J. McCarthy. Mathematical logic in artificial intelligence. Daedalus, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... g Y # pl u# vJw k vy k Y g (5) We can encode this more compactly by simply defining u y Y # l u# vJw , and replacing u y in (4) This approach has many advantages. First it is elaboration tolerant [17]. An individual s customized may simply be added to an existing situation calculus axiomatization. If an individual s constraints change, the affectedl u# vJw 3602 fluents in may be elaborated by a simple local rewrite. Further,l u# vJw 36 8 is easily implemented as an ....

J. McCarthy. Mathematical logic in artificial intelligence. Daedalus, pages 297--311, Winter, 1988.

....(4) is replaced by (5) P oss(a; s) P oss(a; s) Desirable(a; s) We can encode this more compactly by simply defining Legal(a; s) P oss(a; s) Desirable(a; s) and replacing P oss with Legal in (4) This approach has many advantages. First it is elaboration tolerant [17]. An individual s customized DD may simply be added to an existing situation calculus axiomatization. If an individual s constraints change, the affected Desirable fluents in DD may be elaborated by a simple local rewrite. Further, Desirable is easily implemented as an augmentation of most ....

J. McCarthy. Mathematical logic in artificial intelligence. Daedalus, pages 297--311, Winter, 1988.

....theory is often easier to compute. These advantages are due to the fact that, in a nested abnormality theory, the circumscription operator can be applied to a small subset of axioms. One attractive feature of nonmonotonic formalizations of knowledge is that they are often elaboration tolerant [ 15 ] to a larger degree than formalizations based on classical logic. It is often possible to enhance a nonmonotonic theory by simply adding new formulas to the axiom set, whereas the corresponding enhancement of a classical axiomatization would require changing the existing axioms. This happens, for ....

John McCarthy. Mathematical logic in Artificial Intelligence. Daedalus, pages 297--311, 1988. Reproduced in [ 16 ] .

....proposed allow a program to reflect on its own behavior and improve its problem solving strategy by simple additions or substitutions of sentences, as it has been shown in the advice taking scenario of section 4. This is, perhaps, the best feature of the language, its elaboration tolerance [17]. The flexibility of adapting to conceptual changes in the specification of a problem or its solution is a very important feature that procedural or dynamic logic languages do not have. 2The maximum cost of strategy 5 is smaller than the maximum cost of strategy d (i.e. 25(Strategy4) Maxcost ....

McCarthy, J. (1988) Mathematical logic in artificial intelligence. Daedalus, 117(1): 297-311.

.... work is that it allows easy incorporation of additional features, such as constraints, which already have been formalized in the absence of narratives, with NATs [15,22] Also, although the nesting of blocks in NATs may at first glance suggest loss of declarativeness and elaboration tolerance [31], we believe it makes it easier to represent knowledge, particularly in the action domain (see [15,22,24] for more on this) This is because we can develop blocks that represent meaningful structural units and use the blocks in other units without worrying about undesired interactions. Besides, a ....

J. McCarthy, Mathematical logic in Artificial Intelligence, Ddalus (1988) 297--311.

....because any knowledge based system must work based on reasoning and logic is the systematic study of fundamental principles that underlie various valid reasoning forms. However, the hot controversy about the role of logic in AI has been repeated so far and probably will continue on as usual [15 18]. An important fact is that the logic as the center of the controversy is classical mathematical logic (CML for short) and or its various extensions, though there are some more logical logic systems. Until recently, what is debated by the researchers working on the fundamentals of AI is, among ....

J. McCarthy, "Mathematical Logic in Artificial Intelligence," in S. R. Graubard (ed.), "The Artificial Intelligence Debate," pp.297-311, MIT Press, 1988.

....0 ; s 0 ) P oss(a[s] s) Desirable(a[s] s) 0 = nil s 0 = do(a[s] s) 5) We can encode this more compactly by simply defining Legal(a; s) P oss(a; s) Desirable(a; s) and replacing P oss with Legal in (4) This approach has many advantages. First it is elaboration tolerant [14] . An individual s customized DD may simply be added to an existing situation calculus axiomatization. If an individual s constraints change, the affected Desirable fluents in DD may be elaborated by a simple local rewrite. Further, Desirable is easily implemented as an augmentation of most ....

J. McCarthy. Mathematical logic in artificial intelligence. Daedalus, pages 297--311, Winter, 1988.

....A second problem is that common sense reasoning in its representational mode has been dominated by a carelessness regarding psychological validity. The pioneer of the field, McCarthy, definitely views artificial intelligence as a branch of computer science rather than as a branch of psychology (McCarthy, 1988). Psychological validity was never a goal of the logician s approach. The conflict between logical and psychological approaches to artificial intelligence is not a new one (Israel, 1985; Kolata, 1982) but there is little to add to this controversy beyond what has already been written (e.g. ....

McCarthy, J. (1988). Mathematical Logic in Artificial Intelligence. Daedalus, 117(1), 297-311.

....Another problem is that common sense reasoning in its representational mode has been dominated by a carelessness regarding psychological validity. The pioneer of the field, McCarthy, definitely views artificial intelligence as a branch of computer science rather than as a branch of psychology (McCarthy, 1988). Psychological validity was never a goal of the logician s approach. The conflict between logical and psychological approaches to artificial intelligence is not a new one (Israel, 1985; Kolata, 1982) but there is little to add to this controversy beyond what has already been written (e.g. ....

McCarthy, J. (1988). Mathematical Logic in Artificial Intelligence. Daedalus, 117(1), 297-311.

....of the Initiates, Terminates and Happens predicates from individual clauses like those in (Y1.1) to (Y1.3) and (Y2.2) to (Y2.4) As well as being notationally more convenient, this allows a theory to be constructed in a more modular fashion. It also makes our theories more elaboration tolerant [McCarthy, 1988], in the sense that new actions, new fluents, new effects of actions, and new event occurrences can easily be accommodated by an extant theory. The usual way to address this issue is to adopt some form of non monotonic formalism, such as default logic [Reiter, 1980] or circumscription [McCarthy, ....

J.McCarthy, Mathematical Logic in Artificial Intelligence, Daedalus, Winter 1988, pp. 297--311.

.... as constraints, which have been formalized in the absence of narratives, using nested abnormal5 ity theories by Giunchiglia, Kartha, and Lifschitz [KarLif94,GiuKarLif95] Also, although the nesting of blocks in NATs may at first glance suggest loss of declarativeness and elaboration tolerance [McC88] we believe it makes it easier to represent knowledge, particularly in the action domain (See [Lif95,KarLif94,GiuKarLif95] for more on this) This is because we can develop blocks that represent meaningful structural units and use the blocks in other units without worrying about undesired ....

McCarthy J 1988. Mathematical logic in Artificial Intelligence. Daedalus, pages 297-311.

.... it allows easy incorporation of additional features, such as constraints, which already have been formalized in the absence of narratives, with NATs [KarLif94,GiuKarLif95] Also, although the nesting of blocks in NATs may at first glance suggest loss of declarativeness and elaboration tolerance [McC88] we believe it makes it easier to represent knowledge, particularly in the action domain (see [Lif95,KarLif94,GiuKarLif95] for more on this) This is because we can develop blocks that represent meaningful structural units and use the blocks in other units without worrying about undesired ....

McCarthy J 1988. Mathematical logic in Artificial Intelligence. Daedalus, pp. 297-311.

....of strategies proposed, allow a program to reflect on its own behavior, and improve its problem solving strategy by simple additions or substitutions of sentences, much in the same way it happens in natural language. This is perhaps the best feature of the language, its elaboration tolerance (McCarthy 1988). The flexibility of adapting smoothly to conceptual changes in the specification of a problem or its solution is a very important feature that procedural or dynamic logic languages do not have. There are a number of interesting issues about the declarative formalization of strategies we have not ....

McCarthy, J. 1988. Mathematical logic in artificial intelligence. Daedalus 117:297--311.

....because any knowledge based system must work based on reasoning and logic is the systematic study of fundamental principles that underlie various valid reasoning forms. However, the hot controversy about the role of logic in AI has been repeated so far and probably will continue on as usual [15 18]. An important fact is that the logic as the center of the controversy is classical mathematical logic (CML for short) and or its various extensions, though there are some more logical logic systems. Until recently, what is debated by the researchers working on the fundamentals of AI is, among ....

J. McCarthy, "Mathematical Logic in Artificial Intelligence," in S. R. Graubard (ed.), "The Artificial Intelligence Debate," pp.297-311, MIT Press, 1988.

....settheoretic concepts may be examined and modified based on existing set theories. No matter what proposal is followed, we believe that further research in this field should be promising and may even lead to a mathematical metaepistemology analogous to metamathematics, as pointed out by McCarthy (1988). ACKNOWLEDGMENTS We would like to thank the anonymous referees of Artificial Intelligence Review whose comments were crucial in revising the content of this paper. We are also indebted to Patrick Suppes (CSLI) Wlodek Zadrozny (IBM T. J. Watson) Rohit Parikh (CUNY) and Ramesh Patil (USC ISI) ....

McCarthy, J. (1988). Mathematical Logic in Artificial Intelligence. Daedalus 117:297--311.

....would like a solution constructed out of fluents which are more clearly related to the data obtainable from a robot s sensory apparatus and actions which are more plausibly executable by a robot. It doesn t allow for variations on problem. In other words, it lacks elaboration tolerance, to use McCarthy s term [1988]. Ernie Davis lists a number of elaborations of the egg cracking problem. What happens if: The cook brings the egg to impact very quickly Very slowly The cook lays the egg in the bowl and exerts steady pressure with his hand The cook, Formula Meaning Initiates(e,f,t) Fluent f holds after ....

J.McCarthy, Mathematical Logic in Artificial Intelligence, Daedalus, Winter 1988, pp. 297-- 311.

....In this paper we present a translation of L to nested abnormality theories (NATs) Lifschitz 1995) a new approach to the use of circumscription for representing knowledge. Although the nesting of blocks in NATs may at the first glance suggest loss of declarativeness and elaboration tolerance (McCarthy 1988), we believe it makes it easier to represent knowledge, particularly in the action domain (See (Lifschitz 1995; Kartha Lifschitz 1994; Giunchiglia, Kartha Lifschitz 1995) for more on this) This is because we can develop blocks that represent a meaningful structural unit and use the blocks in ....

McCarthy J 1988. Mathematical logic in Artificial Intelligence. Daedalus, pages 297-311.

....definitions and tools. We then demonstrate the use of these definitions and tools by applying them to examples of language expansion and monotonic versus nonmonotonic reasoning, and examine the limits of the approach. 1 Introduction The notion of Elaboration Tolerance was proposed by McCarthy (McCarthy 1988) for the problem of extending a logical theory, with the intuition that a logical system should have the ability to absorb additions the way Natural Language allows. Several intuitions coincide in this description: axiomatizing a theory in a flexible way; not needing to rebuild one s ontology when ....

McCarthy, J. 1988. Mathematical logic in artificial intelligence. Daedalus 117(1):297--311.

....representation of knowledge in AI has been stressed by many researchers. In their fundamental paper McCarthy and Hayes [MH69] wrote: A computer program capable of acting intelligently in the world must have a general representation of the world in terms of which its inputs are interpreted and in [McC87] McCarthy adds: Expressing information in declarative sentences is far more modular than expressing it in segments of computer program or in tables. Sentences can be true in much wider context than specific programs can be used. The supplier of a fact does not have to understand much how the ....

....Reasoning In the middle of 1970 s, Minsky [Min75] and McCarthy [McC77] pointed out that pure classical logic is inadequate to represent the common sense nature of human reasoning. This difficulty is caused primarily by the non monotonic character of human reasoning. Using McCarthy s words [McC87]: While much human reasoning corresponds to that of traditional logic, some important human common sense reasoning seems not to be monotonic. We reach conclusions from certain premisses that we would not reach if certain other sentences were included in our premisses. For example, learning that I ....

J. McCarthy. Mathematical Logic in Artificial Intelligence. Research report, Stanford University, 1987.

....and accurate artificial language can be created. Model theoretic semantics was founded by Tarski. Although his primary target was formal language, he also hoped that the ideas could be applied to reform everyday language (Tarski, 1944) This approach characterizes the logic based branch of AI (McCarthy, 1988; Nilsson, 1991) For a language L, defined by a finite formal grammar, a model M consists of the relevant part of some domain, which can be described in another language ML, and an interpretation I, which maps the items in L onto the objects in the domain, labeled by words in ML. ML is referred ....

....Implications 136 7.5 NARS as an inheritance network By working on a reasoning system with its formal language and inference rules, one does not necessarily commit oneself to the assumptions of traditional logic based AI paradigms. Designed as a reasoning system, but not a logicist one (McCarthy, 1988; Nilsson, 1991) NARS actually shares more philosophical assumptions with the subsymbolic or connectionist movement (Hofstadter, 1985; Holland, 1986; Holland et al. 1986; Rumelhart and McClelland, 1986; Smolensky, 1988) despite the fact that I chose to formalize and implement these assumptions ....

McCarthy, J. (1988). Mathematical logic in artificial intelligence. Daedalus, 117(1):297--311.

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J. McCarthy. Mathematical logic in artificial intelligence. Daedalus, 1988.

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McCarthy, J. 1988. Mathematical logic in artificial intelligence. Daedalus.

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J. McCarthy. Mathematical logic in artificial intelligence, pages 297--311. Daedalus, 1988.

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John McCarthy. Mathematical logic in artificial intelligence. Daedalus, pages 297--311, 1988.

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John McCarthy. Mathematical logic in Artificial Intelligence. Daedalus, pages 297--311, 1988.

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