Related papers: Well-foundedness proof for first-order reflection
Given a first-order sentence, a model-checking computation tests whether the sentence holds true in a given finite structure. Data provenance extracts from this computation an abstraction of the manner in which its result depends on the…
It is widely claimed that the natural axiom systems$\unicode{x2013}$including the large cardinal axioms$\unicode{x2013}$form a well-ordered hierarchy. Yet, as is well-known, it is possible to exhibit non-linearity and ill-foundedness by…
This paper discusses the method of formative rules for first-order term rewriting, which was previously defined for a higher-order setting. Dual to the well-known usable rules, formative rules allow dropping some of the term constraints…
Proofs are traditionally syntactic, inductively generated objects. This paper reformulates first-order logic (predicate calculus) with proofs which are graph-theoretic rather than syntactic. It defines a combinatorial proof of a formula…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
It is known that any rational abstract numeration system is faithfully, and effectively, represented by an N-rational series. A simple proof of this result is given which yields a representation of this series which in turn allows a simple…
In this note, we characterize affine and non-affine Coxeter systems among all Coxeter systems in terms of the structure of their reflection orders. For an infinite irreducible system $(W,S)$, we show that affineness can be characterized in…
It is well-known that extending the Hilbert axiomatic system for first-order intuitionistic logic with an exclusion operator, that is dual to implication, collapses the domains of models into a constant domain. This makes it an interesting…
In mathematical logic there are two seemingly distinct kinds of principles called "reflection principles." Semantic reflection principles assert that if a formula holds in the whole universe, then it holds in a set-sized model. Syntactic…
We present a so-called labelling method to insert cost annotations in a higher-order functional program, to certify their correctness with respect to a standard compilation chain to assembly code including safe memory management, and to…
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…
This paper discusses the formalization of proofs "by diagram chasing", a standard technique for proving properties in abelian categories. We discuss how the essence of diagram chases can be captured by a simple many-sorted first-order…
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…
We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…
We give a general overview of ordinal notation systems arising from reflection calculi, and extend the to represent impredicative ordinals up to those representable using Buchholz-style collapsing functions.
The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].
Inspired by the efficient proof procedures discussed in {\em Computability logic} \cite{Jap03,Japic,Japfin}, we describe a heuristic proof procedure for first-order logic. This is a variant of Gentzen sequent system and has the following…
This paper deals with a proof theory for a theory of $\Pi_{N}$-reflecting ordinals using a system of ordinal diagrams. This is a sequel to the previous one(APAL 129)in which a theory for $\Pi_{3}$-reflection is analysed proof-theoretically.
We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of…
In this paper, we first briefly survey automated termination proof methods for higher-order calculi. We then concentrate on the higher-order recursive path ordering, for which we provide an improved definition, the Computability Path…