Sweet SIXTEEN : Automation via Embedding into Classical Higher-Order Logic

نویسندگان

  • Alexander Steen
  • Christoph Benzmüller
چکیده

Introduction. Classical logics are based on the bivalence principle, that is, the set of truth-values V has cardinality |V | = 2, usually with V = {T,F} where T and F stand for truthhood and falsity, respectively. Many-valued logics generalize this requirement to more or less arbitrary sets of truth-values, rather referred to as truth-degrees in that context. Popular examples of many-valued logics are Gödel logics, Lukasiewicz logics or fuzzy logics with denumerable (or even larger in the case of fuzzy logic) sets of truth-degrees, and, from the class of finitelymany-valued logics, Dunn/Belnap’s four-valued logic [1,2]. The latter system, although originating from research on relevance logics, has been of strong interest to computer scientists as formal foundation of information and knowledge bases. Here, the set of truth-degrees is given by the power set of {T,F}, i.e. V = {N,T,F,B}, where N denotes the empty set (mnemonic for None), T and F the singleton sets of the respective classical truth-value, and B the set {T,F} (for Both). This work presents an approach for automating a sixteen-valued logic denoted SIXTEEN. This logic has been developed by Shramko and Wansing as a generalization of the mentioned four-valued system to knowledge bases in computer networks [9] and was subsequently further investigated in various contexts (e.g. [8,10]). In SIXTEEN, the truth-degrees are given by the power set of Belnap’s truth values, i.e.

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

Embedding of Quantified Higher-Order Nominal Modal Logic into Classical Higher-Order Logic

In this paper, we present an embedding of higher-order nominal modal logic into classical higher-order logic and study its automation. There exists no automated theorem prover for first-order or higherorder nominal logic at the moment, hence, this is the first automation for this kind of logic. In our work, we focus on nominal tense logic and have successfully proven some first theorems.

متن کامل

1 Embedding of First-Order Nominal Logic into Higher-Order Logic

Nominal logic, also referred to as hybrid logic, is a general term for extensions of ordinary modal logics that introduce a new sort of atomic formulae, the socalled nominals. These nominals are only true at one possible world and false at every other world. The shifter, denoted @, can be used to evaluate the truth of a formula φ at a given world corresponding to nominal i as in @iφ. The simple...

متن کامل

Faithful Semantical Embedding of a Dyadic Deontic Logic in HOL

A shallow semantical embedding of a dyadic deontic logic by Carmo and Jones in classical higher-order logic is presented. This embedding is proven sound and complete, that is, faithful. The work presented here provides the theoretical foundation for the implementation and automation of dyadic deontic logic within off-the-shelf higherorder theorem provers and proof assistants.

متن کامل

HOL based Universal Reasoning

At Unilog’2010 I have proposed classical higher-order logic HOL (Church’s type theory [1,9]) as a uniform framework for combining logics [2]. The main claim has been that many non-classical logics are just natural (embedded) fragments of classical HOL. The approach also supports combinations (e.g. fusions) of embedded logics; in particular, bridge rules can be postulated simply as axioms. In th...

متن کامل

Embedding of Quantified Modal Logic in Higher Order Logic Seminar Paper on Expressive Logics and their Automation

Church’s Simple Theory of Types (STT, also referred to as classical higher-order logic) is an elegant and expressive formal language that can represent complex (higher-order) properties and formulae. In this paper, an encoding of second-order quantified modal logic (QML) in STT, due to C. Benzmüller and L. C. Paulsen, is discussed. Main results include the soundness and completeness of this enc...

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 2015