Fitch–Style Natural Deduction for Modal Paralogics∗

نویسنده

  • Hans Lycke
چکیده

In this paper, I will present a Fitch–style natural deduction proof theory for modal paralogics (modal logics with gaps and/or gluts for negation). Besides the standard classical subproofs, the presented proof theory also contains modal subproofs, which express what would follow from a hypothesis, in case it would be true in some arbitrary world.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Fitch-Style Modal Lambda Calculi

Fitch-style modal deduction, in which modalities are eliminated by opening a subordinate proof, and introduced by shutting one, were investigated in the 1990s as a basis for lambda calculi. We show that such calculi have good computational properties for a variety of intuitionistic modal logics. Semantics are given in cartesian closed categories equipped with an adjunction of endofunctors, with...

متن کامل

Rewriting for Fitch Style Natural Deductions

Logical systems in natural deduction style are usually presented in the Gentzen style. A different definition of natural deduction, that corresponds more closely to proofs in ordinary mathematical practice, is given in [Fitch 1952]. We define precisely a CurryHoward interpretation that maps Fitch style deductions to simply typed terms, and we analyze why it is not an isomorphism. We then descri...

متن کامل

Formalizing natural deduction with assumption bases

We introduce NDL, a new formalization of Fitch-style natural deduction based on the abstraction of assumption bases. NDL proofs tend to be readable, writable, concise, and can be checked very efficiently. We present the abstract syntax of NDL, followed by two different kinds of formal semantics: evaluation and denotational. We then relate the two semantics and show how proof checking becomes ta...

متن کامل

From Gabbay-style rules to labelled deduction

Is there a link between Gabbay-style rules, modal languages with nominals, and labelled deduction? It seems there should be: though they differ in many ways, all share the idea that state-names are important in modal deduction. I shall show how to move from a Gabbay-style rule to labelled deduction via the basic hybrid language. I finish with a discussion of the place of state-names in modal lo...

متن کامل

Natural deduction via graphs: formal definition and computation rules

We introduce the formalism of deduction graphs as a generalization of both Gentzen-Prawitz style natural deduction and Fitch style flag deduction. The advantage of this formalism is that subproofs can be shared, like in flag deductions (and unlike natural deduction), but also that the linearisation used in flag deductions is avoided. Our deduction graphs have both nodes and boxes, which are col...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009