I den här uppsatsen beskrivs den syntaktiska distributionen av en andra negator, e i två svenska dialekter. Det finns tidigare belägg för att e förekommer i slutet av negerade satser i icke-standarddialekter. Uppsatsen redogör också för tidigare forskning om ett relaterat rikssvenskt fenomen (inte... inte), dialektforskning om e samt språktypologisk forskning som relaterar till negation och i synnerhet dubbelnegation. Uppsatsen baseras på en parallell\-korpusundersökning med material från två svenska dialekter, Forsamål och Jarssemål. I undersökningen studeras syntaktiska mönster som är relevanta för distributionen av en andra negator, såsom satstyp, underordning, upprepning av subjekt med mera. Huvudresultatet är att e är mycket frekvent, särskilt efter huvudsatser. E är mycket ovanligt i bisatser, men annars finns det få tendenser till andra syntaktiska mönster i materialet. Olika teorier om vad denna andra negator skulle kunna ha eller ha haft för funktion presenteras. Vidare forskning om den syntaktiska distributionen av e i fler dialekter såväl som dess funktion i desamma behövs. / This bachelor thesis is a description of the syntactic distribution of a second negator, e, in two Swedish dialects. Previous research establishes the occurence of this e in clase-final position in non-standard dialects of Swedish, but does rarely provide in-depth analysis of e as a second negator. A background of previous research on a related phenomena in standard Swedish (inte... inte), research in swedish dialects and the linguistic field of negation and double negation is presented and used in the understanding of e. The data used is from a parallel corpus of Swedish dialects called ''Mormors katt'', the two dialects are Jarrsemål and Forsamål. This data is analyzed for syntactic patterns in the distribution on e, such as subordination, clause type, repeated subject etc. The most important finding is that e is very frequent in the data and that it is especially frequent in main clauses. Different theories on why this is and what function e has are put forward. Futher research on the distribution of e in even more dialects is required.

<p dir="ltr">This dissertation presents a analysis of negation in a spoken language, i.e., Khuzestani Arabic (KhA), and a sign language, i.e., Sadat Tawaher Sign Language (STSL). STSL emerged naturally without any intervention such as deaf education after a man lost his hearing around sixty years ago in a small village named Sadat Tawaher located in southwestern Iran. After this incident, the deaf person's family came up with a gestural system to communicate with him. Despite the fact that everyone in Sadat Tawaher, including the deaf person's family, speaks KhA, I hypothesized that KhA and STSL possess different grammatical ways to express negation. Data gathered using signed productions, story-telling, and grammaticality judgments clearly showed that negation is preverbal in KhA but sentence-final in STSL. </p>

<p>In this thesis we use the syntactic-semantic method of constructive type theory to give meaning to classical logic, in particular Gentzen's LK.</p><p>We interpret a derivation of a classical sequent as a derivation of a contradiction from the assumptions that the antecedent formulas are true and that the succedent formulas are false, where the concepts of truth and falsity are taken to conform to the corresponding constructive concepts, using function types to encode falsity. This representation brings LK to a manageable form that allows us to split the succedent rules into parts. In this way, every succedent rule gives rise to a natural deduction style introduction rule. These introduction rules, taken together with the antecedent rules adapted to natural deduction, yield a natural deduction calculus whose subsequent interpretation in constructive type theory gives meaning to classical logic.</p><p>The Gentzen-Prawitz inversion principle holds for the introduction and elimination rules of the natural deduction calculus and allows for a corresponding notion of convertibility. We take the introduction rules to determine the meanings of the logical constants of classical logic and use the induced type-theoretic elimination rules to interpret the elimination rules of the natural deduction calculus. This produces an interpretation injective with respect to convertibility, contrary to an analogous translation into intuitionistic predicate logic.</p><p>From the interpretation in constructive type theory and the interpretation of cut by explicit substitution, we derive a full precision contraction relation for a natural deduction version of LK. We use a term notation to formalize the contraction relation and the corresponding cut-elimination procedure.</p><p>The interpretation can be read as a Brouwer-Heyting-Kolmogorov (BHK) semantics that justifies classical logic. The BHK semantics utilizes a notion of classical proof and a corresponding notion of classical truth akin to Kolmogorov's notion of pseudotruth. We also consider a second BHK semantics, more closely connected with Kolmogorov's double-negation translation.</p><p>The first interpretation reinterprets the consequence relation while keeping the constructive interpretation of truth, whereas the second interpretation reinterprets the notion of truth while keeping the constructive interpretation of the consequence relation. The first and second interpretations act on derivations in much the same way as Plotkin's call-by-value and call-by-name continuation-passing-style translations, respectively.</p><p>We conclude that classical logic can be given a constructive semantics by laying down introduction rules for the classical logical constants. This semantics constitutes a proof interpretation of classical logic.</p>

In this thesis we use the syntactic-semantic method of constructive type theory to give meaning to classical logic, in particular Gentzen's LK. We interpret a derivation of a classical sequent as a derivation of a contradiction from the assumptions that the antecedent formulas are true and that the succedent formulas are false, where the concepts of truth and falsity are taken to conform to the corresponding constructive concepts, using function types to encode falsity. This representation brings LK to a manageable form that allows us to split the succedent rules into parts. In this way, every succedent rule gives rise to a natural deduction style introduction rule. These introduction rules, taken together with the antecedent rules adapted to natural deduction, yield a natural deduction calculus whose subsequent interpretation in constructive type theory gives meaning to classical logic. The Gentzen-Prawitz inversion principle holds for the introduction and elimination rules of the natural deduction calculus and allows for a corresponding notion of convertibility. We take the introduction rules to determine the meanings of the logical constants of classical logic and use the induced type-theoretic elimination rules to interpret the elimination rules of the natural deduction calculus. This produces an interpretation injective with respect to convertibility, contrary to an analogous translation into intuitionistic predicate logic. From the interpretation in constructive type theory and the interpretation of cut by explicit substitution, we derive a full precision contraction relation for a natural deduction version of LK. We use a term notation to formalize the contraction relation and the corresponding cut-elimination procedure. The interpretation can be read as a Brouwer-Heyting-Kolmogorov (BHK) semantics that justifies classical logic. The BHK semantics utilizes a notion of classical proof and a corresponding notion of classical truth akin to Kolmogorov's notion of pseudotruth. We also consider a second BHK semantics, more closely connected with Kolmogorov's double-negation translation. The first interpretation reinterprets the consequence relation while keeping the constructive interpretation of truth, whereas the second interpretation reinterprets the notion of truth while keeping the constructive interpretation of the consequence relation. The first and second interpretations act on derivations in much the same way as Plotkin's call-by-value and call-by-name continuation-passing-style translations, respectively. We conclude that classical logic can be given a constructive semantics by laying down introduction rules for the classical logical constants. This semantics constitutes a proof interpretation of classical logic.