We put forward a general theory of goal-oriented communication, where communication is not an end in itself, but rather a means to achieving some goals of the communicating parties. The goals can vary from setting to setting, and we provide a general framework for describing any such goal. In this context, “reliable communication ” means overcoming the (potential) initial misunderstanding between parties towards achieving a given goal. We identify a main concept, which we call sensing, that captures the party’s ability to check whether progress is made towards achieving the goal. We then show that if sensing is available, then the gap between a priori mutual understanding and lack of it can be bridged. For example, if providing the parties with an adequate interpreter allows them each to achieve their (possibly different) goals, then they can achieve their goals also without such an interpreter (although they may misunderstand each other and err at the beginning). Or, if each server (in a predetermined class of servers) can help some user (who understands the server) achieve its goal, then there exists a user strategy that achieves the goal no matter with which server it communicates. An early version of this work has appeared as an ECCC report [10].Contents

Compression without a common prior:

In previous works, Juba and Sudan [6] and Goldreich, Juba and Sudan [4] considered the idea of “semantic communication”, wherein two players, a user and a server, attempt to communicate with each other without any prior common language (or communication) protocol. They showed that if communication was goal-oriented and the user could sense progress towards the goal (or verify when it has been achieved), then meaningful communication is possible, in that the user’s goal can be achieved whenever the server is helpful. A principal criticism of their result has been that it is inefficient: in order to determine the “right ” protocol to communicate with the server, the user enumerates protocols and tries them out with the server until it finds one that allows it to achieve its goal. They also show settings in which such enumeration is essentially the best possible solution. In this work we introduce definitions which allow for efficient behavior in practice. Roughly, we measure the performance of users and servers against their own “beliefs ” about natural protocols. We show that if user and server are efficient with respect to their own beliefs and their beliefs are (even just slightly) compatible with each other, then they can achieve their goals very efficiently. We show that this model allows sufficiently “broad-minded ” servers to talk with “exponentially” many different users in polynomial time, while dismissing the “counterexamples” in the previous work as being “narrow-minded, ” or based on “incompatible beliefs.” Portions of this work are presented in modified form in the first author’s Ph.D. thesis. [5, Chapter 4]. Research

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Abstract—This paper studies methods of quantitatively measuring semantic information in communication. We review existing work on quantifying semantic information, then investigate a model-theoretical approach for semantic data compression and reliable semantic communication. We relate our approach to the statistical measurement of information by Shannon, and show that Shannon’s source and channel coding theorems have semantic counterparts. I. BACKGROUND It has long been recognized that the broad subject of communication goes beyond what Shannon’s theory [18] and many of its extensions cover. Weaver [21], just one year after Shannon introduced his information theory, proposed that communication involves problems at three levels as follows: “LEVEL A. How accurately can the symbols of

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