D. Perlis. Languages with self-reference i: Foundations. Arti...cial Intelligence, 25:301-- 322, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....sentence, the liar sentence L: True(L) which leads to a contradiction. Attempts have been made to avoid the negative results of GSdel and Tarski. Kripke [Kripke, 1975] suggested a construction in which True( V True( only holds for some formulae . A closely related suggestion is made by Perlis [Perlis, 1985]. The recent book by Turner [Turner, 1990] provides an excellent and thorough exploration 177 of these and other attempts at encoding truth and provability, but makes it clear that many of the issues arising from self reference are still unresolved. Inter theory inference It is in the work of ....

D. Perlis. Languages with self-reference I: Foundations. Artificial Intelligence, 25:301 322, 1985.

....of this kind of distributed representation and deductions. For instance Wilks [48] in his work on belief ascription, speech acts and so on, advocates the use of distinct sets of beliefs while Fauconnier [7] has a mental space theory which uses environment like entities. Notice that Perlis [36] argues explicitly against the use of multiple hierarchical theories, the main argument being one of quanti cation. In this paper he argues, rightly, that we do not want to quantify over all the di erent levels. His point does not apply here as we are dealing with the propositional case; on the ....

D. Perlis. Languages with Self-Reference I: Foundations. Artif. Intell., 25:301-322, 1985.

....is discussed. 1 Introduction Reflective (or introspective, or self referencing) systems have long been considered in many branches of logic and computer science, and more recently in their intersection area named computational logic or logic programming. Their importance and usefulness in logic [55, 56] and in theorem proving [38] in computer science [30, 51, 60] and in logic programming [7, 40, 47] has been generally recognised (see also [1, 11, 13, 32, 57] for snapshots of research) The common intuitive notion of reflection in such different areas is that of an access relationship between ....

....replace variables x of f ) p is called a reflective predicate, and is to be defined as an approximation of a truth or proof predicate. The approximation has to be such that the intended useful features of self reference are obtained, without running into the well known paradoxes (see e.g. Perlis [55] for a discussion) We will show that two reflection principles are able to model the behaviour of a reflective predicate. The second deductive system is able to represent agents and cooperation between multiple agents (Section 6.2) In particular, we consider rational agents that are ....

D. Perlis. Languages with self-reference I: foundations (or: we can have everything in first-order logic!). Artificial Intelligence, 25:301--322, 1985.

....in a context. MT is distinct from the other contexts, and in particular from PSC. The reasons for this are the same explained for PSC plus four further facts. First, a meta theory distinguished from PSC can describe reasoning within PSC and avoid selfreferential problems (see for instance [27, 31]) Second, a distinguished meta theory can explicitly represent the interactions (through bridge rules) among PSC and s contexts. Third, PSC language is not rich enough to represent deductions. In PSC we can represent and reason about provability in s contexts, but not about derivability of a fact ....

.... that the axioms represent rules that have premises in a context (e.g. T ( P SC ) and conclusion in a different context 25 (e.g. T ( c ) with c 6= P SC ) Moreover, in both AX # and AX , the condition c 6= P SC prevents these axioms to cause inconsistencies based on self reference [27, 31]. Besides reflection principles between s contexts and PSC, it is also possible to have a set of bridge rules among s contexts (see figure 1) For instance, consider the set of bridge rules ffi ij defined in (4) They are represented in MT as: AX ffi : 8s8c i 8c j (T (s; c i ) c i c j oe T ....

D. Perlis. Languages with Self-Reference I: Foundations. Artificial Intelligence, 25:301--322, 1985.

....is legal to perform action a given an argumentation record r. We call L 0 the logic of procedure, or the meta logic. Often L and L 0 will not differ wrt the underlying inference mechanisms, however they differ in the language (unless L is fully self referential and has a quoting mechanism, see [23]) Intuitively, an argumentation about a proposition q proceeds as follows: let r be the current argumentation record; a group member g can perform a certain speech act a if the speech act is possible in r. If a is not legal according to the argumentation protocol, then another member of the ....

....that is, the rules of order can be made the current topic of discussion Note that rules of order speak about propositions expressed in the language of disputation. One possibility would be to amalgamate the languages of L and L 0 , that is to use a self referential language with quoting (see [23] for a study of such languages) and to express the rules of order in that language. Although this might lead to a very uniform and monolithic treatment of argumentation, we would have to use heavy logical machinery even for the simplest kinds of argumentation. We are not 20 interested here in ....

