Related papers: Plausible Reasoning and First-Order Plausible Logi…
Fuzziness and randomicity widespread exist in natural science, engineering, technology and social science. The purpose of this paper is to present a new logic - uncertain propositional logic which can deal with both fuzziness by taking…
Predicting the future is an important component of decision making. In most situations, however, there is not enough information to make accurate predictions. In this paper, we develop a theory of causal reasoning for predictive inference…
This comparative survey explores three formal approaches to reasoning with partly true statements and degrees of truth, within the family of {\L}ukasiewicz logic. These approaches are represented by infinite-valued {\L}ukasiewicz logic…
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…
We address the problem of compiling defeasible theories to Datalog$^\neg$ programs. We prove the correctness of this compilation, for the defeasible logic $DL(\partial_{||})$, but the techniques we use apply to many other defeasible logics.…
In this article, the decidability and computability issues of dynamic probability logic (DPL) are addressed. Firstly, a proof system $\mathcal{H}_{DPL}$ is introduced for DPL and shown that it is weakly complete. Furthermore, this logic has…
We present a declarative language, PP, for the high-level specification of preferences between possible solutions (or trajectories) of a planning problem. This novel language allows users to elegantly express non-trivial, multi-dimensional…
Human reasoning often involves working over limited information to arrive at probabilistic conclusions. In its simplest form, this involves making an inference that is not strictly entailed by a premise, but rather only likely given the…
Recent advances in AI have been significantly driven by the capabilities of large language models (LLMs) to solve complex problems in ways that resemble human thinking. However, there is an ongoing debate about the extent to which LLMs are…
Convincing someone of the truth value of a premise requires understanding and articulating the core logical structure of the argument which proves or disproves the premise. Understanding the logical structure of an argument refers to…
Many representation schemes combining first-order logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable…
Given a natural language statement, how to verify its veracity against a large-scale textual knowledge source like Wikipedia? Most existing neural models make predictions without giving clues about which part of a false claim goes wrong. In…
Linear Logic and Defeasible Logic have been adopted to formalise different features of knowledge representation: consumption of resources, and non monotonic reasoning in particular to represent exceptions. Recently, a framework to combine…
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…
Representing defeasibility is an important issue in common sense reasoning. In reasoning about action and change, this issue becomes more difficult because domain and action related defeasible information may conflict with general inertia…
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…
Possibilistic logic offers a qualitative framework for representing pieces of information associated with levels of uncertainty of priority. The fusion of multiple sources information is discussed in this setting. Different classes of…
Existential fixed point logic (EFPL) is a natural fit for some applications, and the purpose of this talk is to attract attention to EFPL. The logic is also interesting in its own right as it has attractive properties. One of those…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
The combination of evidence in Dempster-Shafer theory is compared with the combination of evidence in probabilistic logic. Sufficient conditions are stated for these two methods to agree. It is then shown that these conditions are minimal…