相关论文: A Topological Application of Labelled Natural Dedu…

Given a family of rational curves depending on a real parameter, defined by its parametric equations, we provide an algorithm to compute a finite partition of the parameter space (${\Bbb R}$, in general) so that the shape of the family…

Term rewriting has a significant presence in various areas, not least in automated theorem proving where it is used as a proof technique. Many theorem provers employ specialised proof tactics for rewriting. This results in an interleaving…

Combining a standard proof search method, such as resolution or tableaux, and rewriting is a powerful way to cut off search space in automated theorem proving, but proving the completeness of such combined methods may be challenging. It may…

We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…

We investigate the new, Turing-complete class of layered systems, whose lefthand sides of rules can only be overlapped at a multiset of disjoint or equal positions. Layered systems define a natural notion of rank for terms: the maximal…

A non-deterministic call-by-need lambda-calculus \calc with case, constructors, letrec and a (non-deterministic) erratic choice, based on rewriting rules is investigated. A standard reduction is defined as a variant of left-most outermost…

In this paper we present a minimal object oriented core calculus for modelling the biological notion of type that arises from biological ontologies in formalisms based on term rewriting. This calculus implements encapsulation, method…

Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…

To appear in Theory and Practice of Logic Programming (TPLP). Tabling is a commonly used technique in logic programming for avoiding cyclic behavior of logic programs and enabling more declarative program definitions. Furthermore, tabling…

We develop a rewriting theory suitable for diagrammatic algebras and lay down the foundations of a systematic study of their higher structures. In this paper, we focus on the question of finding bases. As an application, we give the first…

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…

In the paper, we represent a comparison analysis of the methods of the topological alignment and extract the main mathematical principles forming the base of the concept. The main narrative is devoted to the so-called coupled methods…

We construct reflection and translation operators on the Hilbert space corresponding to the torus by projecting them from the plane. These operators are shown to have the same group properties as their analogue on the plane. The…

In this paper we present the probabilistic typed natural deduction calculus TPTND, designed to reason about and derive trustworthiness properties of probabilistic computational processes, like those underlying current AI applications.…

The main novelty of this paper is to consider an extension of the Calculus of Constructions where predicates can be defined with a general form of rewrite rules. We prove the strong normalization of the reduction relation generated by the…

A rooted planar map is a connected graph embedded in the 2-sphere, with one edge marked and assigned an orientation. A term of the pure lambda calculus is said to be linear if every variable is used exactly once, normal if it contains no…

Dirac notation is widely used in quantum physics and quantum programming languages to define, compute and reason about quantum states. This paper considers Dirac notation from the perspective of automated reasoning. We prove two main…

Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…

Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…

Topics generated by topic models are typically represented as list of terms. To reduce the cognitive overhead of interpreting these topics for end-users, we propose labelling a topic with a succinct phrase that summarises its theme or idea.…