of Nilsson's probabilistic logic, outlining both the benefits of its well-defined model theory and the drawbacks of its proof theory. Within Nilsson's semantic framework, we derive a set…
Recently, deep learning models have made great progress in MWP solving on answer accuracy. However, they are uninterpretable since they mainly rely on shallow heuristics to achieve high performance without understanding and reasoning the…
Large language models (LLMs) have shown substantial capacity for generating fluent, contextually appropriate responses. However, they can produce hallucinated outputs, especially when a user query includes one or more false premises-claims…
We introduce a graceful approach to probabilistic inference called bounded conditioning. Bounded conditioning monotonically refines the bounds on posterior probabilities in a belief network with computation, and converges on final…
Logical inference algorithms for conditional independence (CI) statements have important applications from testing consistency during knowledge elicitation to constraintbased structure learning of graphical models. We prove that the…
In recent years, there has been an increasing interest in exploiting logically specified background knowledge in order to obtain neural models (i) with a better performance, (ii) able to learn from less data, and/or (iii) guaranteed to be…
The cut-elimination procedure for the provability logic is known to be problematic: a L\"ob-like rule keeps cut-formulae intact on reduction, even in the principal case, thereby complicating the proof of termination. In this paper, we…