Like Pearl’s System Z, c-representations provide a constructive approach to compute a ranking function from a conditional belief base from which further (conditional) beliefs can be derived, meeting major quality standards of nonmonotonic reasoning. This paper proposes a network-based structure for c-representations that allows for cutting down the complexity of reasoning significantly by decomposing the conditional belief base over a hypertree. We introduce c-LEG networks capturing the interactions among conditionals on a syntactical basis in full compatibility with the semantics of c-representations. This allows for reasoning in much smaller local contexts while still complying with the global information provided by the full conditional belief base. Moreover, we generalize the so-called safety property, which was recently presented in the context of conditional syntax splitting, to ensure that local c-representations of subbases over the hyperedges can be merged to yield global c-representations of the full conditional belief base. This allows for computing global c-representations step by step in local contexts, following the structure of the hypertree.

In this paper, we present a general framework for ranking sets of arguments in abstract argumentation frameworks based on their plausibility of acceptance. We present a generalisation of Dung’s extension semantics as extension-ranking semantics, which induce a preorder over the power set of all arguments, allowing us to state that one set is “closer” to being acceptable than another. To evaluate the extension-ranking semantics, we introduce a number of principles that a well-behaved extensionranking semantics should satisfy. We consider several simple base relations, each of which models a single central aspect of argumentative reasoning. The combination of these base relations provides us with a family of extension-ranking semantics.

Splitting techniques in knowledge representation help focus on relevant parts of a belief base and reduce the complexity of reasoning generally. In this paper, we propose a generalization of safe conditional syntax splittings that broadens the applicability of splitting postulates for inductive inference from belief bases. In contrast to safe conditional syntax splitting, our generalized notion supports syntax splittings of a belief base ∆ where the subbases of ∆ may share atoms and nontrivial conditionals. We illustrate how this new notion overcomes limitations of previous splitting concepts, and we identify genuine splittings, separating them from simple splittings that do not provide benefits for inductive inference from ∆. We introduce adjusted inference postulates based on our generalization of conditional syntax splitting. We evaluate several inductive inference operators with respect to these postulates, and show that generalized safe conditional syntax splitting is a strictly stronger requirement for inductive inference operators, covering more syntax splitting applications.

It is well-known from probability theory that network-based methods like Bayesian networks constitute remarkable frameworks for efficient probabilistic reasoning. In this paper, we focus on qualitative default reasoning based on Spohn’s ranking functions for which network-based methods have not yet been studied satisfactorily. With constraint networks, we develop a framework for iterative calculations of c-representations, a family of ranking models of conditional belief bases which show outstanding properties from a commonsense and formal point of view, that are characterized by assigning possible worlds a degree of implausibility via penalizing the falsification of conditionals. Constraint networks unveil the dependencies among these penalty points (and hence among the conditionals) and make it possible to compute the penalty points locally on so-called safe sub-bases. As an application of our framework, we show that skeptical c-inferences can be drawn locally from safe sub-bases without losing validity.

The concept of conditional syntax splitting for inductive inference from conditional belief bases has been proposed as a generalization of syntax splitting which also covers cases where the conditionals in the subbases share some atoms. p-Entailment and system Z fail to satisfy conditional syntax splitting, and up to now, only two inductive inference operators, lexicographic inference and system W, have been shown to satisfy this property. In this paper, we introduce the concept of conditional semantic splitting. We show that c-representations satisfy a core postulate relating conditional splittings on the syntax and the semantic level. Based on these findings, we investigate conditional syntax splitting for nonmonotonic inference with c-representations. Regarding single c-representations, we utilize the concept of selection strategies, and show that a straightforward property of the selection strategy leads to inference operators satisfying conditional syntax splittings. Furthermore, we show that c-inference taking all c-representations of a belief base into account also fully complies with conditional syntax splitting.

Total preorders and Spohn’s ranking functions are most popular semantic structures in nonmonotonic reasoning and belief revision. Each ranking function uniquely induces a total preorder, while each total preorder corresponds to infinitely many ranking functions because of the empty layers that ranking functions may have. In this paper, we adopt a dynamic perspective and investigate the role of empty layers in belief revision scenarios. We strengthen the notion of (inferential) equivalence of ranking functions by introducing revision equivalence which postulates the equivalence of ranking functions after (most general) revision operations. Moreover, we single out so-called linearly equivalent ranking functions as prototypes of ranking functions with regularly inserted empty layers. Such ranking functions are most suitable to provide an invariance property for revision equivalence which claims that linear equivalence should be preserved. We show that strategic c-revisions ensure (conditional) revision equivalence of linearly equivalent ranking functions if the strategies are adequately chosen, whereas the Darwiche-Pearl postulates for iterated revision alone are not enough to guarantee revision equivalence of ranking functions. We evaluate various other iterated revision approaches from the literature with respect to revision equivalence and preserving linear equivalence under revision. Furthermore, we present an approach to defining equivalence preserving revision operators for ranking functions from revision operators for total preorders.

