In the area of belief change, contraction operations are used to modify a given belief set or belief base such that certain unwanted consequences no longer follow. In previous work we have introduced a framework for constructing contraction operations that generalizes the well-known partial meet contraction approach, called partial product contractions (PPCs). The main idea was to replace the remainders employed by partial meet contractions with optimal repairs, which were first considered in ontology engineering. We were able to characterize PPCs with variants of well-known rationality postulates, and provided a large number of concrete instances of the general framework. In the present work, we start to investigate whether the rather weak conditions imposed by our framework are sufficient to generalize further classical results from belief change to this setting. To this purpose, we consider Gärdenfors’s supplementary postulates for belief contractions. We are able to show that, under two reasonable additional conditions, PPCs induced by maximizingly and transitively relational selection functions indeed satisfy these postulates, similarly to the classical case. However, unlike the classical case, in our general framework these conditions are not strong enough to prove a characterization theorem. In fact, we provide an example that shows that there are partial product contractions satisfying the supplementary postulates that cannot be obtained from a weakly maximizingly and transitively relational selection function. We also introduce a third condition that ensures that already transitively relational selection functions yield PPCs that satisfy the supplementary postulates.

Removing unwanted consequences from a knowledge base has been investigated in belief change under the name contraction and is called repair in ontology engineering. Simple repair and contraction approaches based on removing statements from the knowledge base (respectively called belief base contractions and classical repairs) have the disadvantage that they are syntax-dependent and may remove more consequences than necessary. Belief set contractions do not have these problems, but may result in belief sets that have no finite representation. Similarly, optimal repairs, which are syntax-independent and maximize the retained consequences, may not exist. Our KR 2024 paper leverage advances in characterizing and computing optimal repairs of ontologies based on the description logics EL to obtain contraction operations that combine the advantages of belief set and belief base contractions. It introduces this new approach in a very general setting, and proves a characterization theorem that relates the obtained contractions with well-known rationality postulates. Then, it describes a variety of interesting instances, not only in the standard repair/contraction setting where one wants to get rid of a consequence, but also in other settings such as variants of forgetting in propositional and description logic.

This special issue of Journal of Logic and Computation brings a selection of papers presented at the 27th Workshop on Logic, Language, Information and Computation (WoLLIC 2021), which was held online, hosted as a Zoom Webinar by University College London. It was the 27th in a series of workshops that started in 1994 with the aim of fostering interdisciplinary research in pure and applied logic . Short versions of 25 papers presented at the Workshop were published in Logic, Language, Information and Computation - 27th International Workshop, WoLLIC 2021, edited by Alexandra Silva, Renata Wassermann and Ruy de Queiroz, Springer Lecture Notes in Computer Science 13038, a volume in the FoLLI-LNCS series. For the present issue, 12 of those 16 extended versions of papers were fully reviewed and appear here in full versions. All papers have been selected and refereed by a fresh panel of referees according to the usual standards of Journal of Logic and Computation. In the call for full versions, the authors were warned that for the paper to be considered for publication, it was expected that the journal version were a significant extension of the paper published in the proceedings of the meeting. The whole content demonstrates the broadness of research interests within the WoLLIC community.

Removing unwanted consequences from a knowledge base has been investigated in belief change under the name contraction and is called repair in ontology engineering. Simple repair and contraction approaches based on removing statements from the knowledge base (respectively called belief base contractions and classical repairs) have the disadvantage that they are syntax-dependent and may remove more consequences than necessary. Belief set contractions do not have these problems, but may result in belief sets that have no finite representation if one works with logics that are not fragments of propositional logic. Similarly, optimal repairs, which are syntax-independent and maximize the retained consequences, may not exist. In this paper, we want to leverage advances in characterizing and computing optimal repairs of ontologies based on the description logics EL to obtain contraction operations that combine the advantages of belief set and belief base contractions. The basic idea is to employ, in the partial meet contraction approach, optimal repairs instead of optimal classical repairs as remainders. We introduce this new approach in a very general setting, and prove a characterization theorem that relates the obtained contractions with well-known postulates. Then, we consider several interesting instances, not only in the standard repair/contraction setting were one wants to get rid of a consequence, but also in other settings such as variants of forgetting in propositional and description logic. We also show that classical belief set contraction is an instance of our approach.

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.

Selective Revision was proposed by Fermé and Hansson as a belief revision operation in which it is possible to accept only a part of the input information. In this paper, we extend Selective Revision to belief bases and also to logics not closed under negation.

Belief change and non-monotonic reasoning are arguably different perspectives on the same phenomenon, namely, jettisoning of currently held beliefs in response to some incompatible evidence. Investigations in this area typically assume, among other things, that the underlying (background) logic is compact, that is, whatever can be inferred from a set of sentences X can be inferred from a finite subset of X. Recent research in the field shows that this compactness assumption can be dispensed without inflicting much damage on the AGM paradigm of belief change. In this paper we investigate the impact of such relaxation on non-monotonic logics instead. In particular, we show that, when compactness is not guaranteed, while the bridge from the AGM paradigm of belief change to expectation logics remains unaffected, the “return trip” from expectation logics to AGM paradigm is no longer guaranteed. We finally explore the conditions under which such guarantee can be given.

