相关论文: Some results on combinators in the system TRC
Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
The \emph{International Obfuscated C Code Contest} was a programming contest for the most creatively obfuscated yet succinct C code. By \emph{contrast}, an interest herein is in programs which are, \emph{in a sense}, \emph{easily} seen to…
We show that for a large class of varieties of algebras, the equational theory of the congruence lattices of the members is not finitely based.
We classify the complexity of the satisfiability problem for extensions of CTL and UB. The extensions we consider are Boolean combinations of path formulas, fairness properties, past modalities, and forgettable past. Our main result shows…
Hybrid branching-time logics are introduced as extensions of CTL-like logics with state variables and the downarrow-binder. Following recent work in the linear framework, only logics with a single variable are considered. The expressive…
This paper establishes the existence of infinitely many solutions for nonlinear problems without any symmetry, achieving three major advances. First, in the setting of semilinear elliptic PDEs, we introduce a refined variational truncation…
We demonstrate how a generic automated theorem prover can be applied to establish the non-orderability of groups. Our approach incorporates various tools such as positive cones, torsions, generalised torsions and cofinal elements.
We prove that localization functors of crossed modules of groups do not always admit fiberwise (or relative) versions. To do so we characterize the existence of a fiberwise localization by a certain normality condition and compute explicit…
We describe a new method of finding interpolants for classical logic using certain refutation system as a starting point. Refutation can be thought of as an alternative approach to the analysis of formal systems: instead of focusing on…
We show that strict deterministic propositional dynamic logic with intersection is highly undecidable, solving a problem in the Stanford Encyclopedia of Philosophy. In fact we show something quite a bit stronger. We introduce the…
In this paper, we give a new linear time correctness condition for proof nets of Multiplicative Linear Logic without units. Our approach is based on a rewriting system over trees. We have only three rewrite rules. Compared with previous…
The notion of clause set cycle abstracts a family of methods for automated inductive theorem proving based on the detection of cyclic dependencies between clause sets. By discerning the underlying logical features of clause set cycles, we…
This paper proposes a notion termed perturbation-tolerant structural controllability (PTSC) to study the generic property of controllability preservation/resilience of structured linear systems under structured perturbations. A structured…
We present a combinatorial proof for the existence of the sign refined grid homology in lens spaces, and a self contained proof that $\partial_{\mathbb{Z}}^2 = 0$. We also present a Sage program that computes $\widehat{\mathrm{GH}}…
We show various supercongruences for truncated series which involve central binomial coefficients and harmonic numbers. The corresponding infinite series are also evaluated.
We propose a cut-free cyclic system for Transitive Closure Logic (TCL) based on a form of hypersequents, suitable for automated reasoning via proof search. We show that previously proposed sequent systems are cut-free incomplete for basic…
Logics with team semantics provide alternative means for logical characterization of complexity classes. Both dependence and independence logic are known to capture non-deterministic polynomial time, and the frontiers of tractability in…
A new criterion is developed which provides a check as to whether a chosen set of polarization observables is complete with respect to the determination of all independent $T$-matrix elements of a reaction of the type $a+b\to c+d+...$. As…
We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…