Expressive Power and Decidability for Memory Logics

Areces, Carlos; Figueira, Diego; Figueira, Santiago; Mera, Sergio

doi:10.1007/978-3-540-69937-8_7

Cited by 12 publications

(17 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The framework can also be used for logics whose model theory has not been fully developed so far (e.g., Memory Logics [2,3]). In all cases, we only need to check that the requirements of the framework are met.…”

Section: Concrete Resultsmentioning

confidence: 99%

“…Memory logics, introduced in [1] and further investigated in, e.g., [2,4,3], allow modeling dynamic behavior through explicit memory operators that change the structure where evaluation takes place. Memory logics extends the syntax and semantics of BML with operators that store and retrieve elements of the domain into a memory -a subset of the domains of the model.…”

Section: Memory Logicsmentioning

confidence: 99%

“…An adequate translation from any memory logic obtained by combination of the operators described above can be defined by composition of the translation from memory logics to HL(↓) found in [2] with the translation from HL(↓) to FO given in [5]. Model translation is also fairly straightforward.…”

Section: Memory Logicsmentioning

confidence: 99%

See 2 more Smart Citations

Characterization, definability and separation via saturated models

Areces

Carreiro

Figueira

2014

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

Three important results about the expressivity of a modal logic L are the Characterization Theorem (that identifies a modal logic L as a fragment of a better known logic), the Definability theorem (that provides conditions under which a class of L-models can be defined by a formula or a set of formulas of L), and the Separation Theorem (that provides conditions under which two disjoint classes of L-models can be separated by a class definable in L).We provide general conditions under which these results can be established for a given choice of model class and modal language whose expressivity is below first order logic. Besides some basic constraints that most modal logics easily satisfy, the fundamental condition that we require is that the class of ω-saturated models in question has the Hennessy-Milner property with respect to the notion of observational equivalence under consideration. Given that the Characterization, Definability and Separation theorems are among the cornerstones in the model theory of L, this property can be seen as a test that identifies the adequate notion of observational equivalence for a particular modal logic.

show abstract

Section: Concrete Resultsmentioning

confidence: 99%

Section: Memory Logicsmentioning

confidence: 99%

See 1 more Smart Citation

Characterization, definability and separation via saturated models

Areces

Carreiro

Figueira

2014

Theoretical Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…I.e., we can use the forget operator f to eliminate the current point of evaluation from the memory S, while the erase operator e completely wipes out the memory S. We have introduced this family of logics, that we called memory logics, and investigated its expressive power in [12,13,14]. The language we have just described is very flexible, and it can be used to easily characterize model properties.…”

mentioning

confidence: 99%

“…In [13,14], for example, we have shown that ML( r , k ) 2 , the modal language extended with r and k , is strictly more expressive than the basic modal logic but strictly less expressive than the hybrid logic HL(↓). If we add the e operator to ML( r , k ), the resulting language is still strictly less expressive than the hybrid logic HL(↓).…”

mentioning

confidence: 99%

Completeness Results for Memory Logics

Areces

Figueira

Mera³

2008

Logical Foundations of Computer Science

Self Cite

View full text Add to dashboard Cite

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.

show abstract