scholarly journals Belief Update within Propositional Fragments

2018 ◽  
Vol 61 ◽  
pp. 807-834 ◽  
Author(s):  
Nadia Creignou ◽  
Raïda Ktari ◽  
Odile Papini
Keyword(s):  
Knowledge Representation ◽  
Belief Revision ◽  
Classical Logic ◽  
Propositional Logic ◽  
Belief Change ◽  
Research Area ◽  
Belief Contraction ◽  
Belief Merging ◽  
Change Operation ◽  
Horn Fragment

Belief change within the framework of fragments of propositional logic is one of the main and recent challenges in the knowledge representation research area. While previous research works focused on belief revision, belief merging, and belief contraction, the problem of belief update within fragments of classical logic has not been addressed so far. In the context of revision, it has been proposed to refine existing operators so that they operate within propositional fragments, and that the result of revision remains in the fragment under consideration. This approach is not restricted to the Horn fragment but also applicable to other propositional fragments like Krom and affine fragments. We generalize this notion of refinement to any belief change operator. We then focus on a specific belief change operation, namely belief update. We investigate the behavior of the refined update operators with respect to satisfaction of the KM postulates and highlight differences between revision and update in this context.

scholarly journals Two Sides of the Same Coin: Belief Revision and Enforcing Arguments

2018 ◽  
Author(s):  
Adrian Haret ◽  
Johannes P. Wallner ◽  
Stefan Woltran
Keyword(s):  
Belief Revision ◽  
Propositional Logic ◽  
Belief Change ◽  
Knowledge Bases ◽  
Abstract Argumentation ◽  
Axiomatic Treatment ◽  
Close Relationship ◽  
Representation Result ◽  
Two Sides ◽  
Argumentation Systems

We study a type of change on knowledge bases inspired by the dynamics of formal argumentation systems, where the goal is to enforce acceptance of certain arguments. We put forward that enforcing acceptance of arguments can be viewed as a member of the wider family of belief change operations, and that an axiomatic treatment of it is therefore desirable. In our case, laying down axioms enables a precise account of the close connection between enforcing arguments and belief revision. Our analysis of enforcing arguments proceeds by (i) axiomatizing it as an operation in propositional logic and providing a representation result in terms of rankings on sets of interpretations, (ii) showing that it stands in close relationship to belief revision, and (iii) using it as a gateway towards a principled treatment of enforcement in abstract argumentation.

scholarly journals Belief Update in the Horn Fragment

2018 ◽  
Author(s):  
Nadia Creignou ◽  
Adrian Haret ◽  
Odile Papini ◽  
Stefan Woltran
Keyword(s):  
Recent Work ◽  
Propositional Logic ◽  
Possible Worlds ◽  
Belief Change ◽  
Representation Result ◽  
Total Preorders ◽  
Horn Fragment ◽  
Shed Light

In line with recent work on belief change in fragments of propositional logic, we study belief update in the Horn fragment. We start from the standard KM postulates used to axiomatize belief update operators; these postulates lend themselves to semantic characterizations in terms of partial (resp. total) preorders on possible worlds. Since the Horn fragment is not closed under disjunction, the standard postulates have to be adapted for the Horn fragment. Moreover, a restriction on the preorders (i.e., Horn compliance) and additional postulates are needed to obtain sensible characterizations for the Horn fragment, and this leads to our main contribution: a representation result which shows that the class of update operators captured by Horn compliant partial (resp. total) preorders over possible worlds is precisely that given by the adapted and augmented Horn update postulates. With these results at hand, we provide concrete Horn update operators and are able to shed light on Horn revision operators based on partial preorders.

Belief Contraction in Non-classical logics as Hyperintensional Belief Change

2021 ◽  
Author(s):  
Marlo Souza ◽  
Renata Wassermann
Keyword(s):  
Belief Revision ◽  
General Framework ◽  
Belief Change ◽  
Description Logics ◽  
Belief Contraction

AGM's belief revision is one of the main paradigms in the study of belief change operations. Despite its popularity and importance to the area, it is well recognised that AGM's work relies on a strong idealisation of the agent's capabilities and the nature of beliefs themselves. Particularly, it is recognised in the literature that Belief and Knowledge are hyperintensional attitudes, i.e. they can differentiate between contents that are necessarily equivalent, but to our knowledge, only a few works have explicitly considered how hyperintensionality affects belief change. This work investigates abstract operations of hyperintensional belief change and their connection to belief change in non-classical logics, such as belief contraction operations for Horn Logics and Description Logics. Our work points to hyperintensional belief change as a general framework to unify results in belief change for non-classical logics.

scholarly journals Entrenchment-Based Horn Contraction

2014 ◽  
Vol 51 ◽  
pp. 227-254 ◽  
Author(s):  
Z. Zhuang ◽  
M. Pagnucco
Keyword(s):  
Representation Theorem ◽  
Propositional Logic ◽  
Belief Change ◽  
Approximation Technique ◽  
Classical Propositional Logic ◽  
Horn Logic ◽  
Restricted Form ◽  
Horn Fragment ◽  
Benchmark Approach

The AGM framework is the benchmark approach in belief change. Since the framework assumes an underlying logic containing classical Propositional Logic, it can not be applied to systems with a logic weaker than Propositional Logic. To remedy this limitation, several researchers have studied AGM-style contraction and revision under the Horn fragment of Propositional Logic (i.e., Horn logic). In this paper, we contribute to this line of research by investigating the Horn version of the AGM entrenchment-based contraction. The study is challenging as the construction of entrenchment-based contraction refers to arbitrary disjunctions which are not expressible under Horn logic. In order to adapt the construction to Horn logic, we make use of a Horn approximation technique called Horn strengthening. We provide a representation theorem for the newly constructed contraction which we refer to as entrenchment-based Horn contraction. Ideally, contractions defined under Horn logic (i.e., Horn contractions) should be as rational as AGM contraction. We propose the notion of Horn equivalence which intuitively captures the equivalence between Horn contraction and AGM contraction. We show that, under this notion, entrenchment-based Horn contraction is equivalent to a restricted form of entrenchment-based contraction.

scholarly journals Iterated contraction of propositions and conditionals under the principle of conditional preservation

10.29007/3q8l ◽  
2018 ◽  
Author(s):  
Gabriele Kern-Isberner ◽  
Tanja Bock ◽  
Kai Sauerwald ◽  
Christoph Beierle
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Ranking Function ◽  
Ranking Functions ◽  
Belief Contraction ◽  
Seminal Work ◽  
Iterated Belief Revision ◽  
Iterated Contraction

Research on iterated belief change has focussed mostly on belief revision, only few papers have addressed iterated belief contraction. Most prominently, Darwiche and Pearl published seminal work on iterated belief revision the leading paradigm of which is the so-called principle of conditional preservation. In this paper, we use this principle in a thoroughly axiomatized form to develop iterated belief contraction operators for Spohn's ranking functions. We show that it allows for setting up constructive approaches to tackling the problem of how to contract a ranking function by a proposition or a conditional, respectively, and that semantic principles can also be derived from it for the purely qualitative case.

Text as tautology: an exploration in inference, transitivity, and logical compression

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Andrew Potter
Keyword(s):  
Knowledge Representation ◽  
Propositional Logic ◽  
Research Literature ◽  
Transitive Inference ◽  
Structure Theory ◽  
Rhetorical Structure ◽  
Logical Models ◽  
Logical Operations ◽  
Selection Of

Abstract Rhetorical structure theory (RST) and relational propositions have been shown useful in analyzing texts as expressions in propositional logic. Because these expressions are systematically derived, they may be expected to model discursive reasoning as articulated in the text. If this is the case, it would follow that logical operations performed on the expressions would be reflected in the texts. In this paper the logic of relational propositions is used to demonstrate the applicability of transitive inference to discourse. Starting with a selection of RST analyses from the research literature, analyses of the logic of relational propositions are performed to identify their corresponding logical expressions and within each expression to identify the inference path implicit within the text. By eliminating intermediary relational propositions, transitivity is then used to progressively compress the expression. The resulting compressions are applied to the corresponding texts and their compressed RST analyses. The application of transitive inference to logical expressions results in abridged texts that are intuitively coherent and logically compatible with their originals. This indicates an underlying isomorphism between the inferential structure of logical expressions and discursive coherence, and it confirms that these expressions function as logical models of the text. Potential areas for application include knowledge representation, logic and argumentation, and RST validation.

(DIS)BELIEF CHANGE AND ARGUED FEED-BACK DIALOG

2005 ◽  
Vol 13 (05) ◽  
pp. 511-538
Author(s):  
LAURENT PERRUSSEL ◽  
JEAN-MARC THÉVENIN
Keyword(s):  
Belief Revision ◽  
Belief Change ◽  
Preference Relation ◽  
Belief State ◽  
Temporal Aspects ◽  
Incoming Information ◽  
Multi Agent

This paper focuses on the features of belief change in a multi-agent context where agents consider beliefs and disbeliefs. Disbeliefs represent explicit ignorance and are useful to prevent agents to entail conclusions due to their ignorance. Agents receive messages holding information from other agents and change their belief state accordingly. An agent may refuse to adopt incoming information if it prefers its own (dis)beliefs. For this, each agent maintains a preference relation over its own beliefs and disbeliefs in order to decide if it accepts or rejects incoming information whenever inconsistencies occur. This preference relation may be built by considering several criteria such as the reliability of the sender of statements or temporal aspects. This process leads to non-prioritized belief revision. In this context we first present the * and − operators which allow an agent to revise, respectively contract, its belief state in a non-prioritized way when it receives an incoming belief, respectively disbelief. We show that these operators behave properly. Based on this we then illustrate how the receiver and the sender may argue when the incoming (dis)belief is refused. We describe pieces of dialog where (i) the sender tries to convince the receiver by sending arguments in favor of the original (dis)belief and (ii) the receiver justifies its refusal by sending arguments against the original (dis)belief. We show that the notion of acceptability of these arguments can be represented in a simple way by using the non-prioritized change operators * and −. The advantage of argumentation dialogs is twofold. First whenever arguments are acceptable the sender or the receiver reconsider its belief state; the main result is an improvement of the reconsidered belief state. Second the sender may not be aware of some sets of rules which act as constraints to reach a specific conclusion and discover them through argumentation dialogs.

scholarly journals Modeling Belief in Dynamic Systems, Part II: Revision and Update

1999 ◽  
Vol 10 ◽  
pp. 117-167 ◽  
Author(s):  
N. Friedman ◽  
J. Y. Halpern
Keyword(s):  
Artificial Intelligence ◽  
Belief Revision ◽  
Dynamic Systems ◽  
Belief Change ◽  
Companion Paper ◽  
Minimal Change ◽  
Special Cases ◽  
Epistemic Modalities ◽  
Over Time ◽  
New Framework

The study of belief change has been an active area in philosophy and AI. In recent years two special cases of belief change, belief revision and belief update, have been studied in detail. In a companion paper (Friedman & Halpern, 1997), we introduce a new framework to model belief change. This framework combines temporal and epistemic modalities with a notion of plausibility, allowing us to examine the change of beliefs over time. In this paper, we show how belief revision and belief update can be captured in our framework. This allows us to compare the assumptions made by each method, and to better understand the principles underlying them. In particular, it shows that Katsuno and Mendelzon's notion of belief update (Katsuno & Mendelzon, 1991a) depends on several strong assumptions that may limit its applicability in artificial intelligence. Finally, our analysis allow us to identify a notion of minimal change that underlies a broad range of belief change operations including revision and update.

scholarly journals On density of truth of the intuitionistic logic in one variable

2008 ◽  
Vol DMTCS Proceedings vol. AI,... (Proceedings) ◽  
Author(s):  
Zofia Kostrzycka
Keyword(s):  
Intuitionistic Logic ◽  
Classical Logic ◽  
Propositional Logic ◽  
Propositional Variable ◽  
Intuitionistic Propositional Logic ◽  
International Audience

International audience In this paper we focus on the intuitionistic propositional logic with one propositional variable. More precisely we consider the standard fragment $\{ \to ,\vee ,\bot \}$ of this logic and compute the proportion of tautologies among all formulas. It turns out that this proportion is different from the analog one in the classical logic case.

Probabilistic Models for the Semantic Web

2010 ◽  
pp. 74-105 ◽  
Author(s):  
Livia Predoiu
Keyword(s):  
Semantic Web ◽  
Knowledge Representation ◽  
Classical Logic ◽  
Probabilistic Models ◽  
Expressive Power ◽  
Knowledge Representation And Reasoning ◽  
Uncertain Information ◽  
New Approaches ◽  
The Web

Recently, there has been an increasing interest in formalisms for representing uncertain information on the Semantic Web. This interest is triggered by the observation that knowledge on the web is not always crisp and we have to be able to deal with incomplete, inconsistent and vague information. The treatment of this kind of information requires new approaches for knowledge representation and reasoning on the web as existing Semantic Web languages are based on classical logic which is known to be inadequate for representing uncertainty in many cases. While different general approaches for extending Semantic Web languages with the ability to represent uncertainty are explored, we focus our attention on probabilistic approaches. We survey existing proposals for extending semantic web languages or formalisms underlying Semantic Web languages in terms of their expressive power, reasoning capabilities as well as their suitability for supporting typical tasks associated with the Semantic Web.

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