Definability by Programs in First-Order Structures
نویسنده
چکیده
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ti 1. Preliminarv detinitilms and results . . . . . . . . . . . . . . . . . . . . . . . . . Algebraic characterizations of the unwind property .................. A structure with the unwind property for every iterative (but not every recursive 1 program . The truth-table property ............................. Structures with the truth-table property [but not the unwind property) for every iterative program .................................... ,4ppendix 1: The pebble game on infinite dags ..................... ippendix 2: Remaining proofs .............. ............ References .....................................
منابع مشابه
Loop-separable programs and their first-order definability
An answer set program with variables is first-order definable on finite structures if the set of its finite answer sets can be captured by a first-order sentence. Characterizing classes of programs that are first-order definable on finite structures is theoretically challenging and of practical relevance to Answer Set Programming. In this paper, we identify a non-trivial class of answer set pro...
متن کاملComplexity of First Order ID-Logic
First Order ID-Logic interprets general first order, nonmonotone, inductive definability by generalizing the wellfounded semantics for logic programs. We show that, for general (thus perhaps infinite) structures, inference in First Order ID-Logic is completeΠ2 over the natural numbers. We also prove a Skolem Theorem for the logic: every consistent formula of First Order ID-Logic has a countable...
متن کاملA Game-theoretic Characterization on the First-order Indefinability of Answer Set Programs
Under the general theory of stable models [17, 24], a first-order answer set program is semantically equivalent to a second-order sentence. Then a first-order answer set program is called first-order definable on finite structures if the set of finite answer sets of the program can be captured by a first-order sentence. First-order definability is a desirable property which provides alternative...
متن کاملArithmetical definability over finite structures
Arithmetical definability has been extensively studied over the natural numbers. In this paper, we take up the study of arithmetical definability over finite structures, motivated by the correspondence between uniform and . We prove finite analogs of three classic results in arithmetical definability, namely that and TIMES can first-order define PLUS, that and DIVIDES can first-order define TIM...
متن کاملModal Definability over a Class of Structures with Two Equivalence Relations
More than 40 years the correspondence between modal logic and first-order logic, when they are interpreted in relational structures, is on the main stream of the investigations of many modal logicians. The most interesting in this direction is a series of results on modal and first-order definability proved by Chagrova in the 1990s. In particular, from them it follows the undecidability of both...
متن کاملOn the Progression Semantics and Boundedness of Answer Set Programs
In this paper, we propose a progression semantics for firstorder answer set programs. Based on this new semantics, we are able to define the notion of boundedness for answer set programming. We prove that boundedness coincides with the notions of recursion-free and loop-free under program equivalence, and is also equivalent to first-order definability of answer set programs on arbitrary structu...
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:
- Theor. Comput. Sci.
دوره 25 شماره
صفحات -
تاریخ انتشار 1983