Reasoning with Inconsistencies in Propositional Peer-to-Peer Inference Systems

International audiencen a peer-to-peer inference system, there is no centralized control or hierarchical organization: each peer is equivalent in functionality and cooperates with other peers in order to solve a collective reasoning task. Since peer theories model possibly different viewpoints, even if each local theory is consistent, the global theory may be inconsistent. We exhibit a distributed algorithm detecting inconsistencies in a fully decentralized setting. We provide a fully distributed reasoning algorithm, which computes only well-founded consequences of a formula, i.e., with a consistent set of support

Distributed Reasoning in a Peer-to-Peer Setting: Application to the Semantic Web

In a peer-to-peer inference system, each peer can reason locally but can also solicit some of its acquaintances, which are peers sharing part of its vocabulary. In this paper, we consider peer-to-peer inference systems in which the local theory of each peer is a set of propositional clauses defined upon a local vocabulary. An important characteristic of peer-to-peer inference systems is that the global theory (the union of all peer theories) is not known (as opposed to partition-based reasoning systems). The main contribution of this paper is to provide the first consequence finding algorithm in a peer-to-peer setting: DeCA. It is anytime and computes consequences gradually from the solicited peer to peers that are more and more distant. We exhibit a sufficient condition on the acquaintance graph of the peer-to-peer inference system for guaranteeing the completeness of this algorithm. Another important contribution is to apply this general distributed reasoning setting to the setting of the Semantic Web through the Somewhere semantic peer-to-peer data management system. The last contribution of this paper is to provide an experimental analysis of the scalability of the peer-to-peer infrastructure that we propose, on large networks of 1000 peers

Cognitive context and arguments from ontologies for learning

The deployment of learning resources on the web by different experts has resulted in the accessibility of multiple viewpoints about the same topics. In this work we assume that learning resources are underpinned by ontologies. Different formalizations of domains may result from different contexts, different use of terminology, incomplete knowledge or conflicting knowledge. We define the notion of cognitive learning context which describes the cognitive context of an agent who refers to multiple and possibly inconsistent ontologies to determine the truth of a proposition. In particular we describe the cognitive states of ambiguity and inconsistency resulting from incomplete and conflicting ontologies respectively. Conflicts between ontologies can be identified through the derivation of conflicting arguments about a particular point of view. Arguments can be used to detect inconsistencies between ontologies. They can also be used in a dialogue between a human learner and a software tutor in order to enable the learner to justify her views and detect inconsistencies between her beliefs and the tutor’s own. Two types of arguments are discussed, namely: arguments inferred directly from taxonomic relations between concepts, and arguments about the necessary an

A Multi-Layered Architecture for Collaborative and Decentralized Consequence Finding

The consequence finding problem consists in producing all the consequences of a logical theory or, depending on the application context, in a restricted subset of these consequences. When the available knowledge is naturally scattered among different sources of information, computing such consequences with respect to the global theory in a decentralized way is a challenging problem. This paper presents Somewhere2, a multilayered architecture that may be used to solve such consequence finding problems in peer-to-peer networks of collaborating entities, that may evolve over time. The general layout of this architecture is described as well as the roles of its main components. Thanks to a careful and modular design, the resulting framework is very generic. This facilitates alternative implementations of specific components as well as its extension with additional features. First experimental results are presented, illustrating the scalability and robustness of this architecture. This framework may be used as a robust building block for more advanced distributed applications, such as Peer Data Management Systems

Query Processing in a P2P Network of Taxonomy-based Information Sources

In this study we address the problem of answering queries over a peer-to-peer system of taxonomy-based sources. A taxonomy states subsumption relationships between negation-free DNF formulas on terms and negation-free conjunctions of terms. To the end of laying the foundations of our study, we first consider the centralized case, deriving the complexity of the decision problem and of query evaluation. We conclude by presenting an algorithm that is efficient in data complexity and is based on hypergraphs. We then move to the distributed case, and introduce a logical model of a network of taxonomy-based sources. On such network, a distributed version of the centralized algorithm is then presented, based on a message passing paradigm, and its correctness is proved. We finally discuss optimization issues, and relate our work to the literature

