Information theory has provided foundations for the theories of several application areas critical for modern society, including communications, computer storage, and AI. A key aspect of Shannon's 1948 theory is a sharp lower bound on the number of bits needed to encode and communicate a string of symbols. When he introduced the theory, Shannon famously excluded any notion of semantics behind the symbols being communicated. This semantics-free notion went on to have massive impact on communication and computing technologies, even as multiple proposals for reintroducing semantics in a theory of information were being made, notably one where Carnap and Bar-Hillel used logic and reasoning to capture semantics. In this paper we present, for the first time, a Shannon-style analysis of a communication system equipped with a deductive reasoning capability, implemented using logical inference. We use some of the most important techniques developed in information theory to demonstrate significant and sometimes surprising gains in communication efficiency availed to us through such capability, demonstrated also through practical codes. We thus argue that proposals for a semantic information theory should include the power of deductive reasoning to magnify the value of transmitted bits as we strive to fully unlock the inherent potential of semantics.

翻译：信息论为现代社会中多个关键应用领域的理论奠定了基础，包括通信、计算机存储和人工智能。香农于1948年提出的理论中，一个关键方面是对编码和传输一串符号所需比特数的严格下界。在提出该理论时，香农著名地排除了被传输符号背后的任何语义概念。这种无语义的概念随后对通信和计算技术产生了巨大影响，尽管期间出现了多个重新在信息理论中引入语义的提案，其中最著名的是卡尔纳普和巴尔-希勒尔利用逻辑与推理来捕捉语义的尝试。本文首次对配备演绎推理能力的通信系统进行了香农式的分析，该推理能力通过逻辑推理实现。我们运用信息论中发展出的若干重要技术，证明了这种能力可带来显著且有时令人惊讶的通信效率提升，并通过实际编码方案加以验证。因此我们认为，语义信息理论的提案应当包含演绎推理的能力，以放大传输比特的价值，从而充分释放语义的内在潜力。