Standard approachs to belief change assume that the underlying logic contains classical propositional logic. Recently there has been interest in investigating approaches to belief change, specifically contraction, in which the underlying logic is not as expressive as full propositional logic. In this paper we consider approaches to belief contraction in Horn knowledge bases. We develop two broad approaches for Horn contraction, corresponding to the two major approaches in belief change, based on Horn belief sets and Horn belief bases. We argue that previous approaches, which have taken Horn remainder sets as a starting point, have undesirable properties, and moreover that not all desirable Horn contraction functions are captured by these approaches. This is shown in part by examining model-theoretic considerations involving Horn contraction. For Horn belief set contraction, we develop an account based in terms of weak remainder sets. Maxichoice and partial meet Horn contraction is specified, along with a consideration of package contraction. Following this we consider Horn belief base contraction, in which the underlying knowledge base is not necessarily closed under the Horn consequence relation. Again, approaches to maxichoice and partial meet belief set contraction are developed. In all cases, constructions of the specific operators and sets of postulates are provided, and representation results are obtained. As well, we show that problems arising with earlier work are resolved by these approaches.

This is a case-study in knowledge representation. We analyze the 'one hundred prisoners and a lightbulb' puzzle. In this puzzle it is relevant what the agents (prisoners) know, how their knowledge changes due to observations, and how they affect the state of the world by changing facts, i.e., by their actions. These actions depend on the history of previous actions and observations. Part of its interest is that all actions are local, i.e. not publicly observable, and part of the problem is therefore how to disseminate local results to other agents, and make them global. The various solutions to the puzzle are presented as protocols (iterated functions from agent's local states, and histories of actions, to actions). The computational aspect is about average runtime termination under conditions of random ('fair') scheduling. The paper consists of three parts. First, we present different versions of the puzzle, and their solution. This includes a probabilistic version, and a version assuming synchronicity (the interval between prisoners' interrogations is known). The latter is very informative for the prisoners, and allows different protocols (with faster expected termination). Then, we model the puzzle in an epistemic logic incorporating dynamic operators for the effects of information changing events. Such events include both informative actions, where agents become more informed about the non-changing state of the world, and factual changes, wherein the world and the facts describing it change themselves as well. Finally, we give the expected termination results of several protocols when assuming random scheduling. This paper integrates the literature and presents novel contributions. Novel are: Firstly, Protocol 2 and Protocol 4. Secondly, the modelling in dynamic epistemic logic in its entirety - we do not know of a case study that combines factual and informational dynamics in a setting of non-public events, or of a similar proposal to handle asynchronous behaviour in a dynamic epistemic logic. Thirdly, our computational results on Protocol 2 and results from the manuscript from author Wu.

By logical proportion, we mean a statement that expresses a semantical equivalence between two pairs of propositions. In these pairs, each element is compared to the other in terms of similarities and/or dissimilarities. An example of such a proportion is the well known analogical proportion: a is to b as c is to d . Analogical proportions have been recently characterized in logical terms, but there are many other proportions that are worth of interest. Some of them can be related to the analogical pattern, others are related to semantical equivalence between conditional objects and express statements such as a ressembles to b and differs from b in the same way as c with respect to d. We show that there are 5 direct proportions, including the analogical one and 4 others having a conditional object flavor, where the change (if any) from a to b goes in the same direction as the change from c to d (if any), together with 5 reverse proportions obtained by switching c and d. Moreover, there exists only one auto-reverse proportion called paralogy and stating that what a and b have in common, c and d have it as well. It is then established that there is none other proportion than these ones (with the exception of 4 degenerated ones) that satisfies a natural “full identity” requirement. The paper proposes a structured and unified view of these logical proportions and discusses their characteristic properties. It extends previous works where only proportions related to analogy were considered. It also explores the use of these logical proportions in transduction-like inference, where new items are classified on the basis of already classified items without trying to induce a generic model, considering similarities and differences between items only. Taking advantage of different proportions, a transduction procedure is proposed.

