Related papers: Universal properties of truth
Ontologies formalise how the concepts from a given domain are interrelated. Despite their clear potential as a backbone for explainable AI, existing ontologies tend to be highly incomplete, which acts as a significant barrier to their more…
In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of…
We study existential theories of henselian valued fields of positive characteristic with parameters from a trivially valued subfield. Compared to previous work, we relax perfectness and separability assumptions, and instead work with the…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
Predicate abstraction provides a powerful tool for verifying properties of infinite-state systems using a combination of a decision procedure for a subset of first-order logic and symbolic methods originally developed for finite-state model…
As transformers have gained prominence in natural language processing, some researchers have investigated theoretically what problems they can and cannot solve, by treating problems as formal languages. Exploring such questions can help…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
Uncertainty may be taken to characterize inferences, their conclusions, their premises or all three. Under some treatments of uncertainty, the inferences itself is never characterized by uncertainty. We explore both the significance of…
We investigate to what extent persistent homology benefits from the properties of the usual homology theory.
It is easy to show that a pseudovariety which is reducible with respect to an implicit signature $\sigma$ for the equation $x=y$ can also be defined by $\sigma$-identities. We present several negative examples for the converse using…
We study logic for reasoning with if-then formulas describing dependencies between attributes of objects which are observed in consecutive points in time. We introduce semantic entailment of the formulas, show its fixed-point…
The Unified Modeling Language is extensible, and so can be regarded as a family of languages. Implicitly or explicitly, any particular UML model should be accompanied by a definition of the particular UML family member used for the model.…
We discuss the problems of incompleteness and inexpressibility. We introduce almost self-referential formulas, use them to extend set theory, and relate their expressive power to that of infinitary logic. We discuss the nature of proper…
What is the nature of reality? How should be an answer to this question? At this level, we are so deep that all our concepts are obscure. Quantum theory (QT) is at this level. The quest for interpreting it fails because the clarity of our…
A standard form of analysis for linguistic typology is the universal implication. These implications state facts about the range of extant languages, such as ``if objects come after verbs, then adjectives come after nouns.'' Such…
In this paper we argue that, to its detriment, transparency research overlooks many foundational concepts of artificial intelligence. As an illustrating example we focus on uncertainty quantification in the context of counterfactual…
A general framework of latent trait item response models for continuous responses is given. In contrast to classical test theory models, which traditionally distinguish between true scores and error scores, the responses are clearly linked…
The paper adresses the problem of reasoning with ambiguities. Semantic representations are presented that leave scope relations between quantifiers and/or other operators unspecified. Truth conditions are provided for these representations…
This paper is concerned with the question of when a theory is refutable with certainty on the basis of sequence of primitive observations. Beginning with the simple definition of falsifiability as the ability to be refuted by some finite…
The design of metaprogramming languages requires appreciation of the tradeoffs that exist between important language characteristics such as safety properties, expressive power, and succinctness. Unfortunately, such tradeoffs are little…