The Modal Completeness of ILW
نویسندگان
چکیده
This paper contains a completeness proof for the system ILW, a rather bewildering axiom system belonging to the family of interpretability logics. We have treasured this little proof for a considerable time, keeping it just for ourselves. Johan’s fiftieth birthday appears to be the right occasion to get it out of our wine cellar.
منابع مشابه
Modal Matters for Interpretability Logics
This paper is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the fundaments are laid for later results. These fundaments consist of a thorough treatment of a construction method to obtain modal models. This construction method is used to reprove some known results in the area of interpretability like the modal comp...
متن کاملSmart labels
The notion of a critical successor [dJV90] has been central to all modal completeness proofs in interpretability logics. In this paper we shall work with an alternative notion, that of an assuring successor. As we shall see, this makes life a lot easier. After a general treatment of assuringness, we shall apply it to obtain a completeness results for ILW, a result first proved by de Jongh and V...
متن کاملModal Matters in Interpretability Logics
In this paper we expose a method for building models for interpretability logics. The method can be compared to the method of taking unions of chains in classical model theory. Many applications of the method share a common part. We isolate this common part in a main lemma. Doing so, many of our results become applications of this main lemma. We also briefly describe how our method can be gener...
متن کاملThe Semantics of Modal Predicate Logic I. Counterpart-Frames
We introduce a new semantics for modal predicate logic, with respect to which a rich class of first-order modal logics is complete, namely all normal first-order modal logics that are extensions of free quantified K. This logic is defined by combining positive free logic with equality PFL . = and the propositional modal logic K. We then uniformly construct—for each modal predicate logic L—a can...
متن کاملPost Completeness in Congruential Modal Logics
Well-known results due to David Makinson show that there are exactly two Post complete normal modal logics, that in both of them, the modal operator is truthfunctional, and that every consistent normal modal logic can be extended to at least one of them. Lloyd Humberstone has recently shown that a natural analog of this result in congruential modal logics fails, by showing that not every congru...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1999