Syntax splitting is a property of inductive inference operators that ensures we can restrict our attention to parts of the conditional belief base that share atoms with a given query. To apply syntax splitting, a conditional belief base needs to consist of syntactically disjoint conditionals. This requirement is often too strong in practice, as conditionals might share atoms. In this paper we introduce the concept of conditional syntax splitting, inspired by the notion of conditional independence as known from probability theory. We show that lexicographic inference and system W satisfy conditional syntax splitting, and connect conditional syntax splitting to several known properties from the literature on non-monotonic reasoning, including the drowning effect.

New information in the context of real life settings usually is accompanied by some kind of supplementary information that indicates context, reliability, or expertise of the information's source. Bounded Revision (BR) displays an iterated belief revision mechanism that takes as input a new information accompanied by a reference sentence acting as supplementary information, which specifies the depth with which the new input shall be integrated in the posterior belief state. The reference sentence specifies which worlds in the prior belief state are affected by the change mechanism. We show that Bounded Revision can be characterized by three simple, yet elegant postulates and corresponds to a special case of a lexicographic revision, which inherits all relevant features of BR. Furthermore, we present methodological implementations of BR including conditional revision with c-revisions, making it directly usable for conditional revision tools.

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals, and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that relationships between belief revision, defeasible conditionals, and nonmonotonic inference similar to those in propositional logic hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

Abstract Answer set programs used in real-world applications often require that the program is usable with different input data. This, however, can often lead to contradictory statements and consequently to an inconsistent program. Causes for potential contradictions in a program are conflicting rules. In this paper, we show how to ensure that a program $\mathcal{P}$ remains non-contradictory given any allowed set of such input data. For that, we introduce the notion of conflict-resolving ${\lambda}$ -extensions. A conflict-resolving ${\lambda}$ -extension for a conflicting rule r is a set ${\lambda}$ of (default) literals such that extending the body of r by ${\lambda}$ resolves all conflicts of r at once. We investigate the properties that suitable ${\lambda}$ -extensions should possess and building on that, we develop a strategy to compute all such conflict-resolving ${\lambda}$ -extensions for each conflicting rule in $\mathcal{P}$ . We show that by implementing a conflict resolution process that successively resolves conflicts using ${\lambda}$ -extensions eventually yields a program that remains non-contradictory given any allowed set of input data.

Abstract dialectical frameworks (in short, ADFs) are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. This idea is generalized by letting acceptance conditions being assigned to complex formulas, resulting in conditional abstract dialectical frameworks (in short, cADFs). We define the semantics of cADFs in terms of a non-truth-functional four-valued logic, and study the semantics in-depth, by showing existence results and proving that all semantics are generalizations of the corresponding semantics for ADFs.

Lexicographic inference is a well-known and popular approach to reasoning with non-monotonic conditionals. It is a logic of very high-quality, as it extends rational closure and avoids the so-called drowning problem. It seems, however, this high quality comes at a cost, as reasoning on the basis of lexicographic inference is of high computational complexity. In this paper, we show that lexicographic inference satisfies syntax splitting, which means that we can restrict our attention to parts of the belief base that share atoms with a given query, thus seriously restricting the computational costs for many concrete queries. Furthermore, we make some observations on the relationship between c-representations and lexicographic inference, and reflect on the relation between syntax splitting and the drowning problem.

Abstract dialectical frameworks (in short, ADFs) are one of the most general and unifying approaches to formal argumentation. As the semantics of ADFs are based on three-valued interpretations, we ask which monotonic three-valued logic allows to capture the main semantic concepts underlying ADFs. We show that possibilistic logic is the unique logic that can faithfully encode all other semantical concepts for ADFs. Based on this result, we also characterise strong equivalence and introduce possibilistic ADFs.

Conditional independence is a crucial concept for efficient probabilistic reasoning. For symbolic and qualitative reasoning, however, it has played only a minor role. Recently, Lynn, Delgrande, and Peppas have considered conditional independence in terms of syntactic multivalued dependencies. In this paper, we define conditional independence as a semantic property of epistemic states and present axioms for iterated belief revision operators to obey conditional independence in general. We show that c-revisions for ranking functions satisfy these axioms, and exploit the relevance of these results for iterated belief revision in general.

