Related papers: Rejecting inadmissible rules in reduced normal for…
Defeasible rules are used in providing computable representations of legal documents and, more recently, have been suggested as a basis for explainable AI. Such applications draw attention to the scalability of implementations. The…
In this paper, we study retrievability of admissible cycles and the dynamics of the networks constructed from admissible cycles with the pseudoinverse learning rule. Retrievability of admissible cycles in networks with $C_0>0$ and $\lambda$…
Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…
Machine learning based decision making systems applied in safety critical areas require reliable high certainty predictions. For this purpose, the system can be extended by an reject option which allows the system to reject inputs where…
The decidability of axiomatic extensions of the modal logic K with modal reduction principles, i.e. axioms of the form $\Diamond^{k} p \rightarrow \Diamond^{n} p$, has remained a long-standing open problem. In this paper, we make…
We develop a framework for modelling and reasoning with uncertainty based on accept and reject statements about gambles. It generalises the frameworks found in the literature based on statements of acceptability, desirability, or…
In this paper, we study the notion of admissibility for randomised strategies in concurrent games. Intuitively, an admissible strategy is one where the player plays `as well as possible', because there is no other strategy that dominates…
Conditional acceptability refers to how plausible a conditional statement is perceived to be. It plays an important role in communication and reasoning, as it influences how individuals interpret implications, assess arguments, and make…
We propose a set of transformation rules for constraint logic programs with negation. We assume that every program is locally stratified and, thus, it has a unique perfect model. We give sufficient conditions which ensure that the proposed…
We consider the problem of model--checking for Process Rewrite Systems (PRSs) in normal form. In a PRS in normal form every rewrite rule either only deals with procedure calls and procedure termination, possibly with value return, (this…
The provability logic of a theory T is the set of modal formulas, which under any arithmetical realization are provable in T . We slightly modify this notion by requiring the arithmetical realizations to come from a specified set $\Gamma$.…
We axiomatize the provability logic of $\HA$ and prove its decidability. Furthermore, we axiomatize the preservativity and relative admissibility relations for several modal logics extending iK4. A principal technical tool is the…
In this article, we examine how clausal resolution can be applied to a specific, but widely used, non-classical logic, namely discrete linear temporal logic. Thus, we first define a normal form for temporal formulae and show how arbitrary…
Given a class C of finite Kripke frames, we consider the uniform distribution on the frames from C with n states. A formula is almost surely valid in C if the probability that it is valid in a random C-frame with n states tends to 1 as n…
Large language models (LLMs) have shown remarkable performance in various tasks but often fail to handle queries that exceed their knowledge and capabilities, leading to incorrect or fabricated responses. This paper addresses the need for…
In this paper we make a contribution to the unification of formal models of defeasible reasoning. We present several translations between formal argumentation frameworks and nonmonotonic logics for reasoning with plausible assumptions. More…
Machine learning models always make a prediction, even when it is likely to be inaccurate. This behavior should be avoided in many decision support applications, where mistakes can have severe consequences. Albeit already studied in 1970,…
In this paper, we study aggregation rules with nontrivial symmetric classes of invariant sets (restricted domains), assuming that they, unlike others, have a logical nature. In the simplest case, we provide a complete classification of such…
We study elementary modal logics, i.e. modal logic considered over first-order definable classes of frames. The classical semantics of modal logic allows infinite structures, but often practical applications require to restrict our…
A general method is given for revising degrees of belief and arriving at consistent decisions about a system of logically constrained issues. In contrast to other works about belief revision, here the constraints are assumed to be fixed.…