Related papers: Reasoning about multiple aspects in DLs: Semantics…
In this paper syntactic objects---concept constructors called part restrictions which realize rational grading are considered in Description Logics (DLs). Being able to convey statements about a rational part of a set of successors, part…
We describe a context-sensitive model of choice, in which the selection process is shaped not only by the attractiveness of items but also by their semantics ('salience'). All items are ranked according to a relation of salience, and a…
We bring forward a logical system of transition algebras that enhances many-sorted first-order logic using features from dynamic logics. The sentences we consider include compositions, unions, and transitive closures of transition…
We present a probabilistic extension of the description logic $\mathcal{ALC}$ for reasoning about statistical knowledge. We consider conditional statements over proportions of the domain and are interested in the probabilistic-logical…
When explaining black-box machine learning models, it's often important for explanations to have certain desirable properties. Most existing methods `encourage' desirable properties in their construction of explanations. In this work, we…
The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…
Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only…
We provide a semantic framework for preference handling in answer set programming. To this end, we introduce preference preserving consequence operators. The resulting fixpoint characterizations provide us with a uniform semantic framework…
Let A be a finite alphabet and let L contained in (A*)^n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an…
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
Preference elicitation plays a central role in interactive recommender systems. Most preference elicitation approaches use either item queries that ask users to select preferred items from a slate, or attribute queries that ask them to…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Lehmann and Magidor's rational closure is acknowledged as a landmark in the field of non-monotonic logics and it has also been re-formulated in the context of Description Logics (DLs). We show here how to model a rational form of entailment…
Description logics (DLs) are standard knowledge representation languages for modelling ontologies, i.e. knowledge about concepts and the relations between them. Unfortunately, DL ontologies are difficult to learn from data and…
Describing systems in terms of choices and their resulting costs and rewards offers the promise of freeing algorithm designers and programmers from specifying how those choices should be made; in implementations, the choices can be realized…
We define a notion of rational closure for the logic SHIQ, which does not enjoys the finite model property, building on the notion of rational closure introduced by Lehmann and Magidor in [23]. We provide a semantic characterization of…
An account of utterance interpretation in discourse needs to face the issue of how the discourse context controls the space of interacting preferences. Assuming a discourse processing architecture that distinguishes the grammar and…
Given a machine learning (ML) model and a prediction, explanations can be defined as sets of features which are sufficient for the prediction. In some applications, and besides asking for an explanation, it is also critical to understand…
Non-normal modal logics, interpreted on neighbourhood models which generalise the usual relational semantics, have found application in several areas, such as epistemic, deontic, and coalitional reasoning. We present here preliminary…
Starting with a likelihood or preference order on worlds, we extend it to a likelihood ordering on sets of worlds in a natural way, and examine the resulting logic. Lewis earlier considered such a notion of relative likelihood in the…