Large-scale probabilistic knowledge bases are becoming increasingly important in academia and industry alike. They are constantly extended with new data, powered by modern information extraction tools that associate probabilities with database tuples. In this paper, we revisit the semantics underlying such systems. In particular, the closed-world assumption of probabilistic databases, that facts not in the database have probability zero, clearly conflicts with their everyday use. To address this discrepancy, we propose an open-world probabilistic database semantics, which relaxes the probabilities of open facts to intervals. While still assuming a finite domain, this semantics can provide meaningful answers when some probabilities are not precisely known. For this open world setting, we propose an efficient evaluation algorithm for unions of conjunctive queries. Our open-world algorithm incurs no overhead compared to closed-world reasoning and runs in time linear in the size of the database for tractable queries. All other queries are #P-hard, implying a data complexity dichotomy between linear time and #P. For queries involving negation, however, open-world reasoning can become NP-, or even NP^PP-hard. Finally, we discuss additional knowledge representation layers that can further strengthen open-world reasoning about big uncertain data.

Open APIs are software intermediaries that make it possible for application programs to interact with data and processes, which can both be viewed as forms of services. In many scenarios, when one wants to obtain or publish a new service, one would like to check whether the new functionality can simply be obtained by suitably composing existing services. In this paper we study this problem by distinguishing between the two forms of services, that we call data-centric and process-centric, respectively. In the former, each API is an abstraction of a query specified on a data source, and composition amounts to building a new query by using the available APIs as views over the data. In the latter, each API abstracts a process made up by sequences of atomic actions, and composition means realizing a new process by suitably using the APIs exposed by the available services. We make the assumption that the semantics of services is specified by means of one of the most basic formalisms used in Computer Science, namely, regular languages. As a result, we get a rich analysis framework, where composition shows similarities to conformant and conditional planning. We describe composition principles and automated synthesis techniques for each of the two settings.

A referring expression in linguistics is any noun phrase identifying an object in a way that will be useful to interlocutors. In the context of a query over a first order knowledge base K, constant symbols occurring in K are the artifacts usually used as referring expressions in certain answers to the query. In this paper, we begin to explore how this can be usefully extended by allowing a class of more general formulas, called Singular Referring Expressions, to replace constants in this role. In particular, we lay a foundation for admitting Singular Referring Expressions in certain answer computation for queries over K. An integral part of this foundation are characterization theorems for identification properties of Singular Referring Expressions for queries annotated with a domain specific language for referring concept types. Finally, we apply this framework in the context of tractable description logic dialects, showing how identification properties can be determined at compile-time for conjunctive queries, and how off-the-shelf conjunctive query evaluation for these dialects can be used in query evaluations, preserving, in all cases, underlying tractability.

Bisimulation provides structural conditions to characterize indistinguishability between nodes on graph-like structures from an external observer. It is a fundamental notion used in many areas. However, many applications use graphs where nodes have data, and where observers can test for equality or inequality of data values (e.g., asking the attribute "name" of a node to be different from that of all its neighbors). The present work constitutes a first investigation of "data aware"' bisimulations on data graphs. We study the problem of computing such bisimulations, based on the observational indistinguishability for XPath — a language that extends modal logic with tests for data equality. We show that in general the problem is pspace-complete, but identify several restrictions that yield better complexity bounds (coNP, ptime) by controlling suitable parameters of the problem; namely, the amount of em non-locality allowed, and the class of models considered (graph, DAG, tree). In particular, this analysis yields a hierarchy of tractable fragments.

We introduce EHS*, a novel temporal-epistemic logic defined on temporal intervals characterised by regular expressions. We investigate the complexity of verifying multi-agent systems against EHS* specifications for a number of fragments of EHS* with results ranging from PSPACE-completeness to non-elementary time. The findings show that, at least for the fragments under analysis, the increase in expressiveness obtained by using regular expressions rather than end-points as standard, can be achieved without increasing the complexity of the problem. We show that the expressiveness of regular expressions can also be adopted at the level of specifications without severe computational cost. To do so we introduce a further temporal-epistemic logic, called EHSre, in which regular expressions are used within propositions, and give a polynomial time reduction of the model checking problem from EHSre to EHS*.

A principled way to study limited forms of reasoning for expressive knowledge bases is to specify the reasoning problem within a suitable logic of limited belief. Ideally such a logic comes equipped with a perspicuous semantics, which provides insights into the nature of the belief model and facilitates the study of the reasoning problem. While a number of such logics were proposed in the past, none of them is able to deal with function symbols except perhaps for the special case of logical constants. In this paper we propose a logic of limited belief with arbitrary function symbols. Among other things, we demonstrate that this form of limited belief has desirable properties such as eventual completeness for a large class of formulas and that it serves as a specification of a form of decidable reasoning for very expressive knowledge bases.

There has been a great deal of interest in AI recently in applying Nevertheless, the intuition that underlies sequential and ideas of game theory to model interacting agents who perfect equilibrium, namely, players should play optimally have possibly different preferences as to the outcome of the even off the equilibrium path, seems to make sense even interaction.

We study an epistemic logic where knowledge is built from what the agents observe (including higher-order visibility) and what the agents learn from public announcements. This fixes two main drawbacks of previous observability-based approaches where who sees what is common knowledge and where the epistemic operators distribute over disjunction. The latter forbids the modeling of most of the classical epistemic problems, starting with the muddy children puzzle. We integrate a dynamic dimension where both facts of the world and the agents’ observability can be modified by assignment programs. We establish that the model checking problem is PSPACE-complete.

In temporal logics, the operator F expresses that at some time in the future something happens, e.g., a request is eventually granted. Unfortunately, there is no bound on the time un- til the eventuality is satisfied which in many cases does not correspond to the intuitive meaning system designers have, namely, that F abstracts the idea that there is a bound on this time although its magnitude is not known. An elegant way to capture this meaning is through Prompt-LTL, which extends LTL with the operator F P ("prompt eventually"). We extend this work by studying alternating-time epistemic temporal logics extended with F P . We study the model-checking problem of the logic Prompt- KATL∗, which is ATL∗ extended with epistemic operators and prompt eventually. We also obtain results for the model-checking problem of some of its fragments. Namely, of Prompt-KATL (ATL with epistemic operators and prompt eventually), Prompt-KCTL∗ (CTL∗ with epistemic operators and prompt eventually), and finally the existential fragments of Prompt-KATL∗ and Prompt-KATL.

Recently, the field of knowledge representation is drawing a lot of inspiration from database theory. In particular, in the area of description logics and ontology languages, interest has shifted from satisfiability checking to query answering, with various query notions adopted from databases, like (unions of) conjunctive queries or different kinds of path queries. Likewise, the finite model semantics is being established as a viable and interesting alternative to the traditional semantics based on unrestricted models. In this paper, we investigate diverse database-inspired reasoning problems for very expressive description logics (all featuring the worrisome trias of inverses, counting, and nominals) which have in common that role paths of unbounded length can be described (in the knowledge base or of the query), leading to a certain non-locality of the reasoning problem. We show that for all the cases considered, undecidability can be established by very similar means. Most notably, we show undecidability of finite entailment of unions of conjunctive queries for a fragment of SHOIQ (the logic underlying the OWL DL ontology language), and undecidability of finite entailment of conjunctive queries for a fragment of SROIQ (the logical basis of the more recent and popular OWL 2 DL standard).