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19
Multilanguage Hierarchical Logics (or: How We Can Do Without Modal Logics)
, 1994
"... MultiLanguage systems (ML systems) are formal systems allowing the use of multiple distinct logical languages. In this paper we introduce a class of ML systems which use a hierarchy of first order languages, each language containing names for the language below, and propose them as an alternative to ..."
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Cited by 180 (47 self)
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MultiLanguage systems (ML systems) are formal systems allowing the use of multiple distinct logical languages. In this paper we introduce a class of ML systems which use a hierarchy of first order languages, each language containing names for the language below, and propose them as an alternative to modal logics. The motivations of our proposal are technical, epistemological and implementational. From a technical point of view, we prove, among other things, that the set of theorems of the most common modal logics can be embedded (under the obvious bijective mapping between a modal and a first order language) into that of the corresponding ML systems. Moreover, we show that ML systems have properties not holding for modal logics and argue that these properties are justified by our intuitions. This claim is motivated by the study of how ML systems can be used in the representation of beliefs (more generally, propositional attitudes) and provability, two areas where modal logics have been extensively used. Finally, from an implementation point of view, we argue that ML systems resemble closely the current practice in the computer representation of propositional attitudes and metatheoretic theorem proving.
Automated Deduction by Theory Resolution
 Journal of Automated Reasoning
, 1985
"... Theory resolution constitutes a set of complete procedures for incorporating theories into a resolution theoremproving program, thereby making it unnecessary to resolve directly upon axioms of the theory. This can greatly reduce the length of proofs and the size of the search space. Theory resoluti ..."
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Cited by 122 (1 self)
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Theory resolution constitutes a set of complete procedures for incorporating theories into a resolution theoremproving program, thereby making it unnecessary to resolve directly upon axioms of the theory. This can greatly reduce the length of proofs and the size of the search space. Theory resolution effects a beneficial division of labor, improving the performance of the theorem prover and increasing the applicability of the specialized reasoning procedures. Total theory resolution utilizes a decision procedure that is capable of determining unsatisfiability of any set of clauses using predicates in the theory. Partial theory resolution employs a weaker decision procedure that can determine potential unsatisfiability of sets of literals. Applications include the building in of both mathematical and special decision procedures, e.g., for the taxonomic information furnished by a knowledge representation system. Theory resolution is a generalization of numerous previously known resolution refinements. Its power is demonstrated by comparing solutions of "Schubert's Steamroller" challenge problem with and without building in axioms through theory resolution. 1 1
The Logical Modelling of Computational MultiAgent Systems
, 1992
"... THE aim of this thesis is to investigate logical formalisms for describing, reasoning about, specifying, and perhaps ultimately verifying the properties of systems composed of multiple intelligent computational agents. There are two obvious resources available for this task. The first is the (largel ..."
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Cited by 61 (17 self)
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THE aim of this thesis is to investigate logical formalisms for describing, reasoning about, specifying, and perhaps ultimately verifying the properties of systems composed of multiple intelligent computational agents. There are two obvious resources available for this task. The first is the (largely AI) tradition of reasoning about the intentional notions (belief, desire, etc.). The second is the (mainstream computer science) tradition of temporal logics for reasoning about reactive systems. Unfortunately, neither resource is ideally suited to the task: most intentional logics have little to say on the subject of agent architecture, and tend to assume that agents are perfect reasoners, whereas models of concurrent systems from mainstream computer science typically deal with the execution of individual program instructions. This thesis proposes a solution which draws upon both resources. It defines a model of agents and multiagent systems, and then defines two execution models, which ...
Multiagent Reasoning with Belief Contexts II: Elaboration Tolerance
 Intelligent Agents: Proceedings of 1994 Workshop on Agent Theories, Architectures, and Languages, number 890 in Lecture Notes in Computer Science
, 1994
"... As discussed in previous papers, belief contexts are a powerful and appropriate formalism for the representation and implementation of propositional attitudes in a multiagent environment. In this paper we show that a formalization using belief contexts is also elaboration tolerant. That is, it is a ..."
