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Uniform proofs as a foundation for logic programming
 ANNALS OF PURE AND APPLIED LOGIC
, 1991
"... A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its ..."
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Cited by 374 (108 self)
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A prooftheoretic characterization of logical languages that form suitable bases for Prologlike programming languages is provided. This characterization is based on the principle that the declarative meaning of a logic program, provided by provability in a logical system, should coincide with its operational meaning, provided by interpreting logical connectives as simple and fixed search instructions. The operational semantics is formalized by the identification of a class of cutfree sequent proofs called uniform proofs. A uniform proof is one that can be found by a goaldirected search that respects the interpretation of the logical connectives as search instructions. The concept of a uniform proof is used to define the notion of an abstract logic programming language, and it is shown that firstorder and higherorder Horn clauses with classical provability are examples of such a language. Horn clauses are then generalized to hereditary Harrop formulas and it is shown that firstorder and higherorