Related papers: Skolemization for Weighted First-Order Model Count…
Skolemization, with Herbrand's theorem, underpins automated theorem proving and various transformations in computer science and mathematics. Skolemization removes strong quantifiers by introducing new function symbols, enabling efficient…
In recent work, we proved that the domain recursion inference rule makes domain-lifted inference possible on several relational probability models (RPMs) for which the best known time complexity used to be exponential. We also identified…
Focusing is a known technique for reducing the number of proofs while preserving derivability. Skolemisation is another technique designed to improve proof search, which reduces the number of back-tracking steps by representing dependencies…
We study the symmetric weighted first-order model counting task and present ApproxWFOMC, a novel anytime method for efficiently bounding the weighted first-order model count in the presence of an unweighted first-order model counting…
Weighted model counting (WMC) is the task of computing the weighted sum of all satisfying assignments (i.e., models) of a propositional formula. Similarly, weighted model sampling (WMS) aims to randomly generate models with probability…
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…
Skolem functions play a central role in the study of first order logic, both from theoretical and practical perspectives. While every Skolemized formula in first-order logic makes use of Skolem constants and/or functions, not all such…
Weighted first-order model counting (WFOMC) is a central task in lifted probabilistic inference: It asks for the weighted sum of all models of a first-order sentence over a finite domain. A long line of work has identified domain-liftable…
The problem of checking satisfiability of linear real arithmetic (LRA) and non-linear real arithmetic (NRA) formulas has broad applications, in particular, they are at the heart of logic-related applications such as logic for artificial…
Reconciling the tension between inductive learning and deductive reasoning in first-order relational domains is a longstanding challenge in AI. We study the problem of answering queries in a first-order relational probabilistic logic…
We consider the task of weighted first-order model counting (WFOMC) used for probabilistic inference in the area of statistical relational learning. Given a formula $\phi$, domain size $n$ and a pair of weight functions, what is the…
First-order model counting (FOMC) is a computational problem that asks to count the models of a sentence in finite-domain first-order logic. In this paper, we argue that the capabilities of FOMC algorithms to date are limited by their…
We present a combination of raising, explicit variable dependency representation, the liberalized delta-rule, and preservation of solutions for first-order deductive theorem proving. Our main motivation is to provide the foundation for our…
In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…
Modal formulae express monadic second-order properties on Kripke frames, but in many important cases these have first-order equivalents. Computing such equivalents is important for both logical and computational reasons. On the other hand,…
This talk describes how a combination of symbolic computation techniques with first-order theorem proving can be used for solving some challenges of automating program analysis, in particular for generating and proving properties about the…
In many probabilistic first-order representation systems, inference is performed by "grounding"---i.e., mapping it to a propositional representation, and then performing propositional inference. With a large database of facts, groundings…
We present a first-order theorem proving framework for establishing the correctness of functional programs implementing sorting algorithms with recursive data structures. We formalize the semantics of recursive programs in many-sorted…
Deciding formulas mixing arithmetic and uninterpreted predicates is of practical interest, notably for applications in verification. Some decision procedures consist in building by structural induction an automaton that recognizes the set…
Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic…