In this paper, we propose an advancement to Tarskian model-theoretic semantics, leading to a unified quantitative theory of semantic information and communication. We start with description of inductive logic and probabilities, which serve as notable tools in development of the proposed theory. Then, we identify two disparate kinds of uncertainty in semantic communication, that of physical and content, present refined interpretations of semantic information measures, and conclude with proposing a new measure for semantic content-information and entropy. Our proposition standardizes semantic information across different universes and systems, hence bringing measurability and comparability into semantic communication. We then proceed with introducing conditional and mutual semantic cont-information measures and point out to their utility in formulating practical and optimizable lossless and lossy semantic compression objectives. Finally, we experimentally demonstrate the value of our theoretical propositions.

翻译：本文提出对塔斯基模型论语义的改进，从而建立了语义信息与通信的统一量化理论。我们首先描述归纳逻辑与概率工具，这些工具在理论构建中发挥重要作用。随后，我们识别出语义通信中物理不确定性与内容不确定性两种不同类型，提出语义信息测度的精细化解释，并最终提出一种新的语义内容信息与熵的测度。我们的理论统一了不同领域和系统中的语义信息，从而为语义通信带来可度量性与可比较性。进一步地，我们引入条件语义内容信息与互语义内容信息测度，并指出其在构建实用且可优化的无损与有损语义压缩目标中的价值。最后，我们通过实验验证了理论命题的实效性。