Related papers: First-Order Bayesian Network Specifications Captur…
A classic result in formal language theory is the equivalence among non-counting, or aperiodic, regular languages, and languages defined through star-free regular expressions, or first-order logic. Past attempts to extend this result beyond…
Krebs et al. (2007) gave a characterization of the complexity class TC0 as the class of languages recognized by a certain class of typed monoids. The notion of typed monoid was introduced to extend methods of algebraic automata theory to…
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 will investigate proof-theoretic and linguistic aspects of first-order linear logic. We will show that adding partial order constraints in such a way that each sequent defines a unique linear order on the antecedent formulas of a sequent…
Language learning refers to the problem of inferring a mathematical model which accurately represents a formal language. Many language learning algorithms learn by asking certain types of queries about the language being modeled. Language…
We give a new, direct proof of the tetrachotomy classification for the model-checking problem of positive equality-free logic parameterised by the model. The four complexity classes are Logspace, NP-complete, co-NP-complete and…
The class of problems complete for NP via first-order reductions is known to be characterized by existential second-order sentences of a fixed form. All such sentences are built around the so-called generalized IS-form of the sentence that…
We present a method for dynamically generating Bayesian networks from knowledge bases consisting of first-order probability logic sentences. We present a subset of probability logic sufficient for representing the class of Bayesian networks…
In this workshop, we present a compact but rigorous introduction to the basic language of nonlinear programming, variational inequalities, and complementarity systems. The goal is twofold. First, we explain the mathematical logic of…
This paper presents a simple framework for Horn clause abduction, with probabilities associated with hypotheses. It is shown how this representation can represent any probabilistic knowledge representable in a Bayesian belief network. The…
This paper presents a Bayesian model for unsupervised learning of verb selectional preferences. For each verb the model creates a Bayesian network whose architecture is determined by the lexical hierarchy of Wordnet and whose parameters are…
Bayesian networks provide a language for qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports…
Bayesian networks are a canonical formalism for representing probabilistic dependencies, yet their integration within logic programming frameworks remains a nontrivial challenge, mainly due to the complex structure of these networks. In…
Pattern matching is a popular feature in functional, imperative and object-oriented programming languages. Language designers should therefore invest effort in a good design for pattern matching. Most languages choose a first-match…
Rational word languages can be defined by several equivalent means: finite state automata, rational expressions, finite congruences, or monadic second-order (MSO) logic. The robust subclass of aperiodic languages is defined by: counter-free…
One measure of the complexity of a first-order theory, and similarly a type, is the complexity of the formulas required to axiomatize it. We say a theory is bounded if there is an axiomatization involving only $\forall_n$-formulas for some…
We consider the problem of answering queries about formulas of first-order logic based on background knowledge partially represented explicitly as other formulas, and partially represented as examples independently drawn from a fixed…
Formal languages are sets of strings of symbols described by a set of rules specific to them. In this note, we discuss a certain class of formal languages, called regular languages, and put forward some elementary results. The properties of…
Application domains that require considering relationships among objects which have real-valued attributes are becoming even more important. In this paper we propose NeuralLog, a first-order logic language that is compiled to a neural…
We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. The proposed framework is the first order extension of the logic of…