Related papers: Conservativity for theories of compositional truth…
It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…
In compositional data analysis an observation is a vector containing non-negative values, only the relative sizes of which are considered to be of interest. Without loss of generality, a compositional vector can be taken to be a vector of…
We consider cut-elimination in the sequent calculus for classical first-order logic. It is well known that this system, in its most general form, is neither confluent nor strongly normalizing. In this work we take a coarser (and…
We present a sequent calculus system for a modal reformulation of a system of nonmonotonic logic due to McCain and Turner: we prove cut elimination for our system. The proof system is in general infinitary: because we can prove cut…
We study the proof theory and algorithms for orthologic, a logical system based on ortholattices, which have shown practical relevance in simplification and normalization of verification conditions. Ortholattices weaken Boolean algebras…
Questions concerning the proof-theoretic strength of classical versus non-classical theories of truth have received some attention recently. A particularly convenient case study concerns classical and nonclassical axiomatizations of…
We present a new set of reductions for derivations in natural deduction that can extract witnesses from closed derivations of simply existential formulas in Heyting Arithmetic (HA) plus the Excluded Middle Law restricted to simply…
We study a well-known technique of using absoluteness for giving choice-free proofs to some statements which are known to be provable with the axiom of choice. The idea is to reduce the problem to an inner model where the axiom of choice…
This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…
Our main result (Theorem A) shows the incompleteness of any consistent sequential theory T formulated in a finite language such that T is axiomatized by a collection of sentences of bounded quantifier-alternation-depth. Our proof employs an…
Unlike extractive summarization, abstractive summarization has to fuse different parts of the source text, which inclines to create fake facts. Our preliminary study reveals nearly 30% of the outputs from a state-of-the-art neural…
Tableaux originate as a decision method for a logical language. They can also be extended to obtain a structure that spells out all the information in a set of sentences in terms of truth value assignments to atomic formulas that appear in…
Various concepts of grammatical compositionality arise in many theories of both natural and artificial languages, and often play a key role in accounts of the syntax-semantics interface. We propose that many instances of compositionality…
We give an algorithm determining whether a hermiticity-preserving superoperator is positive. In our approach we apply techniques of quantifier elimination theory for real numbers. Furthermore, we argue that quantifier elimination theory…
In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of…
The biggest challenge in hybrid systems verification is the handling of differential equations. Because computable closed-form solutions only exist for very simple differential equations, proof certificates have been proposed for more…
The logic of constant domains is intuitionistic logic extended with the so-called forall-shift axiom, a classically valid statement which implies the excluded middle over decidable formulas. Surprisingly, this logic is constructive and so…
A method for the nonintrusive and structure-preserving model reduction of canonical and noncanonical Hamiltonian systems is presented. Based on the idea of operator inference, this technique is provably convergent and reduces to a…
The framework of cyclic proof systems provides a reasonable proof system for logics with inductive definitions. It also offers an effective automated proof search procedure for such logics without finding induction hypotheses. Recent…
Preservation theorems provide a direct correspondence between the syntactic structure of first-order sentences and the closure properties of their respective classes of models. A line of work has explored preservation theorems relativised…