Revision by Comparison (RbC) is a non-prioritized belief revision mechanism on epistemic states that specifies constraints on the plausibility of an input sentence via a designated reference sentence, allowing for kind of relative belief revision. In this paper, we make the strategy underlying RbC more explicit and transfer the mechanism together with its intuitive strengths to a semi-quantitative framework based on ordinal conditional functions where a more elegant implementation of RbC is possible. We furthermore show that RbC can be realized as an iterated revision by so-called weak conditionals. Finally, we point out relations of RbC to credibility-limited belief revision, illustrating the versatility of RbC for advanced belief revision operations.

Extension-based semantics in abstract argumentation provide a criterion to determine whether a set of arguments is acceptable or not. In this paper, we present the notion of extension-ranking semantics, which determines a preordering over sets of arguments, where one set is deemed more plausible than another if it is somehow more acceptable. We obtain extension-based semantics as a special case of this new approach, but it also allows us to make more fine-grained distinctions, such as one set being "more complete'' or "more admissible'' than another. We define a number of general principles to classify extension-ranking semantics and develop concrete approaches. We also study the relation between extension-ranking semantics and argument-ranking based semantics, which rank individual arguments instead of sets of arguments.

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that similar relationships between belief revision, defeasible conditionals and nonmonotonic inference hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

According to Boutillier, Darwiche, Pearl and others, principles for iterated revision can be characterised in terms of changing beliefs about conditionals. For iterated contraction a similar formulation is not known. This is especially because for iterated belief change the connection between revision and contraction via the Levi and Harper identity is not straightforward, and therefore, characterisation results do not transfer easily between iterated revision and contraction. In this article, we develop an axiomatisation of iterated contraction in terms of changing conditional beliefs. We prove that the new set of postulates conforms semantically to the class of operators like the ones given by Konieczny and Pino P\'erez for iterated contraction.

Parikh developed the notion of syntax splitting to describe belief sets with independent parts. He also formulated a postulate demanding that belief revisions respect syntax splittings in belief sets. The concept of syntax splitting was later transferred to epistemic states with total preorders and ranking functions by Kern-Isberner and Brewka along with corresponding postulates for belief revisions. Besides revision, contraction is also a central operation in the field of general belief change. In this paper, we analyse belief contractions with respect to syntax splitting. Based on the work on syntax splitting for revision, we develop syntax splitting postulates for contractions on ranking functions, on epistemic states with total preorder, and on belief sets. Finally, we evaluate different contractions from the literature, namely moderate contraction, natural contraction, lexicographic contraction, and c-contractions with respect to the newly developed contraction postulates.

Syntax splitting, first introduced by Parikh in 1999, is a natural and desirable property of KR systems. Syntax splitting combines two aspects: it requires that the outcome of a certain epistemic operation should only depend on relevant parts of the underlying knowledge base, where relevance is given a syntactic interpretation (relevance). It also requires that strengthening antecedents by irrelevant information should have no influence on the obtained conclusions (independence). In the context of belief revision the study of syntax splitting already proved useful and led to numerous new insights. In this paper we analyse syntax splitting in a different setting, namely nonmonotonic reasoning based on conditional knowledge bases. More precisely, we analyse inductive inference operators which, like system P, system Z, or the more recent c-inference, generate an inference relation from a conditional knowledge base. We axiomatize the two aforementioned aspects of syntax splitting, relevance and independence, as properties of such inductive inference operators. Our main results show that system P and system Z, whilst satisfying relevance, fail to satisfy independence. C-inference, in contrast, turns out to satisfy both relevance and independence and thus fully complies with syntax splitting.

Conditional information is an integral part of representation and inference processes of causal relationships, temporal events, and even the deliberation about impossible scenarios of cognitive agents. For formalizing these inferences, a proper formal representation is needed. Psychological studies indicate that classical, monotonic logic is not the approriate model for capturing human reasoning: There are cases where the participants systematically deviate from classically valid answers, while in other cases they even endorse logically invalid ones. Many analyses covered the independent analysis of individual inference rules applied by human reasoners. In this paper we define inference patterns as a formalization of the joint usage or avoidance of these rules. Considering patterns instead of single inferences opens the way for categorizing inference studies with regard to their qualitative results. We apply plausibility relations which provide basic formal models for many theories of conditionals, nonmonotonic reasoning, and belief revision to asses the rationality of the patterns and thus the individual inferences drawn in the study. By this replacement of classical logic with formalisms most suitable for conditionals, we shift the basis of judging rationality from compatibility with classical entailment to consistency in a logic of conditionals. Using inductive reasoning on the plausibility relations we reverse engineer conditional knowledge bases as explanatory model for and formalization of the background knowledge of the participants. In this way the conditional knowledge bases derived from the inference patterns provide an explanation for the outcome of the study that generated the inference pattern.

