Related papers: First-order logic with incomplete information
In this chapter we give a basic overview of known results regarding Craig interpolation for first-order logic as well as for fragments of first-order logic. Our aim is to provide an entry point into the literature on interpolation theorems…
We investigate a class of first-order temporal-epistemic logics for reasoning about multi-agent systems. We encode typical properties of systems including perfect recall, synchronicity, no learning, and having a unique initial state in…
We present a method of generating first-order logic statements whose complexity can be controlled along multiple dimensions. We use this method to automatically create several datasets consisting of questions asking for the truth or falsity…
We study the complexity of the model checking problem, for fixed model A, over certain fragments L of first-order logic. These are sometimes known as the expression complexities of L. We obtain various complexity classification theorems for…
To combine and query ordered data from multiple sources, one needs to handle uncertainty about the possible orderings. Examples of such "order-incomplete" data include integrated event sequences such as log entries, lists of properties…
Over the past two decades several fragments of first-order logic have been identified and shown to have good computational and algorithmic properties, to a great extent as a result of appropriately describing the image of the standard…
A policy describes the conditions under which an action is permitted or forbidden. We show that a fragment of (multi-sorted) first-order logic can be used to represent and reason about policies. Because we use first-order logic, policies…
This paper describes the first-order logical environment FOLE. Institutions in general, and logical environments in particular, give equivalent heterogeneous and homogeneous representations for logical systems. As such, they offer a…
It is well-known that constructing models of higher-order probabilistic programming languages is challenging. We show how to construct step-indexed logical relations for a probabilistic extension of a higher-order programming language with…
We extend answer set semantics to deal with inconsistent programs (containing classical negation), by finding a ``best'' answer set. Within the context of inconsistent programs, it is natural to have a partial order on rules, representing a…
We propose an extension of Strategy Logic (SL), in which one can both reason about strategizing under imperfect information and about players' knowledge. One original aspect of our approach is that we do not force strategies to be uniform,…
Modular logic programs provide a way of viewing logic programs as consisting of many independent, meaningful modules. This paper introduces first-order modular logic programs, which can capture the meaning of many answer set programs. We…
We give a framework for dealing with 0-1 laws (for first order logic) such that expanding by further random structure tend to give us another case of the framework. From another perspective we deal with 0-1 laws when the number of solutions…
We discuss partial specifications in first-order logic FO and also in a Turing-complete extension of FO. We compare the compositional and game-theoretic approaches to the systems.
In this paper we consider first-order logic theorem proving and model building via approximation and instantiation. Given a clause set we propose its approximation into a simplified clause set where satisfiability is decidable. The…
We present a mechanism for constructing graphical models, specifically Bayesian networks, from a knowledge base of general probabilistic information. The unique feature of our approach is that it uses a powerful first-order probabilistic…
Higher-order logic programming is an interesting extension of traditional logic programming that allows predicates to appear as arguments and variables to be used where predicates typically occur. Higher-order characteristics are indeed…
The notion of bounded expansion captures uniform sparsity of graph classes and renders various algorithmic problems that are hard in general tractable. In particular, the model-checking problem for first-order logic is fixed-parameter…
The basic notions of logic-predicate logic, Peano arithmetic, incompleteness theorems, etc.-have for long been an advanced topic. In the last decades, they became more widely taught, inphilosophy, mathematics, and computer science…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…