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Cited by 51 (6 self)
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As discussed in previous papers, belief contexts are a powerful and appropriate formalism for the representation and implementation of propositional attitudes in a multiagent environment. In this paper we show that a formalization using belief contexts is also elaboration tolerant. That is, it is able to cope with minor changes to input problems without major revisions. Elaboration tolerance is a vital property for building situated agents: it allows for adapting and reusing a previous problem representation in different (but related) situations, rather than building a new representation from scratch. We substantiate our claims by discussing a number of variations to a paradigmatic case study, the Three Wise Men problem. Introduction Belief contexts (Giunchiglia 1993; Giunchiglia & Serafini 1994; Giunchiglia et al. 1993) are a formalism for the representation of propositional attitudes. Their basic feature is modularity: knowledge can be distributed into different and separated mod...
What awareness isn't: A sentential view of implicit and explicit belief
 Proceedings of the 1986 Conference on Theoretical Aspects of Reasoning About Knowledge
, 1986
"... In their attempt to model and reason about the beliefs of agents, artificial intelligence (AI) researchers have borrowed from two different philosophical traditions regarding the folk psychology of belief. In one tradition, belief is a relation between an agent and a proposition, that is, a proposi ..."
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Cited by 21 (0 self)
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In their attempt to model and reason about the beliefs of agents, artificial intelligence (AI) researchers have borrowed from two different philosophical traditions regarding the folk psychology of belief. In one tradition, belief is a relation between an agent and a proposition, that is, a propositional attitude. Formal analyses of propositional attitudes are often given in terms of a possibleworlds semantics. In the other tradition, belief is a relation between an agent and a sentence that expresses a proposition (the sentential approach). The arguments for and against these approaches are complicated, confusing, and often obscure and unintelligible (at least to this author). Nevertheless strong supporters exist for both sides, not only in the philosophical arena (where one would expect it), but also in AI. In the latter field, some proponents of posslbleworlds analysis have attempted to remedy what appears to be its biggest drawback, namely the assumption that an agent believes all the logical consequences of his or her beliefs. Drawing on initial work by Levesque, Fagin and Halpern define a logic of 9eneral awareness that superimposes elements of the sentential approach on a possibleworlds framework. The result, they claim, is an appropriate model for resourcelimited believers. We argue that this is a bad idea: it ends up being equivalent to a more complicated version of the sentential approach. In concluding we cannot refrain from adding to the debate about the utility of possibleworlds analyses of belief.
On the relation between autoepistemic logic and circumscription
 In Proceedings IJCAI89
, 1989
"... Circumscription on the one hand and autoepistemic and default logics on the other seem to have quite different characteristics as formal systems, which makes it difficult to compare them as formalizations of defeasible connmonsense reasoning. In this paper we accomplish two tasks: (1) we extend the ..."
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Cited by 21 (0 self)
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Circumscription on the one hand and autoepistemic and default logics on the other seem to have quite different characteristics as formal systems, which makes it difficult to compare them as formalizations of defeasible connmonsense reasoning. In this paper we accomplish two tasks: (1) we extend the original semantics of autoepistemic logic to a language which includes variables quantified into the context of the autoepistemic operator, and (2) we show that a certain class of autoepistemic theories in the extended language has a minimalmodel semantics corresponding to circumscription. We conclude that all of the firstorder consequences of parallel predicate circumscription can be obtained from this class of autoepistemic theories. The correspondence we construct also sheds light on the problematic treatment of equality in circumscription. 1
Multilanguage First Order Theories of Propositional Attitudes
, 1990
"... The goal of this paper is to present a new family of formal systems, so called multilanguage systems (MLsystems), which allow the use of multiple distinct first order languages and inference rules whose premises and consequences need not belong to the same language. MLsystems are argued to formali ..."
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Cited by 16 (11 self)
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The goal of this paper is to present a new family of formal systems, so called multilanguage systems (MLsystems), which allow the use of multiple distinct first order languages and inference rules whose premises and consequences need not belong to the same language. MLsystems are argued to formalize naturally and elegantly notions like belief, knowledge and, more in general, various forms of propositional attitudes. Some instances of MLsystems are defined and proved equivalent to the modal logic K and some of Konolige's logics for belief.
