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Chief Examiner Andrew Butterfield Teaching Staff Andrew Butterfield Delivery
"... desirable. Maths students with a good feel for 1 st order Predicate Calculus should be able to cope From 2012/13 onwards: logic, set theory ..."
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desirable. Maths students with a good feel for 1 st order Predicate Calculus should be able to cope From 2012/13 onwards: logic, set theory
CS589 Principles of DB Systems Fall 2008 Lecture 4e: Logic (Modeltheoretic view of a DB)
"... Review propositional logic (including truth assignment) Review 1st order predicate calculus (including theory vs. interpretation) Introduce the modeltheoretic description of a relational database and consider how tuple calculus, domain calculus, and datalog use that view. Mention the prooftheoreti ..."
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Review propositional logic (including truth assignment) Review 1st order predicate calculus (including theory vs. interpretation) Introduce the modeltheoretic description of a relational database and consider how tuple calculus, domain calculus, and datalog use that view. Mention the proof
Spatial Reasoning with Propositional Logics
 Principles of Knowledge Representation and Reasoning: Proceedings of the 4th International Conference (KR94
, 1994
"... I present a method for reasoning about spatial relationships on the basis of entailments in propositional logic. Formalisms for representing topological and other spatial information (e.g. [2] [10] [11]) have generally employed the 1storder predicate calculus. Whilst this language is much more expr ..."
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Cited by 111 (16 self)
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I present a method for reasoning about spatial relationships on the basis of entailments in propositional logic. Formalisms for representing topological and other spatial information (e.g. [2] [10] [11]) have generally employed the 1storder predicate calculus. Whilst this language is much more
Knowledge Interchange Format Version 3.0 Reference Manual
, 1992
"... : Knowledge Interchange Format (KIF) is a computeroriented language for the interchange of knowledge among disparate programs. It has declarative semantics (i.e. the meaning of expressions in the representation can be understood without appeal to an interpreter for manipulating those expressions); ..."
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Cited by 484 (14 self)
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); it is logically comprehensive (i.e. it provides for the expression of arbitrary sentences in the firstorder predicate calculus); it provides for the representation of knowledge about the representation of knowledge; it provides for the representation of nonmonotonic reasoning rules; and it provides
Symbolic Model Checking for Realtime Systems
 INFORMATION AND COMPUTATION
, 1992
"... We describe finitestate programs over realnumbered time in a guardedcommand language with realvalued clocks or, equivalently, as finite automata with realvalued clocks. Model checking answers the question which states of a realtime program satisfy a branchingtime specification (given in an ..."
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Cited by 578 (50 self)
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in an extension of CTL with clock variables). We develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates, without constructing the state space. For this purpose, we introduce a calculus on computation trees over realnumbered time. Unfortunately
Logical foundations of objectoriented and framebased languages
 JOURNAL OF THE ACM
, 1995
"... We propose a novel formalism, called Frame Logic (abbr., Flogic), that accounts in a clean and declarative fashion for most of the structural aspects of objectoriented and framebased languages. These features include object identity, complex objects, inheritance, polymorphic types, query methods, ..."
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Cited by 876 (65 self)
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, encapsulation, and others. In a sense, Flogic stands in the same relationship to the objectoriented paradigm as classical predicate calculus stands to relational programming. Flogic has a modeltheoretic semantics and a sound and complete resolutionbased proof theory. A small number of fundamental concepts
The complexity of theoremproving procedures
 IN STOC
, 1971
"... It is shown that any recognition problem solved by a polynomial timebounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved deterministi ..."
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Cited by 1050 (5 self)
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of two given graphs is isomorphic to a subgraph of the second. Other examples are discussed. A method of measuring the complexity of proof procedures for the predicate calculus is introduced and discussed. Throughout this paper, a set of strings 1 means a set of strings on some fixed, large, finite
A translation approach to portable ontology specifications
 KNOWLEDGE ACQUISITION
, 1993
"... To support the sharing and reuse of formally represented knowledge among AI systems, it is useful to define the common vocabulary in which shared knowledge is represented. A specification of a representational vocabulary for a shared domain of discourse — definitions of classes, relations, functions ..."
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Cited by 3365 (9 self)
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, functions, and other objects — is called an ontology. This paper describes a mechanism for defining ontologies that are portable over representation systems. Definitions written in a standard format for predicate calculus are translated by a system called Ontolingua into specialized representations
Construction of abstract state graphs with PVS
, 1997
"... We describe in this paper a method based on abstract interpretation which, from a theoretical point of view, is similar to the splitting methods proposed in [DGG93, Dam96] but the weaker abstract transition relation we use, allows us to construct automatically abstract state graphs paying a reasonab ..."
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Cited by 742 (10 self)
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reasonable price. We consider a particular set of abstract states: the set of the monomials on a set of state predicates ' 1 ; :::; ' ` . The successor of an abstract state m for a transition ø of the program is the least monomial satisfied by all successors via ø of concrete states satisfying m
The fundamental properties of natural numbers
 Journal of Formalized Mathematics
, 1989
"... Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1.h ..."
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Cited by 688 (73 self)
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Summary. Some fundamental properties of addition, multiplication, order relations, exact division, the remainder, divisibility, the least common multiple, the greatest common divisor are presented. A proof of Euclid algorithm is also given. MML Identifier:NAT_1. WWW:http://mizar.org/JFM/Vol1/nat_1
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