相关论文: Ground Canonicity
We propose new sequent calculus systems for orthologic (also known as minimal quantum logic) which satisfy the cut elimination property. The first one is a simple system relying on the involutive status of negation. The second one…
We introduce a reduction order called the weighted path order (WPO) that subsumes many existing reduction orders. WPO compares weights of terms as in the Knuth-Bendix order (KBO), while WPO allows weights to be computed by a wide class of…
This paper enlarges classical syllogistic logic with assertions having to do with comparisons between the sizes of sets. So it concerns a logical system whose sentences are of the following forms: {\sf All $x$ are $y$} and {\sf Some $x$ are…
Higher-order pushdown systems and ground tree rewriting systems can be seen as extensions of suffix word rewriting systems. Both classes generate infinite graphs with interesting logical properties. Indeed, the model-checking problem for…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
We define a notion of model for the $\lambda$$\Pi$-calculus modulo theory and prove a soundness theorem. We then define a notion of super-consistency and prove that proof reduction terminates in the $\lambda$$\Pi$-calculus modulo any…
With the idea of canceling the leading divergence in vacuum energy of $\varphi^4$ field theory a parameter is introduced that interpolates between free Hamiltonian with or without normal ordering. This leads to a condensate ground state…
This paper presents two new approaches to prove termination of rewrite systems with the Knuth-Bendix order efficiently. The constraints for the weight function and for the precedence are encoded in (pseudo-)propositional logic and the…
Proof search has been used to specify a wide range of computation systems. In order to build a framework for reasoning about such specifications, we make use of a sequent calculus involving induction and co-induction. These proof principles…
A 0-1 matrix $M$ contains a 0-1 matrix pattern $P$ if we can obtain $P$ from $M$ by deleting rows and/or columns and turning arbitrary 1-entries into 0s. The saturation function $\mathrm{sat}(P,n)$ for a 0-1 matrix pattern $P$ indicates the…
Hybrid logic extends modal logic with special propositions called nominals, each of which is true at only one state in a model. This enables us to describe some properties of binary relations, such as irreflexivity and anti-symmetry, which…
This paper discusses proof-theoretic semantics, the project of specifying the meanings of the logical constants in terms of rules of inference governing them. I concentrate on Michael Dummett's and Dag Prawitz' philosophical motivations and…
We consider the semiconjugate factorization and reduction of order for non-autonomous, nonlinear, higher order difference equations containing linear arguments. These equations have appeared in several mathematical models in biology and…
Quantification, i.e., the task of training predictors of the class prevalence values in sets of unlabeled data items, has received increased attention in recent years. However, most quantification research has concentrated on developing…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
When a proposition has no proof in an inference system, it is sometimes useful to build a counter-proof explaining, step by step, the reason of this non-provability. In general, this counter-proof is a (possibly) infinite co-inductive proof…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
We investigate the saturation rank of a finite group scheme, defined over an algebraically closed field $\Bk$ of positive characteristic $p$. We begin by exploring the saturation rank for finite groups and infinitesimal group schemes.…
A $0$-$1$ matrix $M$ is saturating for a $0$-$1$ matrix $P$ if $M$ does not contain a submatrix that can be turned into $P$ by changing some $1$ entries to $0$ entries, and changing an arbitrary $0$ to $1$ in $M$ introduces such a submatrix…
We model collapsible and ordered pushdown systems with term rewriting, by encoding higher-order stacks and multiple stacks into trees. We show a uniform inverse preservation of recognizability result for the resulting class of term…