To date, there is almost no work on the use of adverbs in sentiment analysis, nor has there been any work on the use of adverb-adjective combinations (AACs). We propose an AAC-based sentiment analysis technique that uses a linguistic analysis of adverbs of degree. We define a set of general axioms (based on a classification of adverbs of degree into five categories) that all adverb scoring techniques must satisfy. Instead of aggregating scores of both adverbs and adjectives using simple scoring functions, we propose an axiomatic treatment of AACs based on the linguistic classification of adverbs. Three specific AAC scoring methods that satisfy the axioms are presented. We describe the results of experiments on an annotated set of 200 news articles (annotated by 10 students) and compare our algorithms with some existing sentiment analysis algorithms. We show that our results lead to higher accuracy based on Pearson correlation with human subjects.