In an ongoing project aiming at a comprehensive AI-based tool to support clinical decisions in medical cancer therapy, the ontology OCTA is being developed. Its purpose is to provide general knowledge about active ingredients, therapy regimens, etc. that can be used by such a clinical decision support system. In this paper, we present a new extension of OCTA modelling co-medication and drug interactions, enabling the answering of queries relevant for medical decision making dealing with these aspects.

AGM theory is the most influential formal account of belief revision. Nevertheless, there are some issues with the original proposal. In particular, Parikh has pointed out that completely irrelevant information may be affected in AGM revision. To remedy this, he proposed an additional axiom (P) aiming to capture (ir)relevance by a notion of syntax splitting. In this paper we generalize syntax splitting from logical sentences to epistemic states, a step which is necessary to cover iterated revision. The generalization is based on the notion of marginalization of epistemic states. Furthermore, we study epistemic syntax splitting in the context of ordinal conditional functions. Our approach substantially generalizes the semantical treatment of (P) in terms of faithful preorders recently presented by Peppas and colleagues.

While the axiomatic system P is an important standard for plausible nonmonotonic reasoning, inference relations obtained from system Z or from c-representations have been designed which go beyond system P. In this paper, we propose the new concept of weakly skeptical inference that properly extends the recently introduced skeptical c-inference, but avoids disadvantages of a too liberal credulous inference. We extend the concepts of skeptical, weakly skeptical, and credulous c-inference by taking preferred models obtained from different minimality criteria into account. We illustrate the usefulness of the obtained inference relations, show that they fulfill various desirable properties, and elaborate on their interrelationships.

We investigate the space of ordinal semantics, where the status of an argument is interpreted by a natural number. In doing so we do not only consider the usual acceptability-based approach for generalizing classical semantics to multi-valued semantics, i.e., positioning “undecided” arguments to be in between “in” and “out” arguments, but also a controversiality-based approach where we interpret the value “undecided” as being the most controversial status of an argument. We introduce stratified labelings as a novel semantical approach that follows the idea of a controversiality-based order of truth-values. We investigate general properties for ordinal semantics and of our approach of stratified labelings in particular.

Dealing with uncertainty that is inherently present in any medical domain, is one of the major challenges when designing a medical decision support system. We demonstrate how probabilistic logic can be used to design medical knowledge bases at the example of analysing clinical brain tumor data. We use MECoRe, a system implementing probabilistic conditional logic, to create a knowledge base BT that contains medical knowledge originating from both statistical data as well as from medical experts. Any incomplete or unspecified knowledge is completed by MECoRe in an information-theoretically optimal way by employing the principle of maximum entropy. BT is evaluated with respect to a series of queries regarding diagnosis and prognosis, using a real documented patient case.

Legal reasoning is one of the most obvious application areas for computational models of argumentation as the exchange of arguments and counterarguments is the established means for making decisions in law. In this paper we employ Defeasible Logic Programming (DeLP) for representing legal cases and for giving decision-support, exemplary for private law. We give a formalization of legal provisions that can be used easily by judges for supporting their decision process and present a working system that resembles the decision-making in legal reasoning, in particular, with respect to the burden of proof.

Many works have identified the potential benefits of using argumentation to address a large variety of multiagent problems. In this paper we take this idea one step further and develop the concept of a fully integrated argumentation-based agent architecture that allows us to develop agents that are coherently designed on an underlying argumentation based foundation. Under this architecture, an agent is composed of a collection of modules each of which is equipped with a local argumentation theory. Similarly, the intra-agent control of the agent is governed by local argumentation theories that are sensitive to the current situation of the agent through dynamically enabled feasibility arguments.

