Related papers: Convergent Deduction for Probabilistic Logic
We report on the mechanization of (preference-based) conditional normative reasoning. Our focus is on Aqvist's system E for conditional obligation, and its extensions. Our mechanization is achieved via a shallow semantical embedding in…
Permissive-Nominal Logic (PNL) extends first-order predicate logic with term-formers that can bind names in their arguments. It takes a semantics in (permissive-)nominal sets. In PNL, the forall-quantifier or lambda-binder are just…
There are two main approach to probability, one of set-theoretic character where probability is the measure of a set, and another one of linguistic character where probability is the degree of confidence in a proposition. In this work we…
Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…
Tackling Natural Language Inference with a logic-based method is becoming less and less common. While this might have been counterintuitive several decades ago, nowadays it seems pretty obvious. The main reasons for such a conception are…
Deductive reasoning plays a pivotal role in the formulation of sound and cohesive arguments. It allows individuals to draw conclusions that logically follow, given the truth value of the information provided. Recent progress in the domain…
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
The purpose of this paper is to give an easy to understand with step-by-step explanation to allow interested people to fully appreciate the power of natural deduction for first-order logic. Natural deduction as a proof system can be used to…
Probabilistic Logic Programming (PLP), exemplified by Sato and Kameya's PRISM, Poole's ICL, Raedt et al's ProbLog and Vennekens et al's LPAD, is aimed at combining statistical and logical knowledge representation and inference. A key…
We introduce estimation and test procedures through divergence minimization for models satisfying linear constraints with unknown parameter. Several statistical examples and motivations are given. These procedures extend the empirical…
Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…
To support the understanding of declarative probabilistic programming languages, we introduce a lambda-calculus with a fair binary probabilistic choice that chooses between its arguments with equal probability. The reduction strategy of the…
Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…
The rapid proliferation of large language models and natural language processing (NLP) applications creates a crucial need for uncertainty quantification to mitigate risks such as hallucinations and to enhance decision-making reliability in…
Over the past three decades, the logic programming paradigm has been successfully expanded to support probabilistic modeling, inference and learning. The resulting paradigm of probabilistic logic programming (PLP) and its programming…
Chain-of-thought (CoT) prompting enhances reasoning in large language models (LLMs) but often leads to verbose and redundant outputs, thus increasing inference cost. We hypothesize that many reasoning steps are unnecessary for producing…
Intuitionistic grammar logics fuse constructive and multi-modal reasoning while permitting the use of converse modalities, serving as a generalization of standard intuitionistic modal logics. In this paper, we provide definitions of these…
We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence…
Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many…