F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRST-Technical Report no. 9011-17.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....level. Each level is described by means of formalisms, and each formalism is suited to put in evidence particular aspects involved in the study and analysis of agencies. The privileged formalism in describing agencies is multilanguage system, a formal system devised by Giunchiglia et al. see [22]) that allows to represent an agent as a theory (that is, each agent has its own language to represent facts and its own set of rules of inference to derive new facts from older facts) and the links among agents as special rules of inference called bridge rules, that are rules whose premises and ....

....inferential aspect. In Subsection 4.1 we give the definitions and summarize the major results about MLS. In Subsection 4.2 we apply these ideas to the goal of describing an agency from an inferential point of view. 4. 1 MultiLanguage System Multilanguage systems were devised by Giunchiglia (see [22], 23] 24] for details and applications of MLS) A MLS is a way to link reasonings in different theories by a framework in which theories are independent but connected. Definition 4.1.1: let I be a set of indexes, L i iI a family of languages and W i iI a family of sets of well formed ....

F. Giunchiglia, "Multilanguage Systems", Proceedings AAAI-91 Spring Symposium on Logical Formalization of Commonsense Reasoning, Stanford University, March 26-28, 1991

.... design representations, including circuit diagrams, state machines, timing diagrams, linear temporal logic, and monadic second order logic [11] Such logics, which support multiple syntactic representations (without embedding them in one another) are called heterogeneous [5] or multi language [15]. They are ideal for problem domains, such as hardware design, in which people use multiple notations on individual problems. Since the notations that people use when reasoning about particular domains can evolve over time, reasoning tools for heterogeneous logics need to be extensible in order to ....

Giunchiglia, F. Multilanguage systems. In Proceedings of the AAAI-91 Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991.

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F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRST-Technical Report no. 9011-17.

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F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRST-Technical Report no. 9011-17.

....(described in An integrated approach to Arti cial Intelligence by L. Stringa, IRST technical report No 9012 11) 1 1 Introduction and motivations It has been argued that knowledge should be structured into sets of facts or theories (often called contexts ) some of the many examples are [11, 21, 10, 45, 7, 32, 29, 48, 5]. In [10, 13] the authors take a further step and introduce a new general kind of formal systems allowing multiple distinct languages and call them MultiLanguage systems (ML systems) In [11] it is argued, in fact, that providing each theory with its own language allows us to give a natural and ....

....to Arti cial Intelligence by L. Stringa, IRST technical report No 9012 11) 1 1 Introduction and motivations It has been argued that knowledge should be structured into sets of facts or theories (often called contexts ) some of the many examples are [11, 21, 10, 45, 7, 32, 29, 48, 5] In [10, 13] the authors take a further step and introduce a new general kind of formal systems allowing multiple distinct languages and call them MultiLanguage systems (ML systems) In [11] it is argued, in fact, that providing each theory with its own language allows us to give a natural and elegant proof ....

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F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. IRST-Technical Report no. 9011-17.

....the system states and (iii) the theorem prover can faster analize and answer to queries about a particular state. The temporal evolution of a U tube is taken as an example to show both the proposed framework and the GETFOL implementation. 1 Introduction Recent work in artificial intelligence [GW88, Giu91, McC90, McC91, Sho91] advocates for the use of multiple formal systems (called contexts) both in knowledge representation and in problem solving. Even if there is not a consensus about how contexts should be (formally) defined, there is the common intuition that many (reasoning) phenomena are better modeled as a set ....

....A particular metatheoretic Problem Solving Context (PSC) controls the evolution of the system and keeps track of the temporal evolution. PSC and s contexts are related via bridge rules (i.e. rules enabling the derivation of one fact in a context on the basis of facts derived in other contexts) [Giu91]. Three are the main advantages of the multi contextual approach we adopt. First of all, we keep a clear distinction between the theory describing the particular system at hand and the theory necessary for predicting the system evolution. A different system can be modeled simply by specifying its ....

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F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRST-Technical Report no. 9011-17.

....reasoning system must take into account its components and the interactions between them. In this paper we propose multi context systems (MC systems from now on) as a logical framework for the formal specification of complex reasoning. MC systems have been motivated and formally introduced in [6, 7]; they are also called multilanguage systems (ML systems) to emphasize the fact that they allow the definition of multiple languages, each language associated with a context. The general idea is to model local reasoning as deduction inside a context. A context is formally defined as an axiomatic ....

Giunchiglia, F., Multilanguage systems. In: Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. IRSTTechnical Report no. 9011-17.

....described 2 in section 4 and 5 respectively. Section 6 gives some hints about how MC systems and the proposed architecture are implemented in GETFOL. Finally, in sections 7 and 8 we have the related work and the conclusions. 2 MC systems MC systems have been motivated and formally introduced in [10, 12]. Further investigations and applications have been given in [8] They are also called multilanguage systems (ML systems) to emphasize the fact that they allow for the definition of multiple languages, each language associated with a context. Here we show how the underlying idea of MC systems can ....

F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRST-Technical Report 9011-17, IRST, Trento, Italy.

....and provability, two areas where modal logics have been extensively used. 1 Introduction and motivations It has been argued that knowledge should be structured into sets of facts or theories (often called contexts ) some of the many examples are [GW88, Giu93, Wey80, McC87, KK90] In [Giu91, GS91] the authors take a further step and introduce a new general kind of formal systems allowing multiple distinct languages and call them Multi Language systems (ML systems) In [Giu91] it is argued, in fact, that providing each theory with its own language allows us to give a natural and elegant ....

.... or theories (often called contexts ) some of the many examples are [GW88, Giu93, Wey80, McC87, KK90] In [Giu91, GS91] the authors take a further step and introduce a new general kind of formal systems allowing multiple distinct languages and call them Multi Language systems (ML systems) In [Giu91] it is argued, in fact, that providing each theory with its own language allows us to give a natural and elegant proof theoretic account of multi contextual reasoning and, also, extra flexibility which can be exploited in the representation of many phenomena. In this paper we focus on a particular ....

[Article contains additional citation context not shown here]

F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRSTTechnical Report no. 9011-17.

....Normal Modal Logics : 60 7.3 MK vs. MBK : 63 7. 4 Using Bridge Rules to Obtain Normal Modal Logics : 67 8 Conclusion 69 1 INTRODUCTION 3 1 Introduction [Giu91, Giu92] introduce and define a new kind of formal systems, called MultiLanguage systems (ML systems) ML systems are formal systems allowing multiple distinct languages, each language being associated with its own theory, and inference rules whose premises and consequences belong to distinct languages. ....

....with various modal systems (e.g. T, K4, K45, S4, S5 and G) This section ends with the description of the axiom free versions of the ML systems considered. 2 ML SYSTEMS 4 2 ML Systems The goal of this section is to briefly introduce ML systems. More detailed discussions can be found in [Giu91, Giu92]. A formal system with multiple languages is a natural extension of the notion of axiomatic formal system. An axiomatic formal system S is usually described as a triple consisting of a language (which we take to be a set of well formed formulas or wffs) a set of axioms and a set of inference ....

F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRST-Technical Report no. 9011-17.

....the same logic. In these situations there is a need for inference rules which glue the pieces of deduction together. These rules have premisses and conclusions corresponding to different kinds of assertions. Examples of such rules in existing systems include: bridge rules in multi language systems [28, 30]; the FOL reflection rule; and the inference rules for reading information off of a diagram, and for using linguistic assertions to extend diagrams, in Hyperproof [7, 3] The Nelson Oppen and Shostak [72] algorithms for combining decision procedures suggest mechanisms for integration of additional ....

....further heuristic conditions) l i is the result of applying s to l 0 i , for 1 i n; and x; y are the results of applying s respectively to x 0 ; y 0 . 39 14. Related Work Reasoning theories, and in particular composite reasoning theories, are similar in spirit to multi language systems [30, 28]. They can be considered an intensional view of the deductive aspect of logic (cf. entailment theories and proof calculi [53] In multi language systems, sequents may have hypotheses and conclusion from different languages (sequent systems) and bridge rules may discharge hypotheses across ....

F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRST-Technical Report no. 9011-17.

....logics or different mechanizations of the same logic. In these cases, inference rules with premisses and conclusions corresponding to different kinds of assertions are needed to glue the pieces together. Examples of such rules in existing systems include: bridge rules in multi language systems [19, 21]; reflection rules in FOL and NuPrl; meta rules in the Boyer Moore logic [10] and inference rules for reading information off of a diagram, and for using linguistic assertions to extend diagrams in Hyperproof.NuPrl use these rules as formal mechanisms for integration of inferencers proved to be ....

....structure rs b i 5 5 transla j j j j j j j j Q Q Q Q Q Q Q Qs i 6 6 i 8 8 i 9 9 Figure 13. Generalized Transitivity 15. Related Work Reasoning theories, and in particular composite reasoning theories, are similar in spirit to multi language systems [21, 19]. They can be considered an intensional view of the deductive aspect of logic (cf. entailment theories and proof calculi [43] In multi language systems, sequents may have hypotheses and conclusion from different languages (sequent systems) and bridge rules may discharge hypotheses across ....

F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRSTTechnical Report no. 9011-17.

....222B) described in An integrated approach to Artificial Intelligence by L. Stringa, IRST technical report No 9012 11) 1 Introduction and motivations It has been argued that knowledge should be structured into sets of facts or theories (often called contexts ) some of the many examples are [12, 21, 10, 45, 7, 32, 29, 48, 5]. In [10, 13] the authors take a further step and introduce a new general kind of formal systems allowing multiple distinct languages and call them MultiLanguage systems (ML systems) In [12] it is argued, in fact, that providing each theory with its own language allows us to give a natural and ....

....to Artificial Intelligence by L. Stringa, IRST technical report No 9012 11) 1 Introduction and motivations It has been argued that knowledge should be structured into sets of facts or theories (often called contexts ) some of the many examples are [12, 21, 10, 45, 7, 32, 29, 48, 5] In [10, 13] the authors take a further step and introduce a new general kind of formal systems allowing multiple distinct languages and call them MultiLanguage systems (ML systems) In [12] it is argued, in fact, that providing each theory with its own language allows us to give a natural and elegant proof ....

[Article contains additional citation context not shown here]

F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRST-Technical Report no. 9011-17.

....time, non monotonic principles of reasoning, etc. 3.2. The GETFOL system GETFOL is an extension of FOL that provides additional machinery for the implementation of various forms of reasoning. It allows the use of bridge rules which link reasoning in different contexts in a sound and complete way [19]. Some instances of bridge rules have been used to implement multiagent propositional attitudes, for instance belief, common belief, circumscriptive ignorance and knowledge. Certain bridge rule systems have been proved equivalent to the standard modal logics (K, T, S4, S5) 20] GETFOL has also ....

F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI 1991 Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. IRST-Technical Report no. 9011-17.

....in a context because we have derived other facts in other contexts. Thus, if c : ff denotes the formula ff in the context c, such inference rules look like C 1 : A 1 ; Cn : An C : A ae: Inference rules like ae (with premises and conclusions in different contexts) are called bridge rules [ Giunchiglia, 1991 ] as they allow us to bridge deductions in different contexts. In particular, ae allows us to derive A in C just because we have derived A 1 in C 1 , An in Cn . We say also that A in C is a justified assumption as it is an assumption we make in C which is justified by derivations in other ....

F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRST-Technical Report 9011-17, IRST, Trento, Italy.

....7, 1, 2] the authors of this paper have proposed theories for the formalization of agents attitudes, focusing on beliefs in particular. All these works share the intuition that large parts of reasoning happen locally to agents, with few interactions among them, and use contexts (as formalized in [5, 8], but see also [16] as the formal tool to capture locality of reasoning. The approaches followed by the authors can be thought as following two different but related streams. Giunchiglia and Giunchiglia [7] study the properties of contexts for the formal specification of agents mutual beliefs. ....

F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRST-Technical Report 9011-17, IRST, Trento, Italy.

....formalized using contexts as defined in [6] We take a context c to be a logical theory presented as an axiomatic formal system, i.e. as a triple hL; A; Deltai. L is the language of c, A is the set of axioms of c, Delta is the set of inference rules, also called the deductive machinery, of c [6, 5]. From now on we use the terms context and theory as synonyms) A key issue is the extent to which reasoning is local. The language, the set of facts and the inference rules often depend on the problem. People seem able to build theories which contain enough facts and often not many more ....

F. Giunchiglia. Multilanguage systems. In Proceedings of AAAI Spring Symposium on Logical Formalizations of Commonsense Reasoning, 1991. Also IRST-Technical Report 9011-17, IRST, Trento, Italy.

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