Related papers: Probabilistic Theorem Proving
Logistic regression models are a popular and effective method to predict the probability of categorical response data. However inference for these models can become computationally prohibitive for large datasets. Here we adapt ideas from…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
Tabling in logic programming has been used to eliminate redundant computation and also to stop infinite loop. In this paper we investigate another possibility of tabling, i.e. to compute an infinite sum of probabilities for probabilistic…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…
In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…
We propose a deep learning-based approach to the problem of premise selection: selecting mathematical statements relevant for proving a given conjecture. We represent a higher-order logic formula as a graph that is invariant to variable…
This paper presents a plausible reasoning system to illustrate some broad issues in knowledge representation: dualities between different reasoning forms, the difficulty of unifying complementary reasoning styles, and the approximate nature…
The computational method of parametric probability analysis is introduced. It is demonstrated how to embed logical formulas from the propositional calculus into parametric probability networks, thereby enabling sound reasoning about the…
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.…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
Probabilistic Logic Programming is an effective formalism for encoding problems characterized by uncertainty. Some of these problems may require the optimization of probability values subject to constraints among probability distributions…
We introduce a formal logical language, called conditional probability logic (CPL), which extends first-order logic and which can express probabilities, conditional probabilities and which can compare conditional probabilities. Intuitively…
Probabilistic graphical modeling is a branch of machine learning that uses probability distributions to describe the world, make predictions, and support decision-making under uncertainty. Underlying this modeling framework is an elegant…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
We present a propositional logic with fundamental probabilistic semantics, in which each formula is given a real measure in the interval $[0,1]$ that represents its degree of truth. This semantics replaces the binarity of classical logic,…
Lifted probabilistic inference exploits symmetries in a probabilistic model to allow for tractable probabilistic inference with respect to domain sizes. To apply lifted inference, a lifted representation has to be obtained, and to do so,…
This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional…
Distributed representations (such as those based on embeddings) and discrete representations (such as those based on logic) have complementary strengths. We explore one possible approach to combining these two kinds of representations. We…
We propose a formalization of the three-tier causal hierarchy of association, intervention, and counterfactuals as a series of probabilistic logical languages. Our languages are of strictly increasing expressivity, the first capable of…