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An MLN consists of soft constraints with associated weights which are nonnegative real numbers. In this study we consider a language speaking about a property $P(x)$ and a relation $R(x, y)$. We consider an MLN for which every Boolean combination of $P(x)$ and $R(x, y)$ is a soft constraint (with associated weight). Let $n$ denote the size (cardinality) of the domain. We show that, for every choice of weights, if the weights are scaled by $1/n$ then, for every first-order sentence $\\varphi$, the probability that $\\varphi$ holds tends to either 0 or 1 as $n \\to \\infty$; that is, a 0-1 law for first-order logic holds. Morover, the limit probability does {\\em not} depend on the weights. If we instead ","title":"Random coloured digraphs defined by a Markov logic network","url":"https://arxiv.org/abs/2606.23715","vendor":"arxiv_cs_ai"},"summary":"arXiv:2606.23715v1 Announce Type: cross \nAbstract: A Markov Logic Network (MLN) is a probabilistic relational model used in Statistical Relational Artificial Intelligence for defining a probability distribution on the set of possible worlds with domain $D$ for an arbitrary finite domain $D$. An MLN consists of soft constraints with associated weights which are nonnegative real numbers. In this study we consider a language speaking about a property $P(x)$ and a relation $R(x, y)$. We consider an MLN for which every Boolean combination of $P(x)$ and $R(x, y)$ is a soft constraint (with associated weight). Let $n$ denote the size (cardinality) of the domain. We show that, for every choice of weights, if the weights are scaled by $1/n$ then, for every first-order sentence $\\varphi$, the probability that $\\varphi$ holds tends to either 0 or 1 as $n \\to \\infty$; that is, a 0-1 law for first-order logic holds. Morover, the limit probability does {\\em not} depend on the weights. 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