Related papers: Qualitative reasoning in a two-layered framework

Hyperproperties allow one to specify properties of systems that inherently involve not single executions of the system, but several of them at once: observational determinism and non-inference are two examples of such properties used to…

Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired…

Structured reasoning over natural language inputs remains a core challenge in artificial intelligence, as it requires bridging the gap between unstructured linguistic expressions and formal logical representations. In this paper, we propose…

Many-valued logics in general, and fuzzy logics in particular, usually focus on a notion of consequence based on preservation of full truth, typical represented by the value 1 in the semantics given the real unit interval [0,1]. In a recent…

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…

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…

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…

Language Models (LMs) have shown promising performance in natural language generation. However, as LMs often generate incorrect or hallucinated responses, it is crucial to correctly quantify their uncertainty in responding to given inputs.…

This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…

This paper explores the hard problem of consciousness from a different perspective. Instead of drawing distinctions between the physical and the mental, an exploration of a more foundational relationship is examined: the relationship…

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…

Model inadequacy and measurement uncertainty are two of the most confounding aspects of inference and prediction in quantitative sciences. The process of scientific inference (the inverse problem) and prediction (the forward problem)…

The quality of rationales is essential in the reasoning capabilities of language models. Rationales not only enhance reasoning performance in complex natural language tasks but also justify model decisions. However, obtaining impeccable…

Making a decision is often a matter of listing and comparing positive and negative arguments. In such cases, the evaluation scale for decisions should be considered bipolar, that is, negative and positive values should be explicitly…

Uncertainty estimation is critical for deploying reasoning language models, yet remains poorly understood under extended chain-of-thought reasoning. We study parallel sampling as a fully black-box approach using verbalized confidence and…

The paper is a contribution both to the theoretical foundations and to the actual construction of efficient automatizable proof procedures for non-classical logics. We focus here on the case of finite-valued logics, and exhibit: (i) 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…

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…

Information accounting provides a better foundation for hypothesis testing than does uncertainty quantification. A quantitative account of science is derived under this perspective that alleviates the need for epistemic bridge principles,…

We take the view that physical quantities are values generated by processes in measurement, not pre-existent objective quantities, and that a measurement result is strictly a product of the apparatus and the subject of the measurement. We…