Memory logics are a family of modal logics in which standard relational structures are augmented with data structures and additional operations to modify and query these structures. In this paper we present sound and complete axiomatizations for some members of this family. We analyse the use of nominals to achieve completeness, and present one example in which they can be avoided.Key words: Modal Logics, Hybrid Logics, Memory Logics, Completeness.
Modal Logics with MemoryModal logics [1, 2] can be considered nowadays as languages specially designed to describe properties of relational structures. They try to find a balance between expressive power, easy of use, and computational complexity. Many attempts have been made in recent years to increase modal logic expressivity by adding some notion of state to standard relational structures. This is a natural need, since modal logics are used in many different scenarios as tools for modeling behavior.One example of such logics are epistemic logic with dynamic operators. These languages are used to express the evolution of knowledge by means of knowledge-changing actions. Such logics are often called Dynamic Epistemic Logics (DEL) [3], and a large number of DELs has been proposed [4,5,6,7]. These logics differ considerably in expressive power among themselves, but the common idea is to represent knowledge evolution by accessing and changing the model structure through logic operators. For example, representing the fact that an agent obtains the information that ϕ is true in state w amounts to eliminating all possible successor states where ϕ does not hold.Other examples of logics which have the ability to model behavior are some of the languages used by the software verification community. The logic XCTL of Email addresses: carlos.areces@loria.fr (Carlos Areces), santiago@dc.uba.ar (Santiago Figueira), smera@dc.uba.ar (Sergio Mera) 1 Sergio Mera is partially supported by a grant of Fundación YPF.