The Dynamics of Syntactic Knowledge
 JOURNAL OF LOGIC AND COMPUTATION
, 2006
"... The syntactic approach to epistemic logic avoids the logical omniscience problem by taking knowledge as primary rather than as defined in terms of possible worlds. In this study, we combine the syntactic approach with modal logic, using transition systems to model reasoning. We use two syntactic epi ..."
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Cited by 13 (5 self)
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The syntactic approach to epistemic logic avoids the logical omniscience problem by taking knowledge as primary rather than as defined in terms of possible worlds. In this study, we combine the syntactic approach with modal logic, using transition systems to model reasoning. We use two syntactic epistemic modalities: ‘knowing at least ’ a set of formulae and ‘knowing at most’ a set of formulae. We are particularly interested in models restricting the set of formulae known by an agent at a point in time to be finite. The resulting systems are investigated from the point of view of axiomatization and complexity. We show how these logics can be used to formalise nonomniscient agents who know some inference rules, and study their relationship to other systems of syntactic epistemic logics,
Complete axiomatizations of finite syntactic epistemic states
 In Proceedings of the 3rd International Workshop on Declarative Agent Languages and Technologies (DALT
, 2005
"... Abstract. An agent who bases his actions upon explicit logical formulae has at any given point in time a finite set of formulae he has computed. Closure or consistency conditions on this set cannot in general be assumed – reasoning takes time and real agents frequently have contradictory beliefs. Th ..."
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Cited by 10 (2 self)
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Abstract. An agent who bases his actions upon explicit logical formulae has at any given point in time a finite set of formulae he has computed. Closure or consistency conditions on this set cannot in general be assumed – reasoning takes time and real agents frequently have contradictory beliefs. This paper discusses a formal model of knowledge as explicitly computed sets of formulae. It is assumed that agents represent their knowledge syntactically, and that they can only know finitely many formulae at a given time. Existing syntactic characterizations of knowledge seem to be too general to have any interesting properties, but we extend the meta language to include an operator expressing that an agent knows at most a particular finite set of formulae. The specific problem we consider is the axiomatization of this logic. A sound system is presented. Strong completeness is impossible, so instead we characterize the theories for which we can get completeness. Proving that a theory actually fits this characterization, including proving weak completeness of the system, turns out to be nontrivial. One of the main results is a collection of algebraic conditions on sets of epistemic states described by a theory, which are sufficient for completeness. The paper is a contribution to a general abstract theory of resource bounded agents. Interesting results, e.g. complex algebraic conditions for completeness, are obtained from very simple assumptions, i.e. epistemic states as arbitrary finite sets and operators for knowing at least and at most. 1
Strongly complete axiomatizations of ”knowing at most” in standard syntactic assignments
 In Francesca Toni and Paolo Torroni, editors, Preproceedings of the 6 th International Workshop on Computational Logic in Multiagent Systems (CLIMA VI
, 2005
"... Abstract. Standard syntactic assignments (SSAs) model knowledge directly rather than as truth in all possible worlds as in modal epistemic logic, by assigning arbitrary truth values to atomic epistemic formulae. It is a very general approach to epistemic logic, but has no interesting logical propert ..."
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Cited by 9 (2 self)
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Abstract. Standard syntactic assignments (SSAs) model knowledge directly rather than as truth in all possible worlds as in modal epistemic logic, by assigning arbitrary truth values to atomic epistemic formulae. It is a very general approach to epistemic logic, but has no interesting logical properties — partly because the standard logical language is too weak to express properties of such structures. In this paper we extend the logical language with a new operator used to represent the proposition that an agent “knows at most ” a given finite set of formulae and study the problem of strongly complete axiomatization of SSAs in this language. Since the logic is not semantically compact, a strongly complete finitary axiomatization is impossible. Instead we present, first, a strongly complete infinitary system, and, second, a strongly complete finitary system for a slightly weaker variant of the language. 1