Logical Operations and Invariance
نویسنده
چکیده
I present a notion of invariance under arbitrary surjective mappings for operators on a relational finite type hierarchy generalizing the so called Tarski-Sher criterion for logicality and I characterize the invariant operators as definable in a fragment of the first-order language. These results are compared with those obtained by Feferman and it is argued that further clarification of the notion of invariance is needed if one wants to use it to characterize logicality.
منابع مشابه
Modal logic and invariance
Consider any logical system, what is its natural repertoire of logical operations? This question has been raised in particular for first-order logic and its extensions with generalized quantifiers, and various characterizations in terms of semantic invariance have been proposed. In this paper, our main concern is with modal and dynamic logics. Drawing on previous work on invariance for first-or...
متن کاملLogicality and Invariance
This paper deals with the problem of giving a principled characterization of the class of logical constants. According to the so-called Tarski-Sher thesis, an operation is logical iff it is invariant under permutation. In the model-theoretic tradition, this criterion has been widely accepted as giving a necessary condition for an operation to be logical. But it has been also widely criticized o...
متن کاملSet-theoretical Invariance Criteria for Logicality
This is a survey of work on set-theoretical invariance criteria for logicality. It begins with a review of the Tarski-Sher thesis in terms, first, of permutation invariance over a given domain and then of isomorphism invariance across domains, both characterized by McGee in terms of definability in the language L ∞,∞. It continues with a review of critiques of the Tarski-Sher thesis, and a prop...
متن کاملThe concept of logic entropy on D-posets
In this paper, a new invariant called {it logic entropy} for dynamical systems on a D-poset is introduced. Also, the {it conditional logical entropy} is defined and then some of its properties are studied. The invariance of the {it logic entropy} of a system under isomorphism is proved. At the end, the notion of an $ m $-generator of a dynamical system is introduced and a version of the Kolm...
متن کاملCentral auditory neurons display flexible feature recombination functions.
Recognition of natural stimuli requires a combination of selectivity and invariance. Classical neurobiological models achieve selectivity and invariance, respectively, by assigning to each cortical neuron either a computation equivalent to the logical "AND" or a computation equivalent to the logical "OR." One powerful OR-like operation is the MAX function, which computes the maximum over input ...
متن کاملذخیره 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 ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Philosophical Logic
دوره 36 شماره
صفحات -
تاریخ انتشار 2007