相关论文: Two-layered logics for probabilities and belief fu…
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 consider a many-sorted variant of Japaridze's polymodal provability logic $\mathsf{GLP}$. In this variant, which is denoted $\mathsf{GLP}^\ast$, propositional variables are assigned sorts $\alpha \leq \omega$, where variables of finite…
Logical depth and sophistication are two quantitative measures of the non-trivial organization of an object. Although apparently different, these measures have been proven equivalent, when the logical depth is renormalized by the busy…
Several concepts of approximate reasoning in uncertainty processing are linked to the processing of distribution functions. In this paper we make use of probabilistic framework of approximate reasoning by proposing a Lebesgue-type approach…
Modelling complex information systems often entails the need for dealing with scenarios of inconsistency in which several requirements either reinforce or contradict each other. In this kind of scenarios, arising e.g. in knowledge…
There is a third way of implementing probability models and practicing. This is to answer questions put in terms of observables. This eliminates frequentist hypothesis testing and Bayes factors and it also eliminates parameter estimation.…
Quantitative logic reasons about the degree to which formulas are satisfied. This paper studies the fundamental reasoning principles of higher-order quantitative logic and their application to reasoning about probabilistic programs and…
The work reported here introduces Defeasible Logic Programming (DeLP), a formalism that combines results of Logic Programming and Defeasible Argumentation. DeLP provides the possibility of representing information in the form of weak rules…
Every scientific endeavour consists of (at least) two components: A hypothesis on the one hand and data on the other. There is always a more or less abstract level - some theory, a set of concepts, certain relations of ideas - and a…
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
This paper gives a generative model of the interpretation of formal logic for data-driven logical reasoning. The key idea is to represent the interpretation as likelihood of a formula being true given a model of formal logic. Using the…
Markov logic uses weighted formulas to compactly encode a probability distribution over possible worlds. Despite the use of logical formulas, Markov logic networks (MLNs) can be difficult to interpret, due to the often counter-intuitive…
Much work has been done to give semantics to probabilistic programming languages. In recent years, most of the semantics used to reason about probabilistic programs fall in two categories: semantics based on Markov kernels and semantics…
Possibilistic logic bases and possibilistic graphs are two different frameworks of interest for representing knowledge. The former stratifies the pieces of knowledge (expressed by logical formulas) according to their level of certainty,…
Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic…
In experimental applications of bounded-reasoning models, behavior is often summarized by distributions of "levels". We argue that such summaries conflate two conceptually distinct dimensions: a player's type, capturing beliefs about what…
This paper considers the notion of possible events which are insignificant in probabilistic analysis (i.e. events that have zero probability). The paper discusses the method of modal logic based on "possible worlds" and discusses a…
Filinski constructed a symmetric lambda-calculus consisting of expressions and continuations which are symmetric, and functions which have duality. In his calculus, functions can be encoded to expressions and continuations using primitive…
Benchmarks for competition-style reasoning have advanced evaluation in mathematics and programming, yet physics remains comparatively explored. Most existing physics benchmarks evaluate only final answers, which fail to capture reasoning…
This is the logical foundation for for Relativity Theory, Probability Theory, and for Quantum Theory. Contents is the following: 1 Introduction. 2 Classical logic. 3 Time and space. 3.1 Recorders. 3.2 Time. 3.3 Space. 3.4 Relativity. 4.…