ترغب بنشر مسار تعليمي؟ اضغط هنا

An interpolant in predicate Godel logic

72   0   0.0 ( 0 )
 نشر من قبل Samuel J. van Gool
 تاريخ النشر 2018
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

A logic satisfies the interpolation property provided that whenever a formula {Delta} is a consequence of another formula {Gamma}, then this is witnessed by a formula {Theta} which only refers to the language common to {Gamma} and {Delta}. That is, the relational (and functional) symbols occurring in {Theta} occur in both {Gamma} and {Delta}, {Gamma} has {Theta} as a consequence, and {Theta} has {Delta} as a consequence. Both classical and intuitionistic predicate logic have the interpolation property, but it is a long open problem which intermediate predicate logics enjoy it. In 2013 Mints, Olkhovikov, and Urquhart showed that constant domain intuitionistic logic does not have the interpolation property, while leaving open whether predicate Godel logic does. In this short note, we show that their counterexample for constant domain intuitionistic logic does admit an interpolant in predicate Godel logic. While this has no impact on settling the question for predicate Godel logic, it lends some credence to a common belief that it does satisfy interpolation. Also, our method is based on an analysis of the semantic tools of Olkhovikov and it is our hope that this might eventually be useful in settling this question.



قيم البحث

اقرأ أيضاً

246 - George Metcalfe 2011
Analytic proof calculi are introduced for box and diamond fragments of basic modal fuzzy logics that combine the Kripke semantics of modal logic K with the many-valued semantics of Godel logic. The calculi are used to establish completeness and complexity results for these fragments.
We begin the development of structure theory for a first order theory stable over a monadic predicate.
Linear logical frameworks with subexponentials have been used for the specification of among other systems, proof systems, concurrent programming languages and linear authorization logics. In these frameworks, subexponentials can be configured to all ow or not for the application of the contraction and weakening rules while the exchange rule can always be applied. This means that formulae in such frameworks can only be organized as sets and multisets of formulae not being possible to organize formulae as lists of formulae. This paper investigates the proof theory of linear logic proof systems in the non-commutative variant. These systems can disallow the application of exchange rule on some subexponentials. We investigate conditions for when cut-elimination is admissible in the presence of non-commutative subexponentials, investigating the interaction of the exchange rule with local and non-local contraction rules. We also obtain some new undecidability and decidability results on non-commutative linear logic with subexponentials.
154 - Itai Ben Yaacov 2009
We develop several aspects of local and global stability in continuous first order logic. In particular, we study type-definable groups and genericity.
165 - Cheng Hao 2011
In this article we investigate the notion and basic properties of Boolean algebras and prove the Stones representation theorem. The relations of Boolean algebras to logic and to set theory will be studied and, in particular, a neat proof of completen ess theorem in propositional logic will be given using Stones theorem from Boolean algebra.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا