8 found
Order:
  1.  17
    An Institution-Independent Proof of Craig Interpolation Theorem.Răzvan Diaconescu - 2004 - Studia Logica 77 (1):59 - 79.
    We formulate a general institution-independent (i.e. independent of the details of the actual logic formalised as institution) version of the Craig Interpolation Theorem and prove it in dependence of Birkhoff-style axiomatizability properties of the actual logic.We formalise Birkhoff-style axiomatizability within the general abstract model theoretic framework of institution theory by the novel concept of Birkhoff institution.
    Direct download (6 more)  
     
    Export citation  
     
    My bibliography   9 citations  
  2.  35
    What is a Logic Translation?Till Mossakowski, Răzvan Diaconescu & Andrzej Tarlecki - 2009 - Logica Universalis 3 (1):95-124.
    We study logic translations from an abstract perspective, without any commitment to the structure of sentences and the nature of logical entailment, which also means that we cover both proof- theoretic and model-theoretic entailment. We show how logic translations induce notions of logical expressiveness, consistency strength and sublogic, leading to an explanation of paradoxes that have been described in the literature. Connectives and quantifiers, although not present in the definition of logic and logic translation, can be recovered by their abstract (...)
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   5 citations  
  3.  14
    On Quasi-Varieties of Multiple Valued Logic Models.Razvan Diaconescu - 2011 - Mathematical Logic Quarterly 57 (2):194-203.
    We extend the concept of quasi-variety of first-order models from classical logic to multiple valued logic and study the relationship between quasi-varieties and existence of initial models in MVL. We define a concept of ‘Horn sentence’ in MVL and based upon our study of quasi-varieties of MVL models we derive the existence of initial models for MVL ‘Horn theories’. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    Direct download (5 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  4.  11
    Abstract Beth Definability in Institutions.Marius Petria & Răzvan Diaconescu - 2006 - Journal of Symbolic Logic 71 (3):1002 - 1028.
    This paper studies definability within the theory of institutions, a version of abstract model theory that emerged in computing science studies of software specification and semantics. We generalise the concept of definability to arbitrary logics, formalised as institutions, and we develop three general definability results. One generalises the classical Beth theorem by relying on the interpolation properties of the institution. Another relies on a meta Birkhoff axiomatizability property of the institution and constitutes a source for many new actual definability results, (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography   1 citation  
  5.  15
    Institution Theory.Răzvan Diaconescu - 2015 - Internet Encyclopedia of Philosophy.
    Institution Theory Institution theory is a very general mathematical study of formal logical systems—with emphasis on semantics—that is not committed to any particular concrete logical system. This is based upon a mathematical definition for the informal notion of logical system, called institution, which includes both syntax and semantics as well as the relationship between … Continue reading Institution Theory →.
    Direct download  
     
    Export citation  
     
    My bibliography  
  6.  18
    Saturated Models in Institutions.Răzvan Diaconescu & Marius Petria - 2010 - Archive for Mathematical Logic 49 (6):693-723.
    Saturated models constitute one of the powerful methods of conventional model theory, with many applications. Here we develop a categorical abstract model theoretic approach to saturated models within the theory of institutions. The most important consequence is that the method of saturated models becomes thus available to a multitude of logical systems from logic or from computing science. In this paper we define the concept of saturated model at an abstract institution-independent level and develop the fundamental existence and uniqueness theorems. (...)
    Direct download (4 more)  
     
    Export citation  
     
    My bibliography  
  7.  14
    Institutions, Madhyamaka and Universal Model Theory.Razvan Diaconescu - 2007 - In Jean-Yves Béziau & Alexandre Costa-Leite (eds.), Perspectives on Universal Logic. pp. 41--65.
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography  
  8.  9
    The Institution-Theoretic Scope of Logic Theorems.Răzvan Diaconescu, Till Mossakowski & Andrzej Tarlecki - 2014 - Logica Universalis 8 (3-4):393-406.
    In this essay we analyse and elucidate the method to establish and clarify the scope of logic theorems offered within the theory of institutions. The method presented pervades a lot of abstract model theoretic developments carried out within institution theory. The power of the proposed general method is illustrated with the examples of interpolation and definability, as they appear in the literature of institutional model theory. Both case studies illustrate a considerable extension of the original scopes of the two classical (...)
    Direct download (2 more)  
     
    Export citation  
     
    My bibliography