Related papers: The Possibilistic Horn Non-Clausal Knowledge Bases
In this paper, we consider the well-known modal logics $\mathbf{K}$, $\mathbf{T}$, $\mathbf{K4}$, and $\mathbf{S4}$, and we study some of their sub-propositional fragments, namely the classical Horn fragment, the Krom fragment, the…
Reasoning about program correctness has been a central topic in static analysis for many years, with Hoare logic (HL) playing an important role. The key notions in HL are partial and total correctness. Both require that program executions…
Compositionality is one of the fundamental abilities of the human reasoning process, that allows to decompose a complex problem into simpler elements. Such property is crucial also for neural networks, especially when aiming for a more…
We investigate the problem of extracting rules, expressed in Horn logic, from neural network models. Our work is based on the exact learning model, in which a learner interacts with a teacher (the neural network model) via queries in order…
This paper presents a logical approach to nonmonotonic reasoning based on the notion of a nonmonotonic consequence relation. A conditional knowledge base, consisting of a set of conditional assertions of the type "if ... then ...",…
Real-valued logics underlie an increasing number of neuro-symbolic approaches, though typically their logical inference capabilities are characterized only qualitatively. We provide foundations for establishing the correctness and power of…
This chapter presents probability logic as a rationality framework for human reasoning under uncertainty. Selected formal-normative aspects of probability logic are discussed in the light of experimental evidence. Specifically, probability…
Unaided human decision making appears to systematically violate consistency constraints imposed by normative theories; these biases in turn appear to justify the application of formal decision-analytic models. It is argued that both claims…
The domain of explainable AI is of interest in all Machine Learning fields, and it is all the more important in clustering, an unsupervised task whose result must be validated by a domain expert. We aim at finding a clustering that has high…
Interval temporal logics provide a general framework for temporal reasoning about interval structures over linearly ordered domains, where intervals are taken as the primitive ontological entities. In this paper, we identify all fragments…
We study formal languages which are capable of fully expressing quantitative probabilistic reasoning and do-calculus reasoning for causal effects, from a computational complexity perspective. We focus on satisfiability problems whose…
Neurosymbolic artificial intelligence is a growing field of research aiming to combine neural network learning capabilities with the reasoning abilities of symbolic systems. Informed multi-label classification is a sub-field of…
In the same sense as classical logic is a formal theory of truth, the recently initiated approach called computability logic is a formal theory of computability. It understands (interactive) computational problems as games played by a…
Cirquent calculus is a proof system with inherent ability to account for sharing subcomponents in logical expressions. Within its framework, this article constructs an axiomatization CL18 of the basic propositional fragment of computability…
Substructural logics are formal logical systems that omit familiar structural rules of classical and intuitionistic logic such as contraction, weakening, exchange (commutativity), and associativity. This leads to a resource-sensitive…
Judgment aggregation is a general framework for collective decision making that can be used to model many different settings. Due to its general nature, the worst case complexity of essentially all relevant problems in this framework is…
During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
We explore a fuzzy modal logic that can formalise probabilistic reasoning about actions and knowledge. In particular, we deal with contexts involving statements about events expressed via modal formulas, e.g., "after doing $a$, the…
In this paper, we present a probabilistic adaptation of an Assume/Guarantee contract formalism. For the sake of generality, we assume that the extended state machines used in the contracts and implementations define sets of runs on a given…