Related papers: A Measure-Free Approach to Conditioning

In interpretable NLP, we require faithful rationales that reflect the model's decision-making process for an explained instance. While prior work focuses on extractive rationales (a subset of the input words), we investigate their…

In this paper a conditional logic is defined and studied. This conditional logic, DmBL, is constructed as a deterministic counterpart to the Bayesian conditional. The logic is unrestricted, so that any logical operations are allowed. A…

Two types of explanations have been receiving increased attention in the literature when analyzing the decisions made by classifiers. The first type explains why a decision was made and is known as a sufficient reason for the decision, also…

We argue that for the proof of Bell's theorem no assumptions about realism or free will are necessary. The key formula \[E(AB|a,b) = \int A(a,b,\lambda)B(a,b,\lambda)\rho(\lambda) d\lambda\] follows from the logic of plausible reasoning…

We describe a representation and a set of inference methods that combine logic programming techniques with probabilistic network representations for uncertainty (influence diagrams). The techniques emphasize the dynamic construction and…

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…

Reasoning under uncertainty is a fundamental challenge in Artificial Intelligence. As with most of these challenges, there is a harsh dilemma between the expressive power of the language used, and the tractability of the computational…

This thesis focuses on advancing probabilistic logic programming (PLP), which combines probability theory for uncertainty and logic programming for relations. The thesis aims to extend PLP to support both discrete and continuous random…

Relational data in its most basic form is a static collection of known facts. However, by learning to infer and deduct additional information and structure, we can massively increase the usefulness of the underlying data. One common form of…

We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…

The intuitive notion of evidence has both semantic and syntactic features. In this paper, we develop an {\em evidence logic} for epistemic agents faced with possibly contradictory evidence from different sources. The logic is based on a…

Assumption-based Argumentation (ABA) is advocated as a unifying formalism for various forms of non-monotonic reasoning, including logic programming. It allows capturing defeasible knowledge, subject to argumentative debate. While, in much…

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…

Rule mining algorithms are one of the fundamental techniques in data mining for disclosing significant patterns in terms of linguistic rules expressed in natural language. In this paper, we revisit the concept of fuzzy implicative rule to…

In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson's constructive logic N4. We do so by formalizing, in this logic, two principles that we call non-contradictory…

We present Bluebell, a program logic for reasoning about probabilistic programs where unary and relational styles of reasoning come together to create new reasoning tools. Unary-style reasoning is very expressive and is powered by…

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear…

In theory, the probabilistic linkage method provides two distinct advantages over non-probabilistic methods, including minimal rates of linkage error and accurate measures of these rates for data users. However, implementations can fall…

There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…

Considerable attention has been given to the problem of non-monotonic reasoning in a belief function framework. Earlier work (M. Ginsberg) proposed solutions introducing meta-rules which recognized conditional independencies in a…