On Decidability of Expressive Description Logics with Composition of Roles in Number Restrictions
Fabio Grandi
备注：
A preliminary version of this paper appeared in Proc. of the 9th Intl' Conf. on Logic for Programming, Artificial Intelligence and Reasoning, LPAR 2002
Description Logics are knowledge representation formalisms which have been used in a wide range of application domains. Owing to their appealing expressiveness, we consider in this paper extensions of the well-known concept language ALC allowing for number restrictions on complex role expressions. These have been first introduced by Baader and Sattler as ALCN(M) languages, with the adoption of role constructors M subset-of {o,-,And,Or}. In particular, they showed in 1999 that, although ALCN(o) is decidable, the addition of other operators may easily lead to undecidability: in fact, ALCN(o,And) and ALCN(o,-,Or) were proved undecidable.
In this work, we further investigate the computational properties of the ALCN family, aiming at narrowing the decidability gap left open by Baader and Sattler's results. In particular, we will show that ALCN(o) extended with inverse roles both in number and in value restrictions becomes undecidable, whereas it can be safely extended with qualified number restrictions without losing decidability.
In this paper syntactic objects---concept constructors called part restrictions which realize rational grading are considered in Description Logics (DLs). Being able to convey statements about a rational part of a set of successors, part restrictions essentially enrich the expressive capabilities of DLs. We examine an extension of well-studied DL ALCQIHR+ with part restrictions, and prove that the reasoning in the extended logic is still decidable. The proof uses tableaux technique augmented with indices technique, designed for dealing with part restrictions.
Hyperproperties are properties of systems that relate different executions traces, with many applications from security to symmetry, consistency models of concurrency, etc. In recent years, different linear-time logics for specifying asynchronous hyperproperties have been investigated. Though model checking of these logics is undecidable, useful decidable fragments have been identified with applications e.g. for asynchronous security analysis. In this paper, we address expressiveness and decidability issues of temporal logics for asynchronous hyperproperties. We compare the expressiveness of t…
Decidability of the Clark's Completion Semantics for Monadic Programs and Queries
对于一般的逻辑程序（即在子句主体中使用否定的程序），有许多不同的语义。这些语义中的大多数是图灵完备的（在某种意义上可以精确化），这意味着它们是不可判定的。为了获得可判定性，需要对程序和查询施加额外的限制。在逻辑编程中，对底层的一阶语言施加限制是很自然的。在本说明中，我们展示了一元一般程序和查询的克拉克完成语义的可判定性。逻辑程序设计理论与实践（Theory and Practice of Logic Programming，TPLP）
We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $Σ_1$ theory is undecidable (already over two letters). We investigate the decidability border by considering fragments where all but a certain number of variables are alternation bounded, meaning that the variable must always be quantified over languages with a bounded number of letter alternations. We prove that when at most two variables are not alternation bounded, the $Σ_1$ fragment is decidable, and that it becomes undecidable when three variab…
On the Decidability and Complexity of Some Fragments of Metric Temporal Logic
度量时态逻辑$\mtlfull$是研究最多的实时逻辑之一。它表现出相当大的多样性的表达性和可判定性的基础上允许的一套模式和时间间隔的限制$I$的性质。\oomit{The classical results of Alur and Henzinger showed that $\mtlfull$ is undecidable where as $\mitl$ which uses only non-singular intervals $NS$ is decidable. In a surprizing result, Ouaknine and Worrell showed that the satisfiability of $\mtl$ is decidable over finite pointwise models, albeit with NPR decision complexity, whereas it remains undecidable for infinite pointwise models or for continuous time.}在本文中，我们通过证明$\mtlsns$（其中$NS$表示非奇异区间）的可满足性在有限逐点严格单调时间上也是可判定的，从而加强了可判定性结果。我们利用时间投影技术给出了从Ouaknine和Worrell的逻辑$\mtls…
The Sticky Path to Expressive Querying: Decidability of Navigational Queries under Existential Rules
TU Dresden（德累斯顿工业大学）；University of Wrocław（弗罗茨瓦夫大学）；Center for Scalable Data Analytics and Artificial Intelligence Dresden/Leipzig（德累斯顿/莱比锡可扩展数据分析与人工智能中心）
The verification of systems combining hard timing constraints with concurrency is challenging. This challenge becomes even harder when some timing constants are missing or unknown. Parametric timed formalisms, such as parametric timed automata (PTAs), tackle the synthesis of such timing constants (seen as parameters) for which a property holds. Such formalisms are highly expressive, but also undecidable, and few decidable subclasses were proposed. We propose here a syntactic restriction on PTAs consisting in removing guards (constraints on transitions) to keep only invariants (constraints on l…
