Related papers: Complexity of Propositional Abduction for Restrict…
Abductive reasoning, reasoning for inferring explanations for observations, is often mentioned in scientific, design-related and artistic contexts, but its understanding varies across these domains. This paper reviews how abductive…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
Tarski gave a general semantics for deductive reasoning: a formula a may be deduced from a set A of formulas iff a holds in all models in which each of the elements of A holds. A more liberal semantics has been considered: a formula a may…
The complete reason behind a decision is a Boolean formula that characterizes why the decision was made. This recently introduced notion has a number of applications, which include generating explanations, detecting decision bias and…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
The satisfiability problem of hybrid logics with the downarrow binder is known to be undecidable. This initiated a research program on decidable and tractable fragments. In this paper, we investigate the effect of restricting the…
Recent years have witnessed a renewed interest in Boolean function in explaining binary classifiers in the field of explainable AI (XAI). The standard approach of Boolean function is propositional logic. We present a modal language of a…
Probabilistic puzzles can be confusing, partly because they are formulated in natural languages - full of unclarities and ambiguities - and partly because there is no widely accepted and intuitive formal language to express them. We propose…
Weighted knowledge bases for description logics with typicality under a "concept-wise" multi-preferential semantics provide a logical interpretation of MultiLayer Perceptrons. In this context, Answer Set Programming (ASP) has been shown to…
Abduction is the task of computing a sufficient extension of a knowledge base (KB) that entails a conclusion not entailed by the original KB. It serves to compute explanations, or hypotheses, for such missing entailments. While this task…
This work investigates the algorithmic complexity of non-classical logics, focusing on superintuitionistic and modal systems. It is shown that propositional logics are usually polynomial-time reducible to their fragments with at most two…
We will study some important properties of Boolean functions based on newly introduced concepts called Special Decomposition of a Set and Special Covering of a Set. These concepts enable us to study important problems concerning Boolean…
A new syntactic characterization of problems complete via Turing reductions is presented. General canonical forms are developed in order to define such problems. One of these forms allows us to define complete problems on ordered…
Propositional logics in general, considered as a set of sentences, can be undecidable even if they have "nice" representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already…
The idea of fully accepting statements when the evidence has rendered them probable enough faces a number of difficulties. We leave the interpretation of probability largely open, but attempt to suggest a contextual approach to full belief.…
Probabilistic argumentation allows reasoning about argumentation problems in a way that is well-founded by probability theory. However, in practice, this approach can be severely limited by the fact that probabilities are defined by adding…
Given a knowledge base and an observation as a set of facts, ABox abduction aims at computing a hypothesis that, when added to the knowledge base, is sufficient to entail the observation. In signature-based ABox abduction, the hypothesis is…
We study the framework of abductive logic programming extended with integrity constraints. For this framework, we introduce a new measure of the simplicity of an explanation based on its degree of \emph{arbitrariness}: the more arbitrary…
Diagnostic reasoning has been characterized logically as consistency-based reasoning or abductive reasoning. Previous analyses in the literature have shown, on the one hand, that choosing the (in general more restrictive) abductive…
This is a survey on propositional proof complexity aimed at introducing the basics of the field with a particular focus on a method known as feasible interpolation. This method is used to construct "hard theorems" for several proof systems…