Related papers: Preferential Structures for Comparative Probabilis…
Conditional logics play an important role in recent attempts to formulate theories of default reasoning. This paper investigates first-order conditional logic. We show that, as for first-order probabilistic logic, it is important not to…
Defeasible statements are statements that are likely, or probable, or usually true, but may occasionally be false. Plausible reasoning makes conclusions from statements that are either facts or defeasible statements without using numbers.…
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…
In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…
In this thesis, we present two approaches to a rigorous mathematical and algorithmic foundation of quantitative and statistical inference in constraint-based natural language processing. The first approach, called quantitative constraint…
Probabilistic logic programs are logic programs where some facts hold with a specified probability. Here, we investigate these programs with a causal framework that allows counterfactual queries. Learning the program structure from…
Different types of reasoning impose different structural demands on representational systems, yet no systematic account of these demands exists across psychology, AI, and philosophy of mind. I propose a framework identifying four structural…
With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet,…
When collaborating with an AI system, we need to assess when to trust its recommendations. If we mistakenly trust it in regions where it is likely to err, catastrophic failures may occur, hence the need for Bayesian approaches for…
When we work with information from multiple sources, the formalism each employs to handle uncertainty may not be uniform. In order to be able to combine these knowledge bases of different formats, we need to first establish a common basis…
A first-order conditional logic is considered, with semantics given by a variant of epsilon-semantics, where p -> q means that Pr(q | p) approaches 1 super-polynomially --faster than any inverse polynomial. This type of convergence is…
There are different approaches to qualitative probability, which includes subjective probability. We developed a representation of qualitative probability based on relational systems, which allows modeling uncertainty by probability…
Statistics is sometimes described as the science of reasoning under uncertainty. Statistical models provide one view of this uncertainty, but what is frequently neglected is the 'invisible' portion of uncertainty: that assumed not to exist…
This paper addresses fundamental issues on the nature of the concepts and structures of fuzzy logic, focusing, in particular, on the conceptual and functional differences that exist between probabilistic and possibilistic approaches. A…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
We extend classical Propositional Logic (PL) by adding a new primitive binary connective $\varphi|\psi$, intended to represent the "superposition" of sentences $\varphi$ and $\psi$, an operation motivated by the corresponding notion of…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
We view sorites in terms of stimuli acting upon a system and evoking this system's responses. Supervenience of responses on stimuli implies that they either lack tolerance (i.e., they change in every vicinity of some of the stimuli), or…
Advances in the general capabilities of large language models (LLMs) have led to their use for information retrieval, and as components in automated decision systems. A faithful representation of probabilistic reasoning in these models may…
This paper considers the complexity and properties of KLM-style preferential reasoning in the setting of propositional logic with team semantics and dependence atoms, also known as propositional dependence logic. Preferential team-based…