Related papers: Logic for approximate entailment in ordered univer…
Incorrectness Separation Logic (ISL) is a proof system that is tailored specifically to resolve problems of under-approximation in programs that manipulate heaps, and it primarily focuses on bug detection. This approach is different from…
We present probabilistic logic programming under inheritance with overriding. This approach is based on new notions of entailment for reasoning with conditional constraints, which are obtained from the classical notion of logical entailment…
We study how well large language models (LLMs) explain their generations through rationales -- a set of tokens extracted from the input text that reflect the decision-making process of LLMs. Specifically, we systematically study rationales…
This paper introduces techniques to integrate WordNet into a Fuzzy Logic Programming system. Since WordNet relates words but does not give graded information on the relation between them, we have implemented standard similarity measures and…
\emph{Approximation Theory} uses nicely-behaved subcategories to understand entire categories, just as projective modules are used to approximate arbitrary modules in classical homological algebra. We use set-theoretic \emph{elementary…
LogicWeb has traditionally lacked devices for dealing with intractable queries. We address this limitation by adopting length-bounded inference, a form of approximate reasoning. A length-bounded inference is of the form $prov(P,G,n)$ which…
Rough set theory is a new mathematical approach to imperfect knowledge. The notion of rough sets is generalized by using an arbitrary binary relation on attribute values in information systems, instead of the trivial equality relation. The…
Rule-based reasoning is an essential part of human intelligence prominently formalized in artificial intelligence research via logic programs. Describing complex objects as the composition of elementary ones is a common strategy in computer…
In Bayesian inference, making deductions about a parameter of interest requires one to sample from or compute an integral against a posterior distribution. A popular method to make these computations cheaper in high-dimensional settings is…
We introduce Bifurcation Logic, BL, which combines a basic classical modality with separating conjunction * together with its naturally associated multiplicative implication, that is defined using the modal ordering. Specifically, a formula…
The standard reasoning problem, concept satisfiability, in the basic description logic ALC is PSPACE-complete, and it is EXPTIME-complete in the presence of unrestricted axioms. Several fragments of ALC, notably logics in the FL, EL, and…
This paper aims to provide an analysis of what it means when we say that a pair of theories, very generously construed, are equivalent in the sense that they are interdefinable. With regard to theories articulated in first order logic, we…
The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…
The growing interest in Explainable Artificial Intelligence (XAI) motivates promising studies of computing optimal Interpretable Machine Learning models, especially decision trees. Such models generally provide optimality in compact size or…
A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative…
Conditionals are useful for modelling, but are not always sufficiently expressive for capturing information accurately. In this paper we make the case for a form of conditional that is situation-based. These conditionals are more expressive…
This paper concerns the relation between imperative process algebra and rely/guarantee logic. An imperative process algebra is complemented by a rely/guarantee logic that can be used to reason about how data change in the course of a…
With the increasing number of deep learning applications, there is a growing demand for explanations. Visual explanations provide information about which parts of an image are relevant for a classifier's decision. However, highlighting of…
An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…
The large and still increasing popularity of deep learning clashes with a major limit of neural network architectures, that consists in their lack of capability in providing human-understandable motivations of their decisions. In situations…