Semantic investigation of canonical Gödel hypersequent systems

نویسنده

  • Ori Lahav
چکیده

We define a general family of hypersequent systems with well-behaved logical rules, of which the known hypersequent calculus for (propositional) Gödel logic, is a particular instance. We present a method to obtain (possibly, non-deterministic) many-valued semantics for every system of this family. The detailed semantic analysis provides simple characterizations of cut-admissibility and axiom-expansion for the systems of this family.

برای دانلود رایگان 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

Non-deterministic Connectives in Propositional Godel Logic

We define the notion of a canonical Gödel system in the framework of single-conclusion hypersequent calculi. A corresponding general (nondeterministic) Gödel valuation semantics is developed, as well as a (non-deterministic) linear intuitionistic Kripke-frames semantics. We show that every canonical Gödel system induces a class of Gödel valuations (and of Kripke frames) for which it is strongly...

متن کامل

A cut-free calculus for second-order Gödel logic

We prove that the extension of the known hypersequent calculus for standard first-order Gödel logic with usual rules for second-order quantifiers is sound and (cut-free) complete for Henkin-style semantics for second-order Gödel logic. The proof is semantic, and it is similar in nature to Schütte and Tait’s proof of Takeuti’s conjecture.

متن کامل

A Hypersequent System for Gödel-Dummett Logic with Non-constant Domains

Gödel-Dummett logic is an extension of first-order intuitionistic logic with the linearity axiom (A ⊃ B)∨ (B ⊃ A), and the so-called “quantifier shift” axiom ∀x(A ∨ B(x)) ⊃ A ∨ ∀xB(x). Semantically, it can be characterised as a logic for linear Kripke frames with constant domains. Gödel-Dummett logic has a natural formalisation in hypersequent calculus. However, if one drops the quantifier shif...

متن کامل

A semantic proof of strong cut-admissibility for first-order Gödel logic

We provide a constructive direct semantic proof of the completeness of the cut-free part of the hypersequent calculus HIF for the standard first-order Gödel logic (thereby proving both completeness of the calculus for its standard semantics, and the admissibility of the cut rule in the full calculus). The results also apply to derivations from assumptions (or “non-logical axioms”), showing in p...

متن کامل

Hypersequent Calculi for some Intermediate Logics with Bounded Kripke Models

In this paper we define cut-free hypersequent calculi for some intermediate logics semantically characterized by bounded Kripke models. In particular we consider the logics characterized by Kripke models of bounded width Bwk, by Kripke models of bounded cardinality Bck and by linearly ordered Kripke models of bounded cardinality Gk. The latter family of logics coincides with finite-valued Gödel...

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

عنوان ژورنال:
  • J. Log. Comput.

دوره 26  شماره 

صفحات  -

تاریخ انتشار 2016