The semantics of rational contractions

This paper is concerned with the revision of beliefs in the face of new and possibly contradicting information. In the Logic of Theory Change developed by Alchourron, Gärdenfors and Makinson this nonmonotonic process consists of a contraction and an expansion of a set of formulas. to achieve minimal change they formulated widely accepted postulates that rational contractions have to fulfill. Contractions as defined by Alchourron, Gärdenfors and Makinson only operate on deductively closed sets of Formulas. Therefore they cannot be used in practical applications, eg. knowledge representation, where only finitely representable sets can be handled. We present a semantical characterization of rational finite contractions (the class of rational contractions maintaining finite representability) which provides an insight into the true nature of these operations. This characterization shows all possibilities to define concrete functions possessing these properties. When regarding concrete contractions known from literature in the light of our characterization we have found that they are all defined according to the same semantical strategy of minimal semantical change. As this strategy does not correspond to the goal of keeping as many important fotmulas as possible in the contracted set, we suggest a finite contraction defined according to the new strategy of maximal maintenance

Datalog± Ontology Consolidation

Knowledge bases in the form of ontologies are receiving increasing attention as they allow to clearly represent both the available knowledge, which includes the knowledge in itself and the constraints imposed to it by the domain or the users. In particular, Datalog ± ontologies are attractive because of their property of decidability and the possibility of dealing with the massive amounts of data in real world environments; however, as it is the case with many other ontological languages, their application in collaborative environments often lead to inconsistency related issues. In this paper we introduce the notion of incoherence regarding Datalog± ontologies, in terms of satisfiability of sets of constraints, and show how under specific conditions incoherence leads to inconsistent Datalog ± ontologies. The main contribution of this work is a novel approach to restore both consistency and coherence in Datalog± ontologies. The proposed approach is based on kernel contraction and restoration is performed by the application of incision functions that select formulas to delete. Nevertheless, instead of working over minimal incoherent/inconsistent sets encountered in the ontologies, our operators produce incisions over non-minimal structures called clusters. We present a construction for consolidation operators, along with the properties expected to be satisfied by them. Finally, we establish the relation between the construction and the properties by means of a representation theorem. Although this proposal is presented for Datalog± ontologies consolidation, these operators can be applied to other types of ontological languages, such as Description Logics, making them apt to be used in collaborative environments like the Semantic Web.Fil: Deagustini, Cristhian Ariel David. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Martinez, Maria Vanina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Falappa, Marcelo Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; ArgentinaFil: Simari, Guillermo Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Ciencias e Ingeniería de la Computación. Universidad Nacional del Sur. Departamento de Ciencias e Ingeniería de la Computación. Instituto de Ciencias e Ingeniería de la Computación; Argentin

Extending Dynamic Doxastic Logic: Accommodating Iterated Beliefs And Ramsey Conditionals Within DDL

In this paper we distinguish between various kinds of doxastic theories. One distinction is between informal and formal doxastic theories. AGM-type theories of belief change are of the former kind, while Hintikka’s logic of knowledge and belief is of the latter. Then we distinguish between static theories that study the unchanging beliefs of a certain agent and dynamic theories that investigate not only the constraints that can reasonably be imposed on the doxastic states of a rational agent but also rationality constraints on the changes of doxastic state that may occur in such agents. An additional distinction is that between non-introspective theories and introspective ones. Non-introspective theories investigate agents that have opinions about the external world but no higher-order opinions about their own doxasticnstates. Standard AGM-type theories as well as the currently existing versions of Segerberg’s dynamic doxastic logic (DDL) are non-introspective. Hintikka-style doxastic logic is of course introspective but it is a static theory. Thus, the challenge remains to devise doxastic theories that are both dynamic and introspective. We outline the semantics for truly introspective dynamic doxastic logic, i.e., a dynamic doxastic logic that allows us to describe agents who have both the ability to form higher-order beliefs and to reflect upon and change their minds about their own (higher-order) beliefs. This extension of DDL demands that we give up the Preservation condition on revision. We make some suggestions as to how such a non-preservative revision operation can be constructed. We also consider extending DDL with conditionals satisfying the Ramsey test and show that Gärdenfors’ well-known impossibility result applies to such a framework. Also in this case, Preservation has to be given up

Is there such a thing as pragmatics? -- Review of Concise Encyclopedia of Pragmatics 2nd ed. (2009)(review revised 2019)

Clearly neither I nor anyone will ever read any substantial part of this massive tome so I will discuss the one article that interests me most and which I think provides the framework necessary for the understanding of all the rest. I refer to the one on Ludwig Wittgenstein (W). Even were I to try to discuss others, we would not get past the first page as all the issues here arise immediately in any discussion of behavior. The differentiation of pragmatics and semantics is largely meaningless. It is defensible that one might subtitle this work ‘Developments of Wittgenstein’s Contextualism’, but of course this term has inevitably been corrupted by philosophers. One might then say that pragmatics and semantics are parts of or coextensive with epistemology and ontology and the descriptive psychology of higher order thought (Searle’s Logical Structure of Rationality) or that they describe how we use noises in specific contexts to give them meaning --i.e., a true or false (propositional) use which Searle calls their Conditions of Satisfaction. Adding the Wittgenstein/Searle work to modern research on thinking provides a framework for pragmatics, semantics and all other human behavior. 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), The Logical Structure of Human Behavior (2019), and Suicidal Utopian Delusions in the 21st Century 4th ed (2019

The lexicographic closure as a revision process

The connections between nonmonotonic reasoning and belief revision are well-known. A central problem in the area of nonmonotonic reasoning is the problem of default entailment, i.e., when should an item of default information representing "if A is true then, normally, B is true" be said to follow from a given set of items of such information. Many answers to this question have been proposed but, surprisingly, virtually none have attempted any explicit connection to belief revision. The aim of this paper is to give an example of how such a connection can be made by showing how the lexicographic closure of a set of defaults may be conceptualised as a process of iterated revision by sets of sentences. Specifically we use the revision process of Nayak.Comment: 7 pages, Nonmonotonic Reasoning Workshop 2000 (special session on belief change), at KR200