While type causality helps us to understand general relationships such as the etiology of a disease (smoking causing lung cancer), token causality aims to explain causal connections in specific instantiated events, such as the diagnosis of a patient (Ravi’s developing lung cancer after a 20-year smoking habit). Understanding why something happened, as in these examples, is central to reasoning in such diverse cases as the diagnosis of patients, understanding why the US financial market collapsed in 2007 and finding a causal explanation for Obama’s victory over Clinton in the US primary. However, despite centuries of work in philosophy and decades of research in computer science, the problem of how to rigorously formalize token causality and how to automate such reasoning has remained unsolved. In this paper, we show how to use type-level causal relationships, represented as temporal logic formulas, together with philosophical principles, to reason about these token-level cases.

Databases and related information systems can benefit from the use of ontologies to enrich the data with general background knowledge. The DL-Lite family of ontology languages was specifically tailored towards such ontology-based data access, enabling an implementation in a relational database management system (RDBMS) based on a query rewriting approach. In this paper, we propose an alternative approach to implementing ontology-based data access in DL-Lite. The distinguishing feature of our approach is to allow rewriting of both the query and the data. We show that, in contrast to the existing approaches, no exponential blowup is produced by the rewritings. Based on experiments with a number of real-world ontologies, we demonstrate that query execution in the proposed approach is often more efficient than in existing approaches, especially for large ontologies. We also show how to seamlessly integrate the data rewriting step of our approach into an RDBMS using views (which solves the update problem) and make an interesting observation regarding the succinctness of queries in the original query rewriting approach.

The aim of semantic science is to allow for the publications of ontologies, observation data, and hypotheses/theories. Hypotheses make predictions on data and on new cases. Those hypotheses that fit the available evidence are called theories. This paper considers how thoeries can be used for predictions in new cases. Theories are typically very narrow and not all of the inputs to a theory are observed, so to make predictions on a particular case, many theories need to be used. Without any global design, the available theories do not necessarily fit together nicely. This paper explains how theories can be combined into theory ensembles to make predictions on a particular case. This is needed to evaluate theories, and to make useful predictions. We motivate and give desiderata for theory ensembles for level 1, feature-based, semantic science, which assumes that the data and the theories can be described in terms of features (random variables).

We present a decidable class of first-order formulas in the general theory of stable models that can be instantiated even in the presence of function constants. The notion of an argument-restricted formula presented here is a natural generalization of both the notion of an argument-restricted program and the notion of a semi-safe sentence that have been studied in different contexts. Based on this new notion, we extend the notion of safety defined by Cabalar, Pearce and Valverde to arbitrary formulas that allow function constants, and apply the result to $\raspl$ programs and programs with arbitrary aggregates, ensuring finite groundability of those programs in the presence of function constants. We also show that under a certain syntactic condition, argument-restricted formulas can be turned into argument-restricted programs.

In discrete dynamical systems change results from actions. As such, given a set of observations, diagnoses often take the form of posited events that result in the observed behaviour. In this paper we revisit formal characterizations of diagnosis, and their relationship to planning. We do so from both a theoretical and a computational perspective. In particular, we extend the characterization of diagnosis to deal with the case of incomplete information, and rich preferences. We also explore the use of state-of-the-art planning technology for the automated generation of diagnoses. Examining several classes of diagnosis problems, we provide both proof of concept and benchmark experiments, the latter showing superior performance to a leading diagnosis engine. Our findings help support the hypothesis that planning technology holds great promise for efficient generation of diagnoses.

Ontologies can be used to provide an enriched vocabulary for the formulation of queries over instance data. We identify query emptiness and predicate emptiness as two central reasoning services in this context. Query emptiness asks whether a given query has an empty answer over all data sets formulated in a given signature. Predicate emptiness is defined analogously, but quantifies universally over all queries that contain a given predicate. In this paper, we determine the computational complexity of query emptiness and predicate emptiness in the EL, DL-Lite, and ALC-families of description logics, investigate the connection to ontology modules, and perform a practical case study to evaluate the new reasoning services.

In this paper, we consider propositional Topological logics are a family of languages for representing topological logics with connectedness, i.e. topological and reasoning about topological data. The non-logical logics in which the only logical connectives are the usual primitives of these languages stand for various topological Boolean operators, but where there is a non-logical primitive relations and operations, and their valid formulas encode our expressing the property of topological connectedness knowledge about those relations and operations. Consider, (or a variant thereof). We show that such topological logics for example, the six relations illustrated in Figure 1. By em-are typically sensitive both to the spaces they are interpreted over and--more particularly--to the subsets of those spaces over which their variables are allowed to range.