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.

....having the status of a non profit organization (e.g. tax exemption, etc. Perlis 1988) Thus we conclude that a possible commonsense set theory should also allow circular sets to be expressed. This is an important issue in representation of meta knowledge and is addressed in (Feferman 1984) and (Perlis 1985). In these references, a method which reifies (creates a syntactic term from a predicate expression) a well formed formula into a name for the well formed formula asserting that the name has strong relationship with the formula, is presented. In this way, any set of well formed formulas are ....

....formula ff(x) has a reification (name) ff(x) with variables free as in ff and distinguished variable x y 2 [ff(x) ff (y) where y does not appear in ff 16 . There is also a definitional equivalence (denoted by ) axiom: w z 8x(x 2 w x 2 z) GK is consistent with respect to ZF (Perlis 1985). Perlis then proposed the following axioms to augment GK: Ext1) x y ext x = ext y (Ext2) x ext x (Ext3) x 2 HC 9y(x = ext y) A ext ) y 1 ; y n 2 HC 8x(OEx x 2 HC) ext[OE] 2 HC 8x(x 2 [OE] OE(x) These axioms provide extensional constructions, i.e. collections ....

Perlis, D. (1985). Languages with Self-Reference I: Foundations. Artificial Intelligence 25(3):301--322.

....Godel provability. Another property of a self representable language is that self referential sentences can be constructed [9] This is not harmful in itself, but a theory with such a language can express paradoxes. The concept of self reference has been studied quite extensively, e.g. by Perlis [70, 71]. There is an overview of self reference and incompleteness in logic by Smorynski [80] 2.3 Amalgamation: Theories that Represent Themselves Given a self representable language LA , we may go one step further and develop a theory TA that represents itself, i.e. having the property that Demo TA ....

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

....its domain of discourse, in particular, a logic for METATEM in which METATEM program rules can be represented. There are several standard methods for developing metalanguages. One of the most widespread is the use of quoting. This technique, proposed by Frege and further developed by many others (Perlis, 1985), gives a way of producing a term in the logic that represents or names a formula in the logic. Thus, if we have the formula p(x) q(x) a new term representing the formula is given by p(x) q(x) As predicates are applied to terms of the language, they can obviously be applied to these naming ....

.... v as the operator representing at the last moment in time . called FML , based on quoting has been developed (Fisher, 1990) The questions of the reduction of naming terms to their constituent parts, the quoting of variables, and the scope of quantification are discussed elsewhere (Perlis, 1985; Fisher, 1990) Furthermore, the FML approach corresponds to the ground representation described in (Hill and Lloyd, 1988) In this report we will present an alternative approach which unifies object level and meta level into a single language without using explicit quoting. In our logic, ....

Perlis, D. (1985). Languages with Self Reference I: Foundations.

....added on to the object language definition. 4 The Representation of Terms To be able to explicitly manipulate the elements of the object language, we need to be able to use the names of object level entities in sentences of the meta language. From the work of Frege, and more recently Perlis [16], a method for achieving this is to quote object level expressions to generate a name for the sequence of symbols representing the expression. Thus, the name of the object a is the symbol a . So, if we wish to say something about the symbol representing a, rather than about a itself, we would ....

....TERMS 269 4.2.1 Quoted Representation A quoted representation of object level terms uses the quoting mechanism described earlier. This produces a meta level constant from an object level term and would seem, at first sight, to only be capable of producing a ground representation. However, Perlis [16] shows how terms can be partially quoted, thus preserving certain variables within the term. For example, p( q(x) r (y) is a partially quoted term. Here q(x) is a new meta level term, s(a) where s is a new meta level function symbol and a is a new meta level constant. However, though r ....

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

....However, very few such experiences have been reported yet. 4 Formal notions for Reflection We discuss here of formal notions used to characterize reflection in programming languages of the three different paradigm, preceded by a historical discussion of reflection in logic freely inspired by [Per85, Per88] Wey80] Bow82] Fef62] and [Cos90] 4.1 Historical discussion Gottlieb Frege developed the first formal quantificational logic over a period of more than two decades culminating in 1903. The idea was to have a universal language for logic. For Frege, an object c and the properties P ....