D. Perlis. Languages with self-reference i: Foundations. Artificial Intelligence 25, pages 301--322, 1985.

....spaces for the formalization of the agents nested beliefs. Konolige formalizes agents nested beliefs using introspective machines [Kon84, Kon85] which are very similar to theories. Kim and Kowalski in [KK90] propose a very similar approach in the area of logic programming. Notice that Perlis [Per85] argues explicitly against the use of multiple hierarchical theories, the main argument being one of quantification. He argues, rightly, that we do not want to quantify over all the different levels. His point does not apply here as we are dealing with the propositional case; on the other hand, we ....

D. Perlis. Languages with Self-Reference I: Foundations. Artif. Intell., 25:301--322, 1985.

....trivial observation that there are people able to speak more than one language, e.g. English and Italian) All the work cited above, namely [JL83, Fau85, WB79, Kon84, McC89] but [GW88] is based on the idea of having a unique language. The same hypothesis is discussed in some length by Perlis in [Per85] as very plausible for the representation of propositional attitudes. We do not think that the argument given by Perlis is convincing at all. A paper which dicusses in detail the issue of having multiple languages and compares it with the various single language approaches is forthcoming; the ....

D. Perlis. Languages with Self-Reference I: Foundations. Artificial Intelligence, 25:301--322, 1985.

....] recognition and the repair of deadlocks in problem solving [ 15 ] 18 ] 9 ] explanation of knowledge bases [ 4 ] and acting under time restrictions [ 16 ] In logic, too, meta levels have been studied (see [ 19 ] for an excellent overview) in particular wrt. self referential phrases [ 14 ] . 2 The object system We studied an assignment problem solver [ 1 ] Its domain specific instantiation is called OFFICE PLAN because it is used specifically for the assignment of employees to o#ces. The system translates transfers generic requirement like don t place smokers and non smokers in ....

D. Perlis. Languages with self-reference I: Foundations. Artificial Intelligence, 25:301--322, 1985.

....We also abandoned the idea of infinite meta level towers generated by meta circular interpreters, as we do not see how to acquire knowledge for a third or any higher levels. Work on reflection in logic has shown that a clear separation between object and meta level ensures avoidance of paradoxes [24]. ML 2 [33] is a language to formalize KADS knowledge level models. It has been used to explicitly represent the model to be reasoned about. Although ML 2 is in logic and hence more declarative than MODEL K, the language lacks operational support for the causal connection and the integration ....

D. Perlis. Languages with self-reference I: Foundations. Artificial Intelligence, 25:301--322, 1985.

....of object oriented software components. 2 Reflection Reflection in computer science in general has been first suggested in the context of artificial intelligence where the construction of self aware systems can be assimilated to the end goal of the field (see the two papers of Perlis [Per85, Per88]) In the context of programming languages, the seminal work of Brian Smith [Smi82, Smi84] has been the departure point of a large research effort both in the functional and the object oriented programming community. It is not our goal to introduce reflection here; the reader is refered to the ....

D. Perlis. Languages with self-reference I: Foundations (or: We can have everything in first-order logic!). Artificial Intelligence, 25:301--322, 1985.

....First, our aim is to provide semantics for HFP and Prolog practice in order to do our computational classical logic , rather than construct self reflective languages which have their own truth predicates. So we do not mind to have the Hold predicate not to apply to itself. See the Perlis papers [Perlis, 1985, Perlis, 1988] for a good coverage of the subject. Second, in the Horn clause fragment of HFP negation is not available and it is possible to have a truth predicate in the object level for the object language itself, without leading to contradiction. The worst we can get are loops, if we use ....

D. Perlis. Languages with self reference I: foundations. Artificial Intelligence, 25:301-- 22, 1985.

....2 ) j Delta 2 We ask, furthermore, that if such fixed points are expressible in the logic 6 then the Delta i are computable from T [C] itself. The problem is to determine the restrictions that has to be imposed so as to avoid the obvious paradoxes of a self referential language. Both in (Perlis, 1985; Perlis, 1988) and in (Montague, 1963) the difficulties of dealing with a first order self referential language are thoroughly analyzed. In particular Montague points out the problems concerned with substitution; we discuss this point in the last section of this paper. It is possible to ....

....a suitable quotation of the sentence ff. However, the difficulties caused by unquoting quoted statements, through substitutions in first order logic languages have been investigated by Montague in (Montague, 1963) who thus argued in favor of modal logic. In contrast to Montague s thesis, Perlis in (Perlis, 1985; Perlis, 1988) argues that modal logics are on no firmer ground than first order logic when equally endowed with substitutive self reference. Perlis introduces a suitable notion of substitution of a name dpe for its expression p in formulae (providing a similar expressiveness of the godelian ....