Computer vision can highly benefit from modern learning methods. In the context of an active vision environment we introduce a machine learning approach which is able to learn strategies of object acquisition. We propose a hybrid learning method, called Sphinx, that combines two approaches originating from seperate disciplines of computer science, namely reinforcement learning on the one hand and belief revision on the other. The former represents knowledge in a numerical way, while the latter is based on symbolic logic and allows reasoning. Sphinx is designed according to human cognition and interacts with its environment by rotating objects depending on past perceptions to acquire those views which are advantageous for recognition. Our method was successfully applied in simulations of object categorization tasks. 1

From a conceptual point of view, belief revision and learning are quite similar. Both methods change the belief state of an intelligent agent by processing incoming information. However, for learning, the focus in on the exploitation of data to extract and assimilate useful knowledge, whereas belief revision is more concerned with the adaption of prior beliefs to new information for the purpose of reasoning. In this paper, we propose a hybrid learning method called SPHINX that combines low-level, non-cognitive reinforcement learning with high-level epistemic belief revision, similar to human learning. The former represents knowledge in a sub-symbolic, numerical way, while the latter is based on symbolic, non-monotonic logics and allows reasoning. Beyond the theoretical appeal of linking methods of very different disciplines of artificial intelligence, we will illustrate the usefulness of our approach by employing SPHINX in the area of computer vision for object recognition tasks. The SPHINX agent interacts with its environment by rotating objects depending on past experiences and newly acquired generic knowledge to choose those views which are most advantageous for recognition.

This paper is on the combination of two powerful approaches to uncertain reasoning: logic programming in a probabilistic setting, on the one hand, and the information-theoretical principle of maximum entropy, on the other hand. More precisely, we present two approaches to probabilistic logic programming under maximum entropy. The first one is based on the usual notion of entailment under maximum entropy, and is defined for the very general case of probabilistic logic programs over Boolean events. The second one is based on a new notion of entailment under maximum entropy, where the principle of maximum entropy is coupled with the closed world assumption (CWA) from classical logic programming. It is only defined for the more restricted case of probabilistic logic programs over conjunctive events. We then analyze the nonmonotonic behavior of both approaches along benchmark examples and along general properties for default reasoning from conditional knowledge bases. It turns out that both approaches have very nice nonmonotonic features. In particular, they realize some inheritance of probabilistic knowledge along subclass relationships, without suffering from the problem of inheritance blocking and from the drowning problem. They both also satisfy the property of rational monotonicity and several irrelevance properties. We finally present algorithms for both approaches, which are based on generalizations of recent techniques for probabilistic logic programming under logical entailment. The algorithm for the first approach still produces quite large weighted entropy maximization problems, while the one for the second approach generates optimization problems of the same size as the ones produced in probabilistic logic programming under logical entailment.

This article presents new methods for probabilistic belief revision and information fusion. By making use of the information theoretical principles of optimum entropy (ME principles), we define a generalized revision operator that aims at simulating the human learning of lessons, and we introduce a fusion operator that handles probabilistic information faithfully. This ME-fusion operator satisfies basic demands, such as commutativity and the Pareto principle. A detailed analysis shows it to merge the corresponding epistemic states. Furthermore, it induces a numerical fusion operator that computes the information theoretical mean of probabilities. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 837–857, 2004.

We define the very rich language of composed conditionals on a three-valued logic and use this language as the communication tool between man and machine. Communication takes place for three reasons: knowledge acquisition, query, and response. Learning, thinking, and answering questions are of a pure information theoretical nature. The pivot of this knowledge processing concept is the amount of information (bit) we receive if a conditional becomes true. We follow an axiomatic approach to information theory rather than the classical probabilistic approach of Shannon; information comes first, and then comes probability. In the light of this philosophy, query and response experience new interpretations. Both, acquisition and response are realized by maximizing entropy and minimizing relative entropy, respectively. The iterative solution of these mathematical optimization problems gives new insights into the adaptation of prior knowledge to new information. Our expert system shell SPIRIT supports this kind of knowledge processing, which will be established by suitable examples. © 2003 Wiley Periodicals, Inc.

Joint distributions of discrete random variables, for instance, in the form of contingency tables, are a well-known means for representing knowledge. Their mathematical exactness and easy computability seem to be ideal preconditions for use as a knowledge base. The complexity of information they embody, however, makes it difficult to assign correct probabilities to events or—on the other hand—to understand the meanings of such probabilities and realize dependencies and independences. In this article, we introduce a method to detect automatically dependencies between random variables, extracting and aggregating the information given only by the probability values of the underlying distribution. No further presuppositions are imposed on the random variables; the method works by intensional reasoning. We use probabilistic logic to derive and describe our results, and the interpretation of the joint distribution is presented as a set of probabilistic rules. Most of the rules have the character of default rules, and hints on possible exceptions may be found as well. Moreover, classifications and hierarchical structures may also be taken into account. Thus, the rules are intended to reflect important features of the objects under consideration. © 1996 John Wiley & Sons, Inc.