Graph database models can be defined as those in which data structures for the schema and instances are modeled as graphs or generalizations of them, and data manipulation is expressed by graph-oriented operations and type constructors. These models took off in the eighties and early nineties alongside object-oriented models. Their influence gradually died out with the emergence of other database models, in particular geographical, spatial, semistructured, and XML. Recently, the need to manage information with graph-like nature has reestablished the relevance of this area. The main objective of this survey is to present the work that has been conducted in the area of graph database modeling, concentrating on data structures, query languages, and integrity constraints.

/pdf/survey-of-graph-database-models-2ssdmgcn9a.pdf

Survey of graph database models

Graph databases have received much attention as of late due to numerous applications in which data is naturally viewed as a graph; these include social networks, RDF and the Semantic Web, biological databases, and many others. There are many proposals for query languages for graph databases that mainly fall into two categories. One views graphs as a particular kind of relational data and uses traditional relational mechanisms for querying. The other concentrates on querying the topology of the graph. These approaches, however, lack the ability to combine data and topology, which would allow queries asking how data changes along paths and patterns enveloping it. In this article, we present a comprehensive study of languages that enable such combination of data and topology querying. These languages come in two flavors. The first follows the standard approach of path queries, which specify how labels of edges change along a path, but now we extend them with ways of specifying how both labels and data change. From the complexity point of view, the right type of formalisms are subclasses of register automata. These, however, are not well suited for querying. To overcome this, we develop several types of extended regular expressions to specify paths with data and study their querying power and complexity. The second approach adopts the popular XML language XPath and extends it from XML documents to graphs. Depending on the exact set of allowed features, we have a family of languages, and our study shows that it includes efficient and highly expressive formalisms for querying both the structure of the data and the data itself.

/pdf/querying-graphs-with-data-3nbju430nn.pdf

Querying Graphs with Data

A proposition is noncontingent, if it is necessarily true or it is necessarily false. In an epistemic context, ‘a proposition is noncontingent’ means that you know whether the proposition is true. In this paper, we study contingency logic with the noncontingency operator Δ but without the necessity operator □. This logic is not a normal modal logic, because Δ(φ → ψ) → (Δφ → Δψ) is not valid. Contingency logic cannot define many usual frame properties, and its expressive power is weaker than that of basic modal logic over classes of models without reflexivity. These features make axiomatizing contingency logics nontrivial, especially for the axiomatization over symmetric frames. In this paper, we axiomatize contingency logics over various frame classes using a novel method other than the methods provided in the literature, based on the ‘almost-definability’ schema AD proposed in our previous work. We also present extensions of contingency logic with dynamic operators. Finally, we compare our work to the related work in the fields of contingency logic and ignorance logic, where the two research communities have similar results but are apparently unaware of each other’s work. One goal of our paper is to bridge this gap.

Contingency and knowing whether

In this paper we present some ideas how to analyse data using logic tools. We define a logic language for expressing data analysis problems and we develop a deductive system for the language to use proof procedures to obtain solutions to these problems.

DAL: A Logic for Data Analysis.

Epistemic logic has become a major field of philosophical logic ever since the groundbreaking work by Hintikka [58]. Despite its various successful applications in theoretical computer science, AI, and game theory, the technical development of the field has been mainly focusing on the propositional part, i.e., the propositional modal logics of “knowing that”. However, knowledge is expressed in everyday life by using various other locutions such as “knowing whether”, “knowing what”, “knowing how” and so on (knowing-wh hereafter). Such knowledge expressions are better captured in quantified epistemic logic, as was already discussed by Hintikka [58] and his sequel works at length. This paper aims to draw the attention back again to such a fascinating but largely neglected topic. We first survey what Hintikka and others did in the literature of quantified epistemic logic, and then advocate a new quantifier-free approach to study the epistemic logics of knowing-wh, which we believe can balance expressivity and complexity, and capture the essential reasoning patterns about knowing-wh. We survey our recent line of work on the epistemic logics of ‘knowing whether”, “knowing what” and “knowing how” to demonstrate the use of this new approach.

