Embedding Tarskian Semantics in Vector Spaces
Embedding Tarskian Semantics in Vector Spaces
复制标题
在向量空间中嵌入 Tarskian 语义
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Taisuke Sato
中科院分区：
文献类型：
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作者：
Taisuke Sato
We propose a new linear algebraic approach to the computation of Tarskian semantics in logic. We embed a finite model M in first-order logic with N entities in N-dimensional Euclidean space R^N by mapping entities of M to N dimensional one-hot vectors and k-ary relations to order-k adjacency tensors (multi-way arrays). Second given a logical formula F in prenex normal form, we compile F into a set Sigma_F of algebraic formulas in multi-linear algebra with a nonlinear operation. In this compilation, existential quantifiers are compiled into a specific type of tensors, e.g., identity matrices in the case of quantifying two occurrences of a variable. It is shown that a systematic evaluation of Sigma_F in R^N gives the truth value, 1(true) or 0(false), of F in M. Based on this framework, we also propose an unprecedented way of computing the least models defined by Datalog programs in linear spaces via matrix equations and empirically show its effectiveness compared to state-of-the-art approaches.
