Borrowing interpolation

Diaconescu, Răzvan

doi:10.1093/logcom/exr007

Cited by 12 publications

(4 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This work opens up two main avenues for further research. One consists of investigations of the possibility to 'borrow' logical properties from FOL to hybridized institutions through the encoding comorphisms developed here, in the style of works such as (Cerioli and Meseguer 1997;Diaconescu 2012a) etc. Important target properties would be interpolation and initial semantics, both of them relevant within the formal specification and verification contexts.…”

Section: Discussionmentioning

confidence: 99%

“…Encoding hybridized institutions into first order logic 755 one I . The latter are especially useful for the borrowing methods; some references are (Diaconescu 2008(Diaconescu , 2012aPetria and Diaconescu 2006). In such encodings the structural complexity cost is shifted to the mapping Φ on the signatures, thus Φ maps signatures of I to theories of I rather than signatures.…”

Section: Presentationsmentioning

confidence: 99%

“…2. The comorphism used in Petria and Diaconescu (2006) and Diaconescu (2012a) encodes partial operations as (functional) relations and while the target presentations also consist of Horn sentences, unlike in the previous case the translations of the sentences (α) is rather complex which meaning that Horn sentences may by translated to non-Horn sentences. However, this comorphism has the benefit that the sentence translations are surjective, which allows the transfer of interpolation properties.…”

Section: Presentationsmentioning

confidence: 99%

See 2 more Smart Citations

Encoding hybridized institutions into first-order logic

Diaconescu

Madeira

2014

Math. Struct. Comp. Sci.

View full text Add to dashboard Cite

A ‘hybridization’ of a logic, referred to as the base logic, consists of developing the characteristic features of hybrid logic on top of the respective base logic, both at the level of syntax (i.e. modalities, nominals, etc.) and of the semantics (i.e. possible worlds). By ‘hybridized institutions’ we mean the result of this process when logics are treated abstractly as institutions (in the sense of the institution theory of Goguen and Burstall). This work develops encodings of hybridized institutions into (many-sorted) first-order logic (abbreviated $\mathcal{FOL}$) as a ‘hybridization’ process of abstract encodings of institutions into $\mathcal{FOL}$, which may be seen as an abstraction of the well-known standard translation of modal logic into $\mathcal{FOL}$. The concept of encoding employed by our work is that of comorphism from institution theory, which is a rather comprehensive concept of encoding as it features encodings both of the syntax and of the semantics of logics/institutions. Moreover, we consider the so-called theoroidal version of comorphisms that encode signatures to theories, a feature that accommodates a wide range of concrete applications. Our theory is also general enough to accommodate various constraints on the possible worlds semantics as well a wide variety of quantifications. We also provide pragmatic sufficient conditions for the conservativity of the encodings to be preserved through the hybridization process, which provides the possibility to shift a formal verification process from the hybridized institution to $\mathcal{FOL}$.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Presentationsmentioning

confidence: 99%

Section: Presentationsmentioning

confidence: 99%

See 1 more Smart Citation

Encoding hybridized institutions into first-order logic

Diaconescu

Madeira

2014

Math. Struct. Comp. Sci.

View full text Add to dashboard Cite

show abstract

“…Computing science and model theoretic motivations have led to a very general approach to interpolation [30] within the theory of institutions that is completely independent of any concrete logical system. This direction of study and research has produced a substantial body of results reported in works such as [30,42,43,45,65,74,[82][83][84][85][86]. In this context, the institution theoretic concept to interpolation had suffered a gradual evolution.…”

Section: Interpolation In Stratified Institutionsmentioning

confidence: 99%

The Axiomatic Approach to Non-Classical Model Theory

Diaconescu

2022

Mathematics

View full text Add to dashboard Cite

Institution theory represents the fully axiomatic approach to model theory in which all components of logical systems are treated fully abstractly by reliance on category theory. Here, we survey some developments over the last decade or so concerning the institution theoretic approach to non-classical aspects of model theory. Our focus will be on many-valued truth and on models with states, which are addressed by the two extensions of ordinary institution theory known as L-institutions and stratified institutions, respectively. The discussion will include relevant concepts, techniques, and results from these two areas.

show abstract

Three Decades of Institution Theory

Diaconescu¹

2012

Universal Logic: An Anthology

View full text Add to dashboard Cite

Borrowing interpolation

Cited by 12 publications

References 53 publications

Encoding hybridized institutions into first-order logic

Encoding hybridized institutions into first-order logic

The Axiomatic Approach to Non-Classical Model Theory

Three Decades of Institution Theory

Contact Info

Product

Resources

About