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Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
Structured recursion schemes such as folds and unfolds have been widely used for structuring both functional programs and program semantics. In this context, it has been customary to implement denotational semantics as folds over an…
An abstract argumentation framework can be used to model the argumentative stance of an agent at a high level of abstraction, by indicating for every pair of arguments that is being considered in a debate whether the first attacks the…
Many applications of automated deduction require reasoning in first-order logic modulo background theories, in particular some form of integer arithmetic. A major unsolved research challenge is to design theorem provers that are "reasonably…
The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled…
We define a new decidable logic for expressing and checking invariants of programs that manipulate dynamically-allocated objects via pointers and destructive pointer updates. The main feature of this logic is the ability to limit the…
Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the…
Large language models have recently shown promising progress in mathematical reasoning when fine-tuned with human-generated sequences walking through a sequence of solution steps. However, the solution sequences are not formally structured…
We consider logic-based argumentation in which an argument is a pair (Fi,al), where the support Fi is a minimal consistent set of formulae taken from a given knowledge base (usually denoted by De) that entails the claim al (a formula). We…
In this paper we show that reversible analysis of logic languages by abstract interpretation can be performed without loss of precision by systematically refining abstract domains. The idea is to include semantic structures into abstract…
This paper improves two existing theorems of interest to neo-logicist philosophers of mathematics. The first is a classification theorem due to Fine for equivalence relations between concepts definable in a well-behaved second-order logic.…
A well-established approach to proving progress properties such as deadlock-freedom and termination is to associate obligations with threads. For example, in most existing work the proof rule for lock acquisition prescribes a standard usage…
Juba recently proposed a formulation of learning abductive reasoning from examples, in which both the relative plausibility of various explanations, as well as which explanations are valid, are learned directly from data. The main…
Recent neural models for relation extraction with distant supervision alleviate the impact of irrelevant sentences in a bag by learning importance weights for the sentences. Efforts thus far have focused on improving extraction accuracy but…
Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly…
This paper presents an end-to-end system for fact extraction and verification using textual and tabular evidence, the performance of which we demonstrate on the FEVEROUS dataset. We experiment with both a multi-task learning paradigm to…
A typical way of analyzing the time complexity of functional programs is to extract a recurrence expressing the running time of the program in terms of the size of its input, and then to solve the recurrence to obtain a big-O bound. For…
The verification community has studied dynamic data structures primarily in a bottom-up way by analyzing pointers and the shapes induced by them. Recent work in fields such as separation logic has made significant progress in extracting…
With their increase in performance, neural network architectures also become more complex, necessitating explainability. Therefore, many new and improved methods are currently emerging, which often generate so-called saliency maps in order…
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…