Tableaux approaches for region based theories of space

Abstract

Uzayn bolgeye dayal teorilerini icin tablo yaklasmn inceledigimizbu tez bes bolumden olusmaktadr. Tezin ilk ksmnda problemintanm ve uygulanan yontemler verilmistir. Tezin ikinci ve ucuncuksmnda uzayn bolgeye dayal teorisinin sentaks, semantik veaksiyomatik ozellikleri tantlarak uzayn bolgeye dayal teorisi icintablo kurallar verilmis ve tablo yonteminin temel kavramlar olan;baslangc tablosu, ack ve kapal tablo, dal, dugum kavramlar ifadeedilerek tablo kurallarnn uygulamalar orneklerle ayrntl olarakacklanmstr. Tablo kurallarnn sonlanma ve saglamlk teoremleri vekantlar verilmistir. Ayrca tablo kurallar icin tamlk teoremininkantnda kullanlan sistematik tablo insa yontemi, dogruluk lemmasve tamlk teoremleri ve ispatlar verilmistir. Ek olarak, uzaynbolgeye dayal teorisinin modellerini genisleterek simetrik, yansmalve gecismeli olmas durumunda tablo kurallar tanmlanarak,sonlanma, saglamlk ve tamlk teoremlerinin kantnda kullanlanyardmc teoremler ve bu teoremlerin kantlar ayrntl olarakverilmistir. Tezin dorduncu ksmnda, bagntl mantklarn birgenislemesi olan evrensel modalite iceren bagntl mantklarn;sentaks, semantik ve aksiyomatik ozellikleri tantlarak, tablokurallar verilmis ve uygulamalar orneklerle ayrntl olarakacklanmstr. Ardndan tablo kurallarnn sonlanma ve saglamlkteoremleri ve kantlar verilmistir. Ayrca tablo kurallar icin dogruluk lemmas ve tamlk teoreminin kantlar verilmistir. Besincibolumde, bagntl mantklarn farkl bir semantigi olan reel sayaralklar uzerindeki yorumu uzerine calslms ve bu baglamda;sentaks, semantik ve aksiyomatik ozellikleri tantlarak, tablokurallar verilmis ve tablo kurallarnn uygulamalar orneklerleayrntl olarak acklanmstr. Ek olarak, tablo kurallarnn sonlanmave saglamlk teoremleri kantlar ile verilmistir. Ayrca tablo kurallaricin dogruluk lemmas ve tamlk teoreminin kant verilmistir.

In this study, we examined tableaux approaches for region basedtheories of space. This thesis consists of ve chapters. In the rstchapter is devoted to statement of the problem, review of contents,methods applied. In Chapter 2 and Chapter 3, we introduce regionbased theories of space. In Chapter 2, we introduce historicalbackground, syntax and semantics, axiomatization of the theory. Insemantics subsection, we present relational semantics and topologicalsemantics. Following sections continue with applications anddenability result in region based theories of space. In Chapter 3, westudy tableau approaches for region based theories of space, we givebasic denitions about tableau approaches, we prove termination,soundness and completeness theorems. In last section of Chapter 3,we give tableaux rules for variants of region based theories of space.In its subsections, we prove soundness and completeness theorem forvariants. In Chapter 4, we presents generalized contact logics. Therst section of Chapter 4 consists of syntax-semantics, denabilityand axiomatizationn. The chapter continue with general tableauapproaches for generalized contact logics. Section 4.4 and 4.3, consistof soundness-completeness theorems and proofs. In the end ofChapter 4, we give tableau rules for variants. And then we givesoundness-completeness theorem and proofs. Chapter 6 is devoted tothe study of interval semantics of contact logics and its tableau approaches. In particular, we give syntax and semantics. After thatwe present tableau rules for contact logics interpreted over intervals.The last two sections are about soundness and completenesstheorems. We give proofs of these theorems.