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Abstract Cognitive Grammar is a radical alternative to the formalist theories that have dominated linguistic theory during the last half century. Instead of an objectivist semantics based on truth conditions or logical deduction, it adopts a conceptualist semantics based on human experience, our capacity to construe situations in alternate ways, and processes of imagination and mental construction. A conceptualist semantics makes possible an account of grammar which views it as being inherently meaningful (rather than an autonomous formal system). Grammar forms a continuum with lexicon, residing in assemblies of symbolic structures, i.e. pairings of conceptual structures and symbolizing phonological structures. Thus all grammatical elements are meaningful. It is shown in detail how Cognitive Grammar handles the major problems a theory of grammar has to deal with: grammatical classes, constructions, the relationship of grammar and lexicon, the capturing of regularities, and imposition of the proper restrictions. It is further shown how the framework applies to central domains of language structure: deixis, nominal structure, clausal structure, and complex sentences. Consideration is also given to discourse, the temporal dimension of grammar, and what it reveals about cognitive processes and the construction of our mental world.