Related papers: Towards Statistical Reasoning in Description Logic…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
We define the notion of rational closure in the context of Description Logics extended with a tipicality operator. We start from ALC+T, an extension of ALC with a typicality operator T: intuitively allowing to express concepts of the form…
We present the language {m P}{cal C}+ for probabilistic reasoning about actions, which is a generalization of the action language {cal C}+ that allows to deal with probabilistic as well as nondeterministic effects of actions. We define a…
Given the large variety of existing logical formalisms it is of utmost importance to select the most adequate one for a specific purpose, e.g. for representing the knowledge relevant for a particular application or for using the formalism…
We present a semantics for adding uncertainty to conditional logics for default reasoning and belief revision. We are able to treat conditional sentences as statements of conditional probability, and express rules for revision such as "If A…
The Ambient Logic (AL) has been proposed for expressing properties of process mobility in the calculus of Mobile Ambients (MA), and as a basis for query languages on semistructured data. In this paper, we study the expressiveness of AL. We…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
Semantics of logic programs has been given by proof theory, model theory and by fixpoint of the immediate-consequence operator. If clausal logic is a programming language, then it should also have a compositional semantics. Compositional…
We generalise the distribution semantics underpinning probabilistic logic programming by distilling its essential concept, the separation of a free random component and a deterministic part. This abstracts the core ideas beyond logic…
This paper develops a declarative language, P-log, that combines logical and probabilistic arguments in its reasoning. Answer Set Prolog is used as the logical foundation, while causal Bayes nets serve as a probabilistic foundation. We give…
Standard Description Logics (DLs) can encode quantitative aspects of an application domain through either number restrictions, which constrain the number of individuals that are in a certain relationship with an individual, or concrete…
In this paper, we address the logic of knowing why, an example of a non-standard epistemic logic dealing with justified knowledge via a new epistemic operator, under the extensions with ideas from dynamic epistemic logic, namely public…
This extended abstract presents a logic, called Lp, that is capable of representing and reasoning with a wide variety of both qualitative and quantitative statistical information. The advantage of this logical formalism is that it offers a…
In this pedagogical text aimed at those wanting to start thinking about or brush up on probabilistic inference, I review the rules by which probability distribution functions can (and cannot) be combined. I connect these rules to the…
Difference Logic (DL) is a fragment of linear arithmetics where atoms are constraints x+k <= y for variables x,y (ranging over Q or Z) and integer k. We study the complexity of deciding the truth of existential DL sentences. This problem…
Large language models excel at generating fluent text but frequently struggle with structured reasoning involving temporal constraints, causal relationships, and probabilistic reasoning. To address these limitations, we propose Temporal…
Inspired by empirical work in neuroscience for Bayesian approaches to brain function, we give a unified probabilistic account of various types of symbolic reasoning from data. We characterise them in terms of formal logic using the…
Logic-based approaches to AI have the advantage that their behavior can in principle be explained with the help of proofs of the computed consequences. For ontologies based on Description Logic (DL), we have put this advantage into practice…
In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…