Perlis, D. (1985). Languages with self-reference I: Foundations. Artificial Intelligence Journal, 25:301--322.

....the previous [Konolige 82] Self reference is not allowed and the construction of paradoxical statements is blocked. However this forbids also non paradoxical self referential statements like those mentioned in the previous section. This lack of expressiveness may be considered a major drawback [Perlis 85] since self referential statements about truth, beliefs or knowledge arise naturally in common sense reasoning. The complex machinery required by the layered approach also does not seem convenient for implementation within reasoning programs nor natural as a formalisation of common sense. When ....

D. Perlis (1985). Languages with self-reference I: foundations, Artificial Intelligence, 25:301-322.

....conservative extension where useful theorems can be proved while consistency is retained. 1 INTRODUCTION The advantages of a syntactic approach to the representation of truth, knowledge and belief have been largely discussed in the literature [ McCarthy 1979) Moore, 1977) Konolige, 1982) (Perlis, 1985), Perlis, 1988) Davies, 1990) Along this line of research several proposals are based on extending a logic calculus with a meta language, for expressing facts about terms and sentences, and with an axiomatization of provability. Provability in an agent s theory is seen as one of the primitive ....

....below in the hierarchy. Self reference is not allowed and the construction of paradoxical sentences is blocked. As a consequence also non paradoxical self referential or mutually referential sentences cannot be represented. This is seen as the major drawback of this approach (see for example (Perlis, 1985), Perlis, 1988) Davies, 1990) self referential statements about truth, belief or knowledge are in fact naturally found in common sense reasoning. Among the amalgamated solutions we can further distinguish among conservative extensions (like the one proposed by Bowen and Kowalski (Bowen and ....

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D. Perlis (1985) "Languages with Self-Reference I: Foundations", Artificial Intelligence, (25), 301--322.

....of this kind of distributed representation and deductions. For instance Wilks [48] in his work on belief ascription, speech acts and so on, advocates the use of distinct sets of beliefs while Fauconnier [7] has a mental space theory which uses environment like entities. Notice that Perlis [36] argues explicitly against the use of multiple hierarchical theories, the main argument being one of quantification. In this paper he argues, rightly, that we do not want to quantify over all the different levels. His point does not apply here as we are dealing with the propositional case; on ....

D. Perlis. Languages with Self-Reference I: Foundations. Artif. Intell., 25:301--322, 1985.

....not well defined. That is, R 6 R does not obey Normal Order (for set membership rather than truth) This does not mean that no such set as R exists; on the contrary, in Gilmore s set theory it is provable that R exists. Kripke provided a similar treatment for truth. Later Feferman [2] and Perlis [10, 11] also working independently, unified these two treatments. The following schemata capture much of this approach: T(a) a where a has no effect on a unless there is an embedded and negated T inside, and then: Finally we also require o o That is, the assertion of the truth of the negated ....

D. Perlis. Languages with self reference I: Foundations. Artificial Intelligence, 25:301-322, 1985.

....of a reasoning agent to exercise control of its own reasoning process, and in particular over its language, has been hinted at a number of times in the literature. Rieger seems to have been the first to enunciate this, in his notion of referenceability [ Rieger, 1974 ] followed by others [ Perlis, 1985 ] McCarthy and Lifschitz, 1987 ] etc. The underlying idea, as we conceive it here, is that the tie between linguistic entities (e.g. words) and their meanings (e.g. objects in the world) is a tie that the agent had better know about and be able to alter when occasion demands. This has a ....

D. Perlis. Languages with self reference I: Foundations. Artificial Intelligence, 25:301--322, 1985.

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D. Perlis. Languages with self-reference i: Foundations. Arti...cial Intelligence, 25:301-- 322, 1985.

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D. Perlis. Languages with Self-Reference I: Foundations. Artif. Intell., 25:301--322, 1985.

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Donald Perlis. Languages with self-reference I: Foundations (or: We can have everything in rst-order logic!). AI, 25:301-322, 1985.

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Perlis, D.: Languages with self-reference I: foundations, Artificial Intelligence, 25 (1985) 301--322.

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D. Perlis. Languages with self-reference I: Foundations. Artificial Intelligence, (25):301--322, 1985.

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D. Perlis. \Languages with self reference I: foundations". Art. Int., vol.25, pp.301-322, 1985.

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D. Perlis. Languages with self-reference i: Foundations. Artificial Intelligence, 1985.

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Perlis, D.: Languages with self-reference I: foundations (or: we can have everything in first-order logic!). Artificial Intelligence 25 (1985) 301--322

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