Reasoning about Minimal Belief and Negation as Failure

We investigate the problem of reasoning in the propositional fragment of MBNF, the logic of minimal belief and negation as failure introduced by Lifschitz, which can be considered as a unifying framework for several nonmonotonic formalisms, including default logic, autoepistemic logic, circumscription, epistemic queries, and logic programming. We characterize the complexity and provide algorithms for reasoning in propositional MBNF. In particular, we show that entailment in propositional MBNF lies at the third level of the polynomial hierarchy, hence it is harder than reasoning in all the above mentioned propositional formalisms for nonmonotonic reasoning. We also prove the exact correspondence between negation as failure in MBNF and negative introspection in Moore's autoepistemic logic

Updating Data Semantics

This paper has three main goals. First, to motivate a puzzle about how ignorance-expressing terms like maybe and if interact: they iterate, and when they do they exhibit scopelessness. Second, to argue that there is an ambiguity in our theoretical toolbox, and that exposing that opens the door to a solution to the puzzle. And third, to explore the reach of that solution. Along the way, the paper highlights a number of pleasing properties of two elegant semantic theories, explores some meta-theoretic properties of dynamic notions of meaning, dips its toe into some hazardous waters, and offers characterization theorems for the space of meanings an indicative conditional can have

How to do things with modals

Mind &Language, Volume 35, Issue 1, Page 115-138, February 2020

Embedding Non-Ground Logic Programs into Autoepistemic Logic for Knowledge Base Combination

In the context of the Semantic Web, several approaches to the combination of ontologies, given in terms of theories of classical first-order logic and rule bases, have been proposed. They either cast rules into classical logic or limit the interaction between rules and ontologies. Autoepistemic logic (AEL) is an attractive formalism which allows to overcome these limitations, by serving as a uniform host language to embed ontologies and nonmonotonic logic programs into it. For the latter, so far only the propositional setting has been considered. In this paper, we present three embeddings of normal and three embeddings of disjunctive non-ground logic programs under the stable model semantics into first-order AEL. While the embeddings all correspond with respect to objective ground atoms, differences arise when considering non-atomic formulas and combinations with first-order theories. We compare the embeddings with respect to stable expansions and autoepistemic consequences, considering the embeddings by themselves, as well as combinations with classical theories. Our results reveal differences and correspondences of the embeddings and provide useful guidance in the choice of a particular embedding for knowledge combination.Comment: 52 pages, submitte

Are "Modal Adverbs" automatically Modal Markers? The Case of French "Certainement" with its Epistemico-Modal and its Evidential Use

The French adverb certainement (‘certainly’) is labelled a “modal adverb”. It has two (sentence adverb) uses according to the literature, called “strong modal use” and “weak modal use”. The strong modal use is indeed strong (epistemico-)modal in that it indicates total certainty, whether subjective or intersubjective. What is called its “weak modal use” is shown to be an evidential use. It indicates primarily that the content qualified by the adverb results from a non-monotonic inference, performed by the speaker, whose conclusions are plausible, defeasible, and thus never totally certain. This is due to the presence of an evidential-inferential component in its meaning. As for the so-called weak modal element of “probability” in its meaning, we reanalyse it as “non- certainty” and argue it is an element of utterance meaning, a property of quasi-assertions to which non-monotonically inferred content gives rise. Finally, we claim that the adverb also has a meaning component that we call “epistemic posture of certainty”, shown to be different from epistemic modality. On the basis of three parameters and their values, we show how certainementcan be interpreted, in a series of contextual configurations, either as an instance of its epistemico- modal use or of its evidential use

Fuzzy autoepistemic logic and its relation to fuzzy answer set programming

Autoepistemic logic is an important formalism for nonmonotonic reasoning. It extends propositional logic by offering the ability to reason about an agent's (lack of) beliefs. Moreover, it is well known to generalize the stable model semantics of answer set programming. Fuzzy logics on the other hand are multi-valued logics, which allow to model the intensity to which properties are satisfied. We combine these ideas to a fuzzy autoepistemic logic which can be used to reason about one's beliefs in the degrees to which properties are satisfied. We show that many properties from classical autoepistemic logic, e.g. the equivalence between autoepistemic models and stable expansions, remain valid under this generalization. In this paper, we consider a version of fuzzy answer set programming and show that its answer sets can be equivalently described as models in fuzzy autoepistemic logic. We also define a fuzzy logic of minimal belief and negation-as-failure and use this as a tool to show that fuzzy autoepistemic logic generalizes fuzzy answer set programming