The dominant trend in contemporary pragmatics has been information-biased, focusing on how information is transmitted from speaker to hearer, while the social and cultural side of communication has not been given the attention it deserves for effective communication. To redress the balance, this paper will expose the problems caused by the bias in information-based principles of Horn and Levinson, first taking the interpretation of an X expressions as an example. Then the author will turn to the other limitation of information-based principles, the restricted scope of application of their Q-principle and the entailment definition of informativeness. In place of Horn scales, the notion of Contrast Sets (CS), words and expressions that are opposed to each other in a particular context, will be proposed, as a further development on Hirschberg scales/posets (partially ordered sets). The most serious failing in information-biased pragmatics, however, is the lack of specification of contextual factors needed in pragmatic inference. Therefore, the author has specified the ingredients of Context as a necessary step toward the socio-cognitive approach. Context is first divided into the Linguistic (LC) and the Situational (SC), the latter further divided into Objective (Time, Place, and Topic) (SC(O)), and Subjective (Participant(s)) (SC(S)) which is itself divided into Intention, Knowledge, Interest, Emotion, Identity, and etc. On the basis of these amendments, the author builds up a model of pragmatic inference, consisting of 8 steps: 1) S makes U; 2) H assumes S observes CP; 3) H interprets U in LC; 4, 6, and 8) H determines Information of U; 5) SC (O) introduced; 7) SC(S) introduced; 9) H comes to Conclusion.