Related papers: The Architecture of Truth
I make the case that the Universe according to unitary (no-collapse) quantum theory has a branching structure, and so can literally be regarded as a "many-worlds" theory. These worlds are not part of the fundamental ontology of quantum…
The fundamental elements of evidential reasoning problems are described, followed by a discussion of the structure of various types of problems. Bayesian inference networks and state space formalism are used as the tool for problem…
Although information theory resolves inconsistencies (known under the form of famous enigmas) of the traditional approach of thermostatistics, its place in the corresponding literature is not what it deserves. This article supports the idea…
Beneficial societal outcomes cannot be guaranteed by aligning individual AI systems with the intentions of their operators or users. Even an AI system that is perfectly aligned to the intentions of its operating organization can lead to bad…
We extend the formalism of I to a global setting for which a theorem on fiber integrals and a Fubini theorem are obtained. We compare our formalism to the previous constructions of motivic integration in the geometric and arithmetic cases.
While it is not generally reflected in the `nice' datasets used for benchmarking machine learning algorithms, the real-world is full of processes that would be best described as many-to-many. That is, a single input can potentially yield…
Argumentation is the process of constructing arguments about propositions, and the assignment of statements of confidence to those propositions based on the nature and relative strength of their supporting arguments. The process is modelled…
This paper shows the initial stages of development, from first principles, of a formal logic to characterise and then explore issues in a broadly defined idea of Veracity, which includes properties of demonstrability, truth, trust and…
The communication of meaning as different from (Shannon-type) information is central to Luhmann's social systems theory and Giddens' structuration theory of action. These theories share an emphasis on reflexivity, but focus on meaning along…
An answer set is a plain set of literals which has no further structure that would explain why certain literals are part of it and why others are not. We show how argumentation theory can help to explain why a literal is or is not contained…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
In this work we investigate the representation of counterfactual conditionals using the vector logic, a matrix-vectors formalism for logical functions and truth values. Inside this formalism, the counterfactuals can be transformed in…
There are different meanings of foundation of mathematics: philosophical, logical, and mathematical. Here foundations are considered as a theory that provides means (concepts, structures, methods etc.) for the development of whole…
Classically, any structure for a signature $\Sigma$ may be completed to a model of a desired regular theory $T$ by means of the chase construction or small object argument. Moreover, this exhibits $\mathrm{Mod}(T)$ as weakly reflective in…
We present a logical framework that enables us to define a formal theory of computational trust in which this notion is analysed in terms of epistemic attitudes towards the possible objects of trust and in relation to existing evidence in…
The notion of class is ubiquitous in computer science and is central in many formalisms for the representation of structured knowledge used both in knowledge representation and in databases. In this paper we study the basic issues…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…
Adopting the scientific method a theoretical model is proposed as foundation for information science and technology, extending the existing theory of signaling: a fact f becomes known in a physical system only following the success of a…