Believe It or Not: Adding Belief Annotations to Databases

We propose a database model that allows users to annotate data with belief statements. Our motivation comes from scientific database applications where a community of users is working together to assemble, revise, and curate a shared data repository. As the community accumulates knowledge and the database content evolves over time, it may contain conflicting information and members can disagree on the information it should store. For example, Alice may believe that a tuple should be in the database, whereas Bob disagrees. He may also insert the reason why he thinks Alice believes the tuple should be in the database, and explain what he thinks the correct tuple should be instead. We propose a formal model for Belief Databases that interprets users' annotations as belief statements. These annotations can refer both to the base data and to other annotations. We give a formal semantics based on a fragment of multi-agent epistemic logic and define a query language over belief databases. We then prove a key technical result, stating that every belief database can be encoded as a canonical Kripke structure. We use this structure to describe a relational representation of belief databases, and give an algorithm for translating queries over the belief database into standard relational queries. Finally, we report early experimental results with our prototype implementation on synthetic data.Comment: 17 pages, 10 figure

Reputation-based decisions for logic-based cognitive agents

Computational trust and reputation models have been recognized as one of the key technologies required to design and implement agent systems. These models manage and aggregate the information needed by agents to efficiently perform partner selection in uncertain situations. For simple applications, a game theoretical approach similar to that used in most models can suffice. However, if we want to undertake problems found in socially complex virtual societies, we need more sophisticated trust and reputation systems. In this context, reputation-based decisions that agents make take on special relevance and can be as important as the reputation model itself. In this paper, we propose a possible integration of a cognitive reputation model, Repage, into a cognitive BDI agent. First, we specify a belief logic capable to capture the semantics of Repage information, which encodes probabilities. This logic is defined by means of a two first-order languages hierarchy, allowing the specification of axioms as first-order theories. The belief logic integrates the information coming from Repage in terms if image and reputation, and combines them, defining a typology of agents depending of such combination. We use this logic to build a complete graded BDI model specified as a multi-context system where beliefs, desires, intentions and plans interact among each other to perform a BDI reasoning. We conclude the paper with an example and a related work section that compares our approach with current state-of-the-art models. © 2010 The Author(s).This work was supported by the projects AEI (TIN2006-15662-C02-01), AT (CONSOLIDER CSD20070022, INGENIO 2010), LiquidPub (STREP FP7-213360), RepBDI (Intramural 200850I136) and by the Generalitat de Catalunya under the grant 2005-SGR-00093.Peer Reviewe

State-of-the-art on evolution and reactivity

This report starts by, in Chapter 1, outlining aspects of querying and updating resources on the Web and on the Semantic Web, including the development of query and update languages to be carried out within the Rewerse project. From this outline, it becomes clear that several existing research areas and topics are of interest for this work in Rewerse. In the remainder of this report we further present state of the art surveys in a selection of such areas and topics. More precisely: in Chapter 2 we give an overview of logics for reasoning about state change and updates; Chapter 3 is devoted to briefly describing existing update languages for the Web, and also for updating logic programs; in Chapter 4 event-condition-action rules, both in the context of active database systems and in the context of semistructured data, are surveyed; in Chapter 5 we give an overview of some relevant rule-based agents frameworks

Review of 'The Outer Limits of Reason' by Noson Yanofsky 403p (2013) (review revised 2019)

I give a detailed review of 'The Outer Limits of Reason' by Noson Yanofsky from a unified perspective of Wittgenstein and evolutionary psychology. I indicate that the difficulty with such issues as paradox in language and math, incompleteness, undecidability, computability, the brain and the universe as computers etc., all arise from the failure to look carefully at our use of language in the appropriate context and hence the failure to separate issues of scientific fact from issues of how language works. I discuss Wittgenstein's views on incompleteness, paraconsistency and undecidability and the work of Wolpert on the limits to computation. To sum it up: The Universe According to Brooklyn---Good Science, Not So Good Philosophy. Those wishing a comprehensive up to date framework for human behavior from the modern two systems view may consult my book ‘The Logical Structure of Philosophy, Psychology, Mind and Language in Ludwig Wittgenstein and John Searle’ 2nd ed (2019). Those interested in more of my writings may see ‘Talking Monkeys--Philosophy, Psychology, Science, Religion and Politics on a Doomed Planet--Articles and Reviews 2006-2019 3rd ed (2019) and Suicidal Utopian Delusions in the 21st Century 4th ed (2019