....Frege had certain comprehension axioms that specifically created object notations P for P , and stated that sentences using properties as predicates could be equivalently rephrased using properties as objects. These axioms in effect state a relationship between a name and what it names [Per85] Has(c; P ) P (c) or equivalently, but closer to Frege s notation: c 2 fxjP (x)g P (c) In the same year Bertrand Russell showed that Frege s system was inconsistent. Russell then proposed that objects be arranged in a hierarchy with different notations and rules, thus avoiding the ....

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

....If you give it fully up, the liar sentence does not produce any problem any more. However, this solution is far too radical, since in such a case meta level and object level co existed without any relation between them. Perlis defined for that reason a weakened form of the definition of truth [14], True( A ) A) where the operator replaces each connective occurrence of the form :True( in A by True( Using Kripke s fixpoint semantics he can build a system in which the liar sentence, L :j :True( L ) is not paradoxical. However, since L is the liar sentence, ....

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

.... the least of which is that they tend to fall prey to inconsistency [95, 132] However, there have been some fairly successful meta language formalisms, including those by Konolige [79] Haas [61] Morgenstern [97] and Davies [32] Some results on retrieving consistency appeared in the late 1980s [101, 102, 36, 133]. 2.3 Towards a Theory of Agency All of the formalisms considered so far have focussed on just one aspect of intelligent agency: either knowledge or belief. However, it is to be expected that any realistic agent theory will be represented in a much richer logical framework. First, neither agents ....

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

....a reflective theory, as opposed to a stratification of theories as in [27, 12] despite the troubles created by paradoxes. This allows expressing facts which simply cannot be stated without the use of self referential viewpoints. Here are some examples. John believes that he has a false belief [21] in(9x in(x; vp(John) F alse(x) vp(John) Agent a believes that whatever he and agent b believe is true, while b does not believe so in(8x in(x; vp(a) in(x; vp(b) True(x) vp(a) in( 8x in(x; vp(a) in(x; vp(b) True(x) vp(b) Agent a and agent b have common knowledge (or ....

....is based on Kleene s three valued logic. In his model the law of excluded middle holds, while the principle of bivalence does not: in( 0 A 0 ; fg) does not hold whenever A is a classical tautology, like B :B. A counterexample is R :R, where R is a paradoxical sentence. The solution by Perlis [21] also does not preserve the principle of bivalence. We adopt therefore a different solution based on the idea of reaching a stable truth value for a formula through an iterative process of revision as in Gupta Herzberger semantic theory [14, 15] We however retain the notion of truth and validity ....

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

....there should be a genuine structural difference between them. For instance, the graphs in Figure 4 all depict the non well founded set Omega because their nodes can be decorated with Omega Gamma AFA has interesting applications. In [8] a modeling scheme for propositions (of natural language [15, 16]) is offered. In this scheme, the triple hP; p; ii denotes that 1 To see this [8] consider a graph G and a decoration D assigning a to a node x of G, i.e. D(x) a. Now consider the decoration D 0 exactly the same as D except that D 0 (x) b. D 0 must also be a decoration for G. But by ....

D. Perlis. Languages with Self-Reference I: Foundations. Artificial Intelligence, 25(3):301--322, 1985.

....choice of a reflective theory, as opposed to a stratification of theories as in [21, 12] despite the troubles created by paradoxes: there are facts that simply cannot be asserted without the use of self referential viewpoints. Here are some examples. John believes that he has a false belief [17] in(9x in(x; vp(John) F alse(x) vp(John) Agent a believes that whatever he and agent b believe is true, while b does not believe so in(8x in(x; vp(a) in(x; vp(b) True(x) vp(a) in( 8x in(x; vp(a) in(x; vp(b) True(x) vp(b) Agent a and agent b have common knowledge (or belief) ....

