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The framework of generalized probabilistic theories is a powerful tool for studying the foundations of quantum physics. It provides the basis for a variety of recent findings that significantly improve our understanding of the rich physical…
Recent pre-trained language models (PLMs) equipped with foundation reasoning skills have shown remarkable performance on downstream complex tasks. However, the significant structure reasoning skill has been rarely studied, which involves…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
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…
Simple representations of documents based on the occurrences of terms are ubiquitous in areas like Information Retrieval, and also frequent in Natural Language Processing. In this work we propose a logical-probabilistic approach to the…
In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is…
Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates,…
This paper addresses the current lack of a unified formal framework in machine learning theory, as well as the absence of robust theoretical foundations for interpretability and ethical safety assurance. We first construct a formal…
Existing decision-theoretic reasoning frameworks such as decision networks use simple data structures and processes. However, decisions are often made based on complex data structures, such as social networks and protein sequences, and rich…
Theoretically as well as experimentally it is investigated how people represent their knowledge in order to make decisions or to share their knowledge with others. Experiment 1 probes into the ways how people 6ather information about the…
Automated decision making is often complicated by the complexity of the knowledge involved. Much of this complexity arises from the context sensitive variations of the underlying phenomena. We propose a framework for representing…
Machines that can replicate human intelligence with type 2 reasoning capabilities should be able to reason at multiple levels of spatio-temporal abstractions and scales using internal world models. Devising formalisms to develop such…
Information pooling has been extensively formalised across various logical frameworks in distributed systems, characterized by diverse information-sharing patterns. These approaches generally adopt an intersection perspective, aggregating…
Diversity measurement underpins the study of biological systems, but measures used vary across disciplines. Despite their common use and broad utility, no unified framework has emerged for measuring, comparing and partitioning diversity.…
Uncertainties in the real world mean that is impossible for system designers to anticipate and explicitly design for all scenarios that a robot might encounter. Thus, robots designed like this are fragile and fail outside of…
Natural language semantics has recently sought to combine the complementary strengths of formal and distributional approaches to meaning. More specifically, proposals have been put forward to augment formal semantic machinery with…
We develop a logical framework for reasoning about knowledge and evidence in which the agent may be uncertain about how to interpret their evidence. Rather than representing an evidential state as a fixed subset of the state space, our…
Clustering uncertain data has emerged as a challenging task in uncertain data management and mining. Thanks to a computational complexity advantage over other clustering paradigms, partitional clustering has been particularly studied and a…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
One of the most ubiquitous problems in optimization is that of finding all the elements of a finite set at which a function $f$ attains its minimum (or maximum). When the codomain of $f$ is equipped with a total order, it is easy to…