Related papers: A simplified version of the Sequent Calculus G3[mi…
Development of a contraction-free BI sequent calculus, be it in the sense of G3i or G4i, has not been successful in literature. We address the open problem by presenting such a sequent system. In fact our calculus involves no structural…
Gentzen's classical sequent calculus LK has explicit structural rules for contraction and weakening. They can be absorbed (in a right-sided formulation) by replacing the axiom P,(not P) by Gamma,P,(not P) for any context Gamma, and…
In this paper, we study sums of shifted products $\sum\limits_{n \leq x} F(n) G(n-h)$ for any $|h| \leq x/2$ and arithmetic functions $F=f*1$ and $G=g*1$, with $f$ and $g$ small. We obtain asymptotic formula for different orders of…
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…
In this paper we show how to find a closed form solution for third order difference operators in terms of solutions of second order operators. This work is an extension of previous results on finding closed form solutions of recurrence…
In the modal mu-calculus, a formula is well-formed if each recursive variable occurs underneath an even number of negations. By means of De Morgan's laws, it is easy to transform any well-formed formula into an equivalent formula without…
This paper shows a simple parameter substitution, which makes use of the reciprocal relation of typical objective functions with typical random parameters. Thereby, the accuracy of first-order probabilistic analysis improves significantly…
We present the Sequent Calculus Trainer, a tool that supports students in learning how to correctly construct proofs in the sequent calculus for first-order logic with equality. It is a proof assistant fostering the understanding of all the…
We introduce the first cut-free nested sequent systems for first-order modal logics that admit increasing, decreasing, constant, and empty domains along with so-called general path conditions and seriality. We obtain such systems by means…
The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler…
Extending and generalizing the approach of 2-sequents (Masini, 1992), we present sequent calculi for the classical modal logics in the K, D, T, S4 spectrum. The systems are presented in a uniform way-different logics are obtained by tuning…
In recent years, G\"odel's ontological proof and variations of it were formalized and analyzed with automated tools in various ways. We supplement these analyses with a modeling in an automated environment based on first-order logic…
Sequence-to-sequence (SEQ2SEQ) models have been successfully applied to automatic math word problem solving. Despite its simplicity, a drawback still remains: a math word problem can be correctly solved by more than one equations. This…
It is known that different categorial grammars have surface representation in a fragment of first order multiplicative linear logic (MLL1). We show that the fragment of interest is equivalent to the recently introduced extended tensor type…
In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
For each $n\in\mathbb{N}$, let $[n]\phi$ mean "the sentence $\phi$ is true in all $\Sigma_{n+1}$-correct transitive sets." Assuming G\"odel's axiom $V = L$, we prove the following graded variant of Solovay's completeness theorem: the set of…
Logic programming has traditiLogic programming has traditionally lacked devices for expressing iterative tasks. To overcome this problem, this paper proposes iterative goal formulas of the form $\seqandq{x}{L} G$ where $G$ is a goal, $x$ is…
This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…
We show that SCL(FOL) can simulate the derivation of non-redundant clauses by superposition for first-order logic without equality. Superposition-based reasoning is performed with respect to a fixed reduction ordering. The completeness…