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

....naive attempts to treat meta language predicates as syntactic modalities run into inconsistency. These difficulties arise, for the large part, from the issue of self reference 14 . 14 A good discussion of these issues may be found in [131] the issue of self reference is examined in detail in [129] and [130] Suppose one wished to use a meta language approach to represent and reason about knowledge and belief. Following standard practice, knowledge may be defined as true belief. One might begin by setting objectlanguage = meta language, so that the object and meta language are the ....

....and False predicates, such that for some formulae f, neither True( d f e ) nor False( d f e ) hold; in effect, one axiomatizes a system in which the law of the excluded middle does not hold. This solution is unintuitive, however, and seems rather ad hoc. Another solution, due to Perlis [129], is to replace (2.11) with an axiom of the form: True( d f e ) f (2.13) where f is the formula obtained from f by replacing every occurrence of True( d y e ) in f by True( d y e ) This simple expedient prevents inconsistency (see [129, pp312 315] for proof) This ....

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

....metalanguage should be separated in an hierarchical fashion, so that selfreference can not occur. Moreover, Montague [25] and Thomason [35] showed that object language and metalanguage can not be combined consistently in the more restricted manner of modal logic. However, more recent studies (e.g. [26, 27, 7, 31]) indicate ways in which object language and metalanguage can be combined, provided that appropriate restrictions are imposed. At least two other objections have been raised against systems that combine object language and metalanguage. One is that the naming conventions necessary to distinguish ....

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

....thing, it is natural to represent the knowledge and beliefs of a computer program by writing sentences representing facts that are known or believed. For another, syntactical treatments can be formalized in the classical predicate calculus, which is the lingua franca of knowledge representation [9,13,14]; since there is good theorem proving technology for this language (e.g. 1 3] such treatments lend themselves directly to implementations. Attractive as they may be, though, syntactical treatments face a serious theoretical difficulty. As we shall see, Richard Montague [12] shows that if the ....

D. Perlis. Language with self references I: Foundation. Artificial Intelligence, 25:301--322, 1985.

....B A, then we could write clause( B A ) f0g, stating that the respective clause is true at time 0, which corresponds to the initial clause B A of [1] We will not discuss this issue any further in this paper. More information about encodings and logics for meta reasoning can be found in [14, 37, 38, 27, 45]. 6.2 Multivalued Temporal Reasoning One advantage of the GAP formalism as opposed to Baudinet s and Abadi and Manna s is that it also allows one to deal with epistemically inconsistent worlds , i.e. interpretations in which at certain times t the information about certain ground atoms is ....

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

....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.

....will be used. 6.3.1 Reification of properties We seek a satisfactory means to express something along the lines of T rend(R; B) R(x) B(x) where R and B are terms in the antecedent and yet R(x) and B(x) are formulas. This can be done in a number of ways, including a quotation device as in [27]: T rend( R ; B ) R(x) B(x) Here we instead employ lowercase letters r and b to designate reified properties corresponding to the formulas R(x) and B(x) T rend(r; b) R(x) B(x) We now illustrate this device as a simple modification to traditional formalisms; then we will discuss a ....

....suppose we are given the trend axiom: T rend(bird; f ly) Then from 6.9 it follows that 8x(x 2 fx j Bird(x)g , x 2 fx j F ly(x)g) 34 Introducing 2 into the language, together with schema (6.8) brings with it the possibility of paradoxes. There are many proposals for dealing with this, e.g. [27, 11, 2]. Here we opt for a very conservative solution to the problem: we suppose an original language L that does not contain the predicate symbols 2 or T rend. We then extend this with set constants fx j OE(x)g for each formula OE(x) in L, as well as with the two symbols 2 and T rend. We employ the ....

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

....learned, old terms change meanings, etc. The reasoner must be able to reason about these changes, to incorporate them into her usage intelligently; and this involves noting tension (contradictions ) between usages. Noting that John is tall contradicts the personal 5 As I myself have done; see [20]. Also see the introduction to [8] observation that John is short, she starts to wonder whether these might be two different persons named John (see [15] Interpreting orders Your boss tells you (a personnel manager) never to hire high school dropouts. One day a job candidate comes to your ....

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. 1 This research was partially supported by NSF grant IRI 9109755. 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 ....

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

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

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

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