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Grammar consists in patterns for assembling symbolically complex expressions. Such expressions are characterized as assemblies of symbolic structures, also called constructions. In large measure, symbolic assemblies are hierarchically arranged: at a given level of organization, component symbolic structures are integrated to form a composite symbolic structure, which can in turn function as component structure at a higher level, and so on. Component structures are integrated both semantically and phonologically, the phonological integration serving to symbolize the semantic integration. Although linguistic meanings are only partially compositional, compositional patterns are essential to the formation and understanding of novel expressions. These patterns are themselves symbolic assemblies, differing from expressions just by virtue of being schematic rather than specific; they are thus referred to as constructional schemas. Abstracted from occurring expressions, these schemas serve as templates for assembling and assessing new ones. A distinction is made between unipolar and bipolar organization, depending on whether the elements involved are delimited solely on semantic or phonological grounds or whether they are delimited by their participation in symbolic relationships. That is, unipolar organization is a matter of phonological or conceptual structure per se, considered independently of symbolic relationships, whereas bipolar organization pertains to the semantic and phonological structures which function in lexicon and grammar. Unipolar and bipolar organization do not have to match at either the semantic or the phonological pole.

The distinction between coordination and subordination is not clear-cut. The essence of coordination is the mental juxtaposition of structures construed as parallel and co-equal. Subordination has a number of dimensions, including form, the participation of one clause in the relationship profiled by another, and a clause's profile being overridden at the composite structure level. Constituency and profiling are often flexible, depending on factors like the size of clauses and their discourse function. The traditional division into adverbial, relative, and complement clauses is based primarily on how clauses are connected with one another. To the extent that these distinctions hold, they are based on semantic function rather than specific structural configurations. In the case of complements, the classic distinction between control and raising constructions is non-fundamental, the latter being just a special case of the former. Finite and nonfinite complements differ not just in form but in meaning and typical function. Predicates taking finite complements pertain to the epistemic status of propositions; those taking nonfinite complements pertain to the realization of occurrences. Complementation involves multiple conceptualizers and levels of conception. Different conceptualizers apprehend the same proposition each from their own perspective, assessing it with respect to their own conception of reality. Complement-taking predicates refer to different phases of this assessment. Impersonal constructions invoke a conceptualizer and the relevant scope of awareness in generalized fashion, suggesting that anyone would make the assessment under the circumstances.

This chapter discusses the X-ray and neutron diffraction methods used to study the atomic structures of aperiodic crystals, addressing indexing diffraction patterns, superspace, ab initio methods, the structure factor of incommensurate structures; and diffuse scattering. The structure solution methods based on the dual space refinements are described, as they are very often applied for the resolution of aperiodic crystal structures. Modulation functions which are used for the refinement of modulated structures and composite structures are presented and illustrated with examples of structure models covering a large spectrum of structures from organic to inorganic compounds, including metals, alloys, and minerals. For a better understanding of the concept of quasicrystalline structures, one-dimensional structure examples are presented first. Further examples of quasicrystals, including decagonal quasicrystals and icosahedral quasicrystals, are analysed in terms of increasing shells of a selected number of polyhedra. The notion of the approximant is compared with classical forms of structures.

First a general description of the concept of crystalline structures is presented with some historical background information. The classical approach of periodic structures is presented along with the important topic of symmetry and its role characterizing physical properties. The limitations of the classical model are then introduced in view of the new experimental observations discovered since the 1970s. New forms of crystalline structures including incommensurately modulated and composite structures are presented along with quasicrystalline structures (quasicrystals). The necessity to extend the theory of space group symmetry is then discussed and the concept of superspace symmetry is introduced in order to describe these new forms of matters.

This chapter explores the philosophical and formal issues surrounding mereological composition. It carefully examines the difference between three main types of fusion: algebraic joins, Leśniewski sums, and Goodman fusions. It also examines different views about their conditions of existence (the so-called ‘special composition question’), including the controversial doctrines of mereological universalism, nihilism, and restricted theories of composition. Next it considers whether fusions are unique and how this impacts extensionality, including presenting a detailed analysis of the thesis known as ‘composition as identity’. A number of ‘structural’ conceptions of composition (and related algebraic principles) are then examined. Finally, parallel to questions about a null object, atomism, and ‘atomless gunk’, the existence of a universal object and the ideas of ‘worldless junk’, and coatomism are considered.