pdf/beyond-knowing-that-a-new-generation-of-epistemic-logics-e9ro0msegh.pdf

Beyond Knowing That: A New Generation of Epistemic Logics

This chapter illustrates two aspects of automata theory related to linear-time temporal logic LTL used for the verification of computer systems. First, we present a translation from LTL formulae to Buchi automata. The aim is to design an elementary translation which is reasonably efficient and produces small automata so that it can be easily taught and used by hand on real examples. Our translation is in the spirit of the classical tableau constructions but is optimized in several ways. Secondly, we recall how temporal operators can be defined from regular languages and we explain why adding even a single operator definable by a context-free language can lead to undecidability.

Specification and Verification using Temporal Logics

We show the completeness of a Hilbert-style system LK defined by M Valiev involving the knowledge operator K dedicated to the reasoning with incomplete information The completeness proof uses a variant of Makinson's canonical model construction Furthermore we prove that the theoremhood problem for LK is co-NP-complete, using techniques similar to those used to prove that the satisfiability problem for propositional S5 is NP-complete

A Completeness Proof for a Logic with an Alternative Necessity Operator

Adding propositional quantification to the modal logics $\mathsf{K, T}$ or S4 is known to lead to undecidability but CTL with propositional quantification under the tree semantics (QCTLt) admits a non-elementary Tower-complete satisfiability problem. We investigate the complexity of strict fragments of $\mathsf{QCTL}^{t}$ as well as of the modal logic $\mathsf{K}$ with propositional quantification under the tree semantics. More specifically, we show that $\mathsf{QCTL}^{t}$ restricted to the temporal operator EX is already Tower-hard, which is unexpected as EX can only enforce local properties. When QCTLt restricted to EX is interpreted on N-bounded trees for some $N\geq 2$ , we prove that the satisfiability problem is $\mathbf{AExp}_{\mathrm{pol}^{-}}$ complete; $\mathbf{AExp}_{\mathrm{pol}}$ -hardness is established by reduction from a recently introduced tiling problem, instrumental for studying the model-checking problem for interval temporal logics. As consequences of our proof method, we prove Tower-hardness of QCTLtrestricted to EF or to EXEF and of the well-known modal logics $\mathsf{K}$ , KD, GL, S4, K4 and D4, with propositional quantification under a semantics based on classes of trees.

/pdf/why-propositional-quantification-makes-modal-logics-on-trees-2muzs88rft.pdf

Why Propositional Quantification Makes Modal Logics on Trees Robustly Hard

We present sound and complete prefixed tableaux systems for various modal logics with enriched languages including the "difference" modal operator [≠] and the "only if" modal operator [--R]. These logics are of special interest in Artificial Intelligence since their expressive power is higher than the standard modal logics and for most of them the satisfiability problem remains decidable. We also include in the paper decision procedures based on these systems. In the conclusion, we relate our work with similar ones from the literature and we propose extensions to other logics.

/pdf/prefixed-tableaux-systems-for-modal-logics-with-enriched-12elde3f7b.pdf

Prefixed tableaux systems for modal logics with enriched languages

One important issue of automated theorem proving is the complexity of the inference rules used in theorem provers. If Krishnamurty's general symmetry rule is to be used, then one should provide some way of computing non trivial symmetries. We show that this problem is NP-complete. But this general rule can be simplified by restricting it to what we call 5- symmetries, yielding the well-known symmetry rule. We show that computing 5-symmetries is in the same complexity class as the graph isomorphism problem, which appears to be neither polynomial nor NP-complete. However it is sufficient to compute the set of all 5-symmetries at the beginning of the proof search, and since it is a permutation group, there exist some efficient techniques from computational group theory to represent this set. We also show how these techniques can be used for applying the S-symmetry rule in polynomial time.

https://ijcai.org/Proceedings/95-1/Papers/038.pdf

On the complexity of extending ground resolution with symmetry rules

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