We consider dynamic versions of epistemic logic as formulated in Baltag and Moss "Logics for epistemic programs" (2004). That paper proposed a logical language (actually families of languages parameterized by action signatures) for dynamic epistemic logic. It had been shown that validity in the language is Pi-1-1-complete, so there are no recursively axiomatized complete logical systems for it. In contrast, this paper proves a weak completeness result for the fragment without action iteration, and a strong completeness result for the fragment without action iteration and common knowledge. Our …
We investigate the expressive power of the two main kinds of program logics for complex, non-regular program properties found in the literature: those extending propositional dynamic logic (PDL), and those extending the modal mu-calculus. This is inspired by the recent discovery of a decidable program logic called Visibly Pushdown Fixpoint Logic with Chop which extends both the modal mu-calculus and PDL over visibly pushdown languages, which, so far, constituted the ends of two pillars of decidable program logics. Here we show that this logic is not only more expressive than either of its two …
Hyperproperties, which generalize trace properties by relating multiple traces, are widely studied in information-flow security. Recently, a number of logics for hyperproperties have been proposed, and there is a need to understand their decidability and relative expressiveness. The new logics have been obtained from standard logics with two principal extensions: temporal logics, like LTL and CTL$^*$, have been generalized to hyperproperties by adding variables for traces or paths. First-order and second-order logics, like monadic first-order logic of order and MSO, have been extended with the…
While syntactic inference restrictions don't play an important role for SAT, they are an essential reasoning technique for more expressive logics, such as first-order logic, or fragments thereof. In particular, they can result in short proofs or model representations. On the other hand, semantically guided inference systems enjoy important properties, such as the generation of solely non-redundant clauses. I discuss to what extend the two paradigms may be unifiable.
Open-world query answering is the problem of deciding, given a set of facts, conjunction of constraints, and query, whether the facts and constraints imply the query. This amounts to reasoning over all instances that include the facts and satisfy the constraints. We study finite open-world query answering (FQA), which assumes that the underlying world is finite and thus only considers the finite completions of the instance. The major known decidable cases of FQA derive from the following: the guarded fragment of first-order logic, which can express referential constraints (data in one place po…
We study increasingly expressive type systems, from $F^μ$ -- an extension of the polymorphic lambda calculus with equirecursive types -- to $F^{μ;}_ω$ -- the higher-order polymorphic lambda calculus with equirecursive types and context-free session types. Type equivalence is given by a standard bisimulation defined over a novel labelled transition system for types. Our system subsumes the contractive fragment of $F^μ_ω$ as studied in the literature. Decidability results for type equivalence of the various type languages are obtained from the translation of types into objects of an appropriate …
A classical result by Lovász asserts that two graphs $G$ and $H$ are isomorphic if and only if they have the same left profile, that is, for every graph $F$, the number of homomorphisms from $F$ to $G$ coincides with the number of homomorphisms from $F$ to $H$. Dvor{á}k and later on Dell, Grohe, and Rattan showed that restrictions of the left profile to a class of graphs can capture several different relaxations of isomorphism, including equivalence in counting logics with a fixed number of variables (which contains fractional isomorphism as a special case) and co-spectrality (i.e., two graphs…
Polynomial closure is a standard operator which is applied to a class of regular languages. In the paper, we investigate three restrictions called left (LPol), right (RPol) and mixed polynomial closure (MPol). The first two were known while MPol is new. We look at two decision problems that are defined for every class C. Membership takes a regular language as input and asks if it belongs to C. Separation takes two regular languages as input and asks if there exists a third language in C including the first one and disjoint from the second. We prove that LPol, RPol and MPol preserve the decidab…