The main paradigms of belief change require the background logic to be Tarskian and finitary. We look at belief update when the underlying logic is not necessarily finitary. We show that in this case the classical construction for KM update does not capture all the rationality postulates for KM belief update. Indeed, this construction, being fully characterised by a subset of the KM update postulates, is weaker. We explore the reason behind this, and subsequently provide an alternative constructive accounts of belief update which is characterised by the full set of KM postulates in this more general framework.

In the AGM paradigm for belief revision, epistemic states are represented by logically closed sets of sentences, the so-called belief sets.An alternative approach uses belief bases, arbitrary sets of sentences.Both approaches have their problems when it comes to contraction operations.Belief bases are more expressive, but, at the same time, they present a serious syntax dependence.Between those two extremes lie a whole gamut of operations called pseudo-contractions, some of which may be interesting alternatives to the classical ones, providing a good balance between syntax dependence and expressivity.In this paper we explore some very natural and general constructions for pseudocontractions, showing some of their properties and giving their axiomatic characterizations.We also illustrate possible practical scenarios where they can be employed.

When a planning task cannot be solved then it can often be made solvable by modifying it a bit: one may change either the set of actions, or the initial state, or the goal description. We show that modification of actions can be reduced to initial state modification. We then apply Katsuno and Mendelzon's distinction between update and revision and show that the modification of the initial state is an update and the modification of the goal description is a revision. We consider variants of Forbus's update and Dalal's revision operation and argue that existing belief change operations do not apply as they stand because their inputs are boolean formulas, while plan task modification involves counterfactual statements. We show that they can be captured in Dynamic Logic of Propositional Assignments DL-PA.

In classical, AGM-style belief change, it is assumed that the underlying logic contains classical propositional logic. This is clearly a limiting assumption, particularly in Artificial Intelligence. Consequently there has been recent interest in studying belief change in approaches where the full expressivity of classical propositional logic is not obtained. In this paper we investigate belief contraction in Horn knowledge bases. We point out that the obvious extension to the Horn case, involving Horn remainder sets as a starting point, is problematic. Not only do Horn remainder sets have undesirable properties, but also some desirable Horn contraction functions are not captured by this approach. For Horn belief set contraction, we develop an account in terms of a model-theoretic characterisation involving weak remainder sets. Maxichoice and partial meet Horn contraction is specified, and we show that the problems arising with earlier work are resolved by these approaches. As well, constructions of the specific operators and sets of postulates are provided, and representation results are obtained. We also examine Horn package contraction, or contraction by a set of formulas. Again, we give a construction and postulate set, linking them via a representation result. Last, we investigate the closely-related notion of forgetting in Horn clauses. This work is arguably interesting since Horn clauses have found widespread use in AI; as well, the results given here may potentially be extended to other areas which make use of Horn-like reasoning, such as logic programming, rule-based systems, and description logics. Finally, since Horn reasoning is weaker than classical reasoning, this work sheds light on the foundations of belief change

We show that Booth et al.'s Horn contraction based on infra-remainder sets corresponds exactly to kernel contraction for belief sets. This result is obtained via a detour through Horn contraction for belief bases, which supports the conjecture that Horn belief change is best viewed as a “hybrid” version of belief set change and belief base change. Moreover, the link with base contraction gives us a more elegant representation result for Horn contraction for belief sets in which a version of the Core-retainment postulate features.

Belief Revision deals with the problem of adding new information to a knowledge base in a consistent way. Ontology Debugging, on the other hand, aims to find the axioms in a terminological knowledge base which caused the base to become inconsistent. In this article, we propose a belief revision approach in order to find and repair inconsistencies in ontologies represented in some description logic (DL). As the usual belief revision operators cannot be directly applied to DLs, we propose new operators that can be used with more general logics and show that, in particular, they can be applied to the logics underlying OWL-DL and Lite.

In this article we present ⁠, a family of logics that is useful to disprove propositional formulas by means of an anytime approximation process. The systems follows the paradigm of a parameterized family of logics established by Schaerf's and Cadoli's system S1. We show that inherits several of the nice properties of S1, while presenting several attractive new properties. The family deals with the full propositional language, has a complete tableau proof system which provides for incremental approximations; furthermore, it constitutes a full approximation of classical logic from above, with an approximation process with better relevance and locality properties than S1. When applied to clausal inference, provides a strong simplification method. An application of to model-based diagnosis is presented, demonstrating how the solution to this problem can benefit from the use of approximations.

Real agents (natural or artificial) are limited in their reasoning capabilities. In this paper, we present a general framework for modelling limited reasoning based on approximate reasoning and discuss its properties. We start from Cadoli and Schaerf's approximate entailment. We first extend their system to deal with the full language of propositional logic. A tableau inference system is proposed for the extended system together with a subclassical semantics; it is shown that this new approximate reasoning system is sound and complete with respect to this semantics. We show how this system can be incrementally used to move from one approximation to the next until the reasoning limitation is reached. We also present a sound and complete axiomatization of the extended system. We note that although the extension is more expressive than the original system, it offers less control over the approximation process. We then propose a more general system and show that it keeps the increased expressivity and recovers the control. A sound and complete formulation for this new system is given and its expressivity and control advantages are formally proved.