We study algebras and phase spaces for linear logics, including non-associative, non-commutative, obeying Lambek’s restriction, and others. We prove some representation theorems: every algebra from the class corresponding to the given logic can be embedded in the algebra of facts of some phase space, even based on a free groupoid. Furthermore, the complete algebras are isomorphic to the algebras of facts of the corresponding phase spaces. At the end, we find some interpretation of cyclic linear negation in terms of syntactic concept lattices.