Related papers: Priority Arguments and Epsilon Substitutions
One of the benefit properties implied by the extensionality axiom of Hilbert's epsilon calculus is that the calculus becomes complete with respect to the choice structures as semantics. Another implication of the axiom, discussed in the…
This article re-examines Lawvere's abstract, category-theoretic proof of the fixed-point theorem whose contrapositive is a `universal' diagonal argument. The main result is that the necessary axioms for both the fixed-point theorem and the…
In the context of abstract argumentation, we present the benefits of considering temporality, i.e. the order in which arguments are enunciated, as well as causality. We propose a formal method to rewrite the concepts of acyclic abstract…
Timothy Carlson's patterns of resemblance employ the notion of $\Sigma_1$-elementarity to describe large computable ordinals. It has been conjectured that a relativization of these patterns to dilators leads to an equivalence with…
Nielsen transformations form the basis of a simple and widely used procedure for solving word equations. We make progress on the problem of determining when this procedure terminates in the presence of length constraints. To do this, we…
The goal of this note is to compare two notions, one coming from the theory of rewrite systems and the other from proof theory: confluence and cut elimination. We show that to each rewrite system on terms, we can associate a logical system:…
In this article, we study the relationship between the exponential dichotomy properties of a triangular system of linear difference equations and its associated diagonal system on Hilbert spaces. We stress that all previous results in this…
We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates…
We study the conservativity of extensions by additional strict equalities of dependent type theories (and more general second-order generalized algebraic theories). The conservativity of Extensional Type Theory over Intensional Type Theory…
We introduce ordinal collapsing principles that are inspired by proof theory but have a set theoretic flavor. These principles are shown to be equivalent to iterated $\Pi^1_1$-comprehension and the existence of admissible sets, over weak…
We consider matrix orthogonal polynomials related to Bessel type matrices of weights that can be defined in terms of a given matrix Pearson equation. From a Riemann-Hilbert problem we derive first and second order differential relations for…
We express Brewka's prioritised default logic (PDL) as argumentation using ASPIC+. By representing PDL as argumentation and designing an argument preference relation that takes the argument structure into account, we prove that the…
We study the derivational complexity of rewrite systems whose termination is provable in the dependency pair framework using the processors for reduction pairs, dependency graphs, or the subterm criterion. We show that the derivational…
We investigate the partitioning of partial orders into a minimal number of heapable subsets. We prove a characterization result reminiscent of the proof of Dilworth's theorem, which yields as a byproduct a flow-based algorithm for computing…
Starting with the recursive extended Euclid's algorithm, we apply a systematic approach using matrix notation to transform it into an iterative algorithm. The partial correctness proof derived from the transformation turns out to be very…
We merge computational mechanics' definition of causal states (predictively-equivalent histories) with reproducing-kernel Hilbert space (RKHS) representation inference. The result is a widely-applicable method that infers causal structure…
This paper continues an established line of research about the relations between argumentation theory, particularly assumption-based argumentation, and different kinds of logic programs. In particular, we extend known result of Caminada,…
Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus…
Despite the number of successful applications of the Extreme Learning Machine (ELM), we show that its underlying foundational principles do not have a rigorous mathematical justification. Specifically, we refute the proofs of two main…
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…