Related papers: Weyl's Quantifiers
This paper presents a novel explanation of the cause of quantum probabilities and the Born rule based on the intuitionistic interpretation of quantum mechanics where propositions obey constructive (intuitionistic) logic. The use of…
Bell's theorem is typically understood as the proof that quantum theory is incompatible with local-hidden-variable models. More generally, we can see the violation of a Bell inequality as witnessing the impossibility of explaining quantum…
Consequence-based reasoning can be used to construct proofs that explain entailments of description logic (DL) ontologies. In the literature, one can find multiple consequence-based calculi for reasoning in the $\mathcal{EL}$ family of DLs,…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…
We introduce A-ranked preferential structures and combine them with an accessibility relation. This framework allows us to formalize contrary to duty obligations. Representation results are proved.
It is well known that most constructive and predicative foundations aiming to develop Bishop's constructive analysis are incompatible with a classical predicative development of analysis as put forward by Weyl in his $\textit{Das…
It is argued that there is no evidence for causality as a metaphysical relation in quantum phenomena. The assumption that there are no causal laws, but only probabilities for physical processes constrained by symmetries, leads naturally to…
The purpose of this paper is to give an easy to understand with step-by-step explanation to allow interested people to fully appreciate the power of natural deduction for first-order logic. Natural deduction as a proof system can be used to…
The semantics of determiner phrases, be they definite de- scriptions, indefinite descriptions or quantified noun phrases, is often as- sumed to be a fully solved question: common nouns are properties, and determiners are generalised…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
While model checking has often been considered as a practical alternative to building formal proofs, we argue here that the theory of sequent calculus proofs can be used to provide an appealing foundation for model checking. Since the…
A definition of what counts as an explanation of mathematical statement, and when one explanation is better than another, is given. Since all mathematical facts must be true in all causal models, and hence known by an agent, mathematical…
We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax…
It is widely claimed that the quantile function is equivariant under increasing transformations. We show by a counterexample that this is not true (even for strictly increasing transformations). However, we show that the quantile function…
For the Toeplitz quantization of complex-valued functions on a $2n$-dimensional torus we prove that the expected number of eigenvalues of small random perturbations of a quantized observable satisfies a natural Weyl law. In numerical…
In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic…
The idea of preserving conditional beliefs emerged recently as a new paradigm apt to guide the revision of epistemic states. Conditionals are substantially different from propositional beliefs and need specific treatment. In this paper, we…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
We consider entailment problems involving powerful constraint languages such as frontier-guarded existential rules in which we impose additional semantic restrictions on a set of distinguished relations. We consider restricting a relation…