Institutionindependent logic programming paradigms p. The use of institutions makes it possible to develop concepts of specification languages like structuring of specifications. However, their proof theoretic nature leads them to a theorylevel semantics without support for hiding. A model theory that is independent of any concrete logical system allows a general. Razvan diaconescu, institutionindependent model theory core. A proof theoretic interpretation of model theoretic hiding. We propose a functional view of ontologies that emphasises their role in determining answers to queries, irrespective of the formalism in which they are written. There are many illustrations though that people here will find easy to understand.
The development includes most of the important methods and concepts of conventional concrete model theory at the abstract institution independent level. Besides their great generality, another important feature of institutions, not present, or poorly present, in. Institutions thus allowed for a smooth, systematic, and uniform development of model theories for unconventional logical systems, as. Towards a functional approach to modular ontologies using. This generality can be achieved by applying the theory of institutions that provides a precise mathematical formulation for the intuitive concept of a logical system. Omitting types theorem any nonprincipal type has a model which omits it. Institutionindependent model theory pdf free download. By abstracting away from the realities of the actual conventional logics, it can be. However, their proof theoretic nature leads them to a theory level semantics without support for hiding.
Downward lowenheimskolem theorem and interpolation in logics. The next section recalls the forcing technique in institutional model theory. We generalize the method of diagrams from conventional model theory to a simple institution independent i. Abstract model theory for specification and programming.
There is a population explosion among the logical systems used in computing science. An institutionindependent proof of the beth definability. First, it provides model theoretic results and analysis for various logics in a generic way. The significance of institutionindependent model theory is manifold. There are many illustrations though that people here will. This book develops model theory independently of any concrete logical system or structure, within the abstract categorytheoretic framework of the so called institution theory. What is the relationship between category theory and model. I redesign of indepth model theory at the level of abstract institutions.
That is, models and sentences may be arbitrary objects. This logic is organized as an institution 14 and we develop a framework for applying known institutionindependent. Logical frameworks like lf have also been equipped with structuring languages. Especially in computer science, where the development of a huge number of specification logics is observable, institutionindependent model theory simplifies. Request pdf razvan diaconescu, institutionindependent model theory we present a syntactic proof of cutelimination for weak grzegorczyk logic go.
Institutionindependent model theory razvan diaconescu. This cited by count includes citations to the following articles in scholar. This generality can be achieved by applying the theory of institutions that provides a precise. Institutionindependent generalization of tarskis elementary. Institutionindependent model theory is emerging as an important form of universal model theory part of the grand project of universal logic promoted. Category theory, which is the next step after set theory, supports a categorified version of model theory, called the theory. The notion of logical system here is formalized as an institution. More specifically, studia logica invites articles on topics in general logic as defined in 1991 mathematical subject classification and on applications of logic to other branches of knowledge such as. Institutions constitute a model oriented meta theory on logical systems similar to how the theory of rings and modules constitute a meta theory for classical linear algebra. Considering the assets of the institutional framework for model theory abstractness, logicindependence we study in this paper both definability notions implicit and explicit from an institutionindependent point of view. Categories we will assume that the reader is familiar with the basic notions of category theory, like functor, natural. The categorical assumptions used here are easy to check in concrete logics such that. This paper consists of a systematical study of the modeltheoretic properties of higher order logic with henkin semantics, in a simpli. The last two chapters 14 and 15 digress from the main topic of the book in that they present some applications of institutionindependent model theory to speci.
Also, as mentioned above, the current algebraic specii cation logics and an increasing number of. Institutionindependent model theory studies in universal. This is the basic paper, giving the basic definitions and results. We argue that the basic premise and predictions of the theory are supported by evidence from the experience of chinas state enterprise reform. The institutionindependent con cept of elementary diagrams presented above has been successfully used in a rather crucial way for developing several results in institutionindependent model theory, including quasivariety theorems and existence of free models for theories 12,17, 123 saturated models in institutions 703 robinson. It provides the most complete form of abstract model theory, free of commitement to any particular logic, the only one including signature morphisms, model reducts, and even mappings morphisms. In the form presented here it has been introduced at the level of institutionindependent model theory in 9 as a categorical property which formalizes the idea that the class of model homomorphisms from a model m can be represented by a natural isomorphism as a class of models of a theory in a signature extending the original signature with. Forcing, downward l owenheimskolem and omitting types. Abstract model theory for specification and programming, by joseph goguen and rod burstall, in journal of the acm, 39, no. Craig for classical predicate calculus in 1957, it has been extended to intuitionistic logic by k.
Institutionindependent model theory razvan diaconescu springer. A notion of framework is introduced that captures the situation of a global language into which both an ontology language and a query language can be translated, in an abstract way. We generalize the method of diagrams from conventional model theory to a simple institutionindependent i. Institutions thus allowed for a smooth, systematic, and uniform. Model theory deals primarily with sets of axioms, on languages which are just sets, and classes of models of theories. Moreover amalgamation of model homomorphisms is known to play a role only in some developments in institutionindependent model theory 2, but even there most involvements of model amalgamation. A textbook dedicated to this topic is under preparation 24,25 is a recent survey. Simion stoilow institute of mathematics of the romanian academy. These are model amalgamation and the method of diagrams. The craig interpolation theorem is a basic result in the model theory of firstorder logic. Elementary diagrams in institutions journal of logic and. Jan 01, 2003 institutionindependent ultraproducts razvan diaconescu.
Craig for classical predicate calculus in 1957, it has been extended to. On the usefulness of carriers, semiinitiality and semiadjuncts for institution independent issues gilles bernot and erwan david lami. Institutionindependent model theory ebook, pdf 79,95 advances in proof theory ebook, pdf. Many logical notions and results can be developed in an institutionindependent way, to mention just a few. Introducing h, an institutionbased formal specification and. Institutionindependent model theory ebook, pdf 79,95 advances in proof theory ebook, pdf 89,95. Institutionindependent ultraproducts institutionindependent ultraproducts razvan diaconescu. Like universal logic in general, universal model theory in particular is not seeking for one single model theory in which all other model. The theory of institutions does not assume anything about the nature of the logical system.
Razvan diaconescu, institutionindependent model theory. Moreover amalgamation of model homomorphisms is known to play a role only in some developments in institution independent model theory 2, but even there most involvements of model amalgamation. Considering the assets of the institutional framework for model theory abstractness, logicindependence we study in this paper both definability notions implicit and explicit from an institution independent point of view. This paper can be regarded as a new step towards this goal, part of a coming series of works in institutionindependent model theory. Razvan diaconescu, institutionindependent model theory, birkhauser basel 2008.
In section3, we develop an institution independent version of dlst that is applicable to many concrete institutions. Journal of the association for computing machinery 391. Examples include firstorder logic, equational logic, hornclause logic, higherorder logic, infinitary logic, dynamic logic, intuitionistic logic, ordersorted logic, and temporal logic. To begin with, we take a modeltheoretic view of logic, putting aside the issues of proof for the time being. Thus general institutional results were applicable to the diversity of logical systems used in computer science. The theory of institutions 40 is a categorical universal model theory which formalises the intuitive notion of logical system, including syntax, semantics, and the satisfaction between them. Studia logica publishes original papers on various logical systems, which utilize methods of contemporary formal logic those of algebra, model theory, proof theory, etc. Institutionindependent model theory by razvan diaconescu 2008 english pdf.
Institutional semantics for manyvalued logics sciencedirect. The notion tries to capture the essence of the concept of logical system. The beginnings of institutionindependent model theory. In section 3 we develop an institutionindependent version of the. Although we feel that the theory is also relevant to other transition economies, future empirical. Institutionindependent model theory provides an abstract approach towards model the ory, without a particular underlying logical system. Simion stoilow institute of mathematics of the romanian. An institutionindependent generalization of tarskis. It also has the potential to support the development of deep model theoretic methods and results since we show that it enjoys rather naturally a couple of properties that pervade a lot of institution independent model theory developments 10. Aug 02, 2016 model theory deals primarily with sets of axioms, on languages which are just sets, and classes of models of theories. Apart from reformulation of standard concepts and results in a very general setting, thus applicable to many logical systems, institutionindependent model theory has. Institutionindependent model theory is emerging as an important form of universal model theory part of the grand project of universal logic promoted by b. Institutions, madhyamaka, and universal model theory.
A model theory that is independent of any concrete logical system allows a general handling of a large variety of logics. We prove an institutional version of tarskis elementary chain theorem applicable to a whole plethora of firstorderaccessible logics, which are. Another analogy can be made with universal algebra versus groups, rings, modules etc. The development includes most of the important methods and. Logic and information workshop, schloss mnchenwiler, 2223 november 2006 d. A multitask theory of the state enterprise reform1 chongen bai the university of hong kong, hong kong and wdi. Institutions thus allowed for a smooth, systematic, and uniform development of model theories for unconventional logical systems, as well as of logicbytranslation. I asked a perhaps not well enough formed question on stack exchange today to see if i am understanding institutions correctly. This generality can be achieved by applying the theory of institutions that. Institution theory and applications simion stoilow institute of. Pdf three decades of institution theory researchgate. To submit an update or takedown request for this paper, please submit an updatecorrectionremoval request.
Especially in computer science, where the development of. The model theory oriented axiomatic approach by goguen and. The notion of institution was created by joseph goguen and rod burstall in the late 1970s, in order to deal with the population explosion among the logical systems used in computer science. Besides their great generality, another important feature of institutions, not present, or poorly present, in other abstract frameworks, is the. Forcing and the omitting type theorem, institutionally. After the theory sections, empirical evidence from chinas reform experience is presented in section 5.
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