Related papers: Introducing the hardline in proof theory
Accretive and monotone operator theory are central branches of nonlinear functional analysis and constitute the abstract study of set-valued mappings between function spaces. This paper deals with the computational properties of certain…
Deciding the positivity of a sequence defined by a linear recurrence with polynomial coefficients and initial condition is difficult in general. Even in the case of recurrences with constant coefficients, it is known to be decidable only…
I give a short overview of Chiral Perturbation Theory, its underlying assumptions and underpinnings. A few examples are included.
The lambda-Pi-calculus modulo theory is a logical framework in which many type systems can be expressed as theories. We present such a theory, the theory U, where proofs of several logical systems can be expressed. Moreover, we identify a…
We define an inference system to capture explanations based on causal statements, using an ontology in the form of an IS-A hierarchy. We first introduce a simple logical language which makes it possible to express that a fact causes another…
Proof theory began in the 1920's as a part of Hilbert's program, which aimed to secure the foundations of mathematics by modeling infinitary mathematics with formal axiomatic systems and proving those systems consistent using restricted,…
We offer a mathematical proof of consistency for Peano Arithmetic PA formalizable in PA. This result is compatible with Goedel's Second Incompleteness Theorem since our consistency proof does not rely on the representation of consistency as…
Godelian sentences of a sufficiently strong and recursively enumerable theory, constructed in Godel's 1931 groundbreaking paper on the incompleteness theorems, are unprovable if the theory is consistent; however, they could be refutable.…
Ordinal analysis is a research program wherein recursive ordinals are assigned to axiomatic theories. According to conventional wisdom, ordinal analysis measures the strength of theories. Yet what is the attendant notion of strength? In…
In this paper, we elaborate ring theoretic properties of nodal orders. In particular, we prove that they are closed under taking crossed products with finite groups.
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…
Simple type theory is formulated for use with the generic theorem prover Isabelle. This requires explicit type inference rules. There are function, product, and subset types, which may be empty. Descriptions (the eta-operator) introduce the…
Argumentation theory is a powerful paradigm that formalizes a type of commonsense reasoning that aims to simulate the human ability to resolve a specific problem in an intelligent manner. A classical argumentation process takes into account…
It is a well known empirical observation that natural axiomatic theories are pre-well-ordered by consistency strength. For any natural theory $T$, the next strongest natural theory is $T+\mathsf{Con}_T$. We formulate and prove a statement…
An ordinal view of independence is studied in the framework of possibility theory. We investigate three possible definitions of dependence, of increasing strength. One of them is the counterpart to the multiplication law in probability…
We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…
In the present paper we are interested in simple forcing notions and Forcing Axioms. A starting point for our investigations was the article [JR1] in which several problems were posed. We answer some of those problems here.
This paper elaborates on a new approach of the question of the proof-theoretic study of concurrent interaction called "proofs as schedules". Observing that proof theory is well suited to the description of confluent systems while…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
The provability logic of a theory $T$ captures the structural behavior of formalized provability in $T$ as provable in $T$ itself. Like provability, one can formalize the notion of relative interpretability giving rise to interpretability…