相关论文: The Horn Non-Clausal Class and its Polynomiality

We present an approach to constrained Horn clause (CHC) verification combining three techniques: abstract interpretation over a domain of convex polyhedra, specialisation of the constraints in CHCs using abstract interpretation of…

Coinduction occurs in two guises in Horn clause logic: in proofs of circular properties and relations, and in proofs involving construction of infinite data. Both instances of coinductive reasoning appeared in the literature before, but a…

We study possible formulations of algebraic propositional proof systems operating with noncommutative formulas. We observe that a simple formulation gives rise to systems at least as strong as Frege---yielding a semantic way to define a…

We introduce the hierarchical compositional network (HCN), a directed generative model able to discover and disentangle, without supervision, the building blocks of a set of binary images. The building blocks are binary features defined…

The class of all $\ast$-continuous Kleene algebras, whose description includes an infinitary condition on the iteration operator, plays an important role in computer science. The complexity of reasoning in such algebras - ranging from the…

Alternation of forward and backward analyses is a standard technique in abstract interpretation of programs, which is in particular useful when we wish to prove unreachability of some undesired program states. The current state-of-the-art…

Hybrid logic with binders is an expressive specification language. Its satisfiability problem is undecidable in general. If frames are restricted to N or general linear orders, then satisfiability is known to be decidable, but of…

A hybrid model involves the cooperation of an interpretable model and a complex black box. At inference, any input of the hybrid model is assigned to either its interpretable or complex component based on a gating mechanism. The advantages…

We address the problem of checking the satisfiability of a set of constrained Horn clauses (CHCs) possibly including more than one query. We propose a transformation technique that takes as input a set of CHCs, including a set of queries,…

In the field of constraint satisfaction problems (CSP), a clause is called redundant if its satisfaction is implied by satisfying all other clauses. An instance of CSP$(P)$ is called non-redundant if it does not contain any redundant…

Hierarchical text classification (HTC) assigns documents to multiple levels of a pre-defined taxonomy. Automated patent subject classification represents one of the hardest HTC scenarios because of domain knowledge difficulty and a huge…

Multi-label classification (MC) is a standard machine learning problem in which a data point can be associated with a set of classes. A more challenging scenario is given by hierarchical multi-label classification (HMC) problems, in which…

We examine possibility to design an efficient solving algorithm for problems of the class \np. It is introduced a classification of \np problems by the property that a partial solution of size $k$ can be extended into a partial solution of…

We study the robustness--the invariance under definition changes--of the cluster class CL#P [HHKW05]. This class contains each #P function that is computed by a balanced Turing machine whose accepting paths always form a cluster with…

In this paper we investigate the complexity-theoretical aspects of cyclic and non-wellfounded proofs in the context of parsimonious logic, a variant of linear logic where the exponential modality ! is interpreted as a constructor for…

It is known that the verification of imperative, functional, and logic programs can be reduced to the satisfiability of constrained Horn clauses (CHCs), and this satisfiability check can be performed by using CHC solvers, such as Eldarica…

We characterise finite axiomatisability and intractability of deciding membership for universal Horn classes generated by finite loop-free hypergraphs.

Constrained Horn Clauses (CHCs) are an intermediate program representation that can be generated by several verification tools, and that can be processed and solved by a number of Horn solvers. One of the main challenges when using CHCs in…

In real-world environments it usually is difficult to specify target operating conditions precisely, for example, target misclassification costs. This uncertainty makes building robust classification systems problematic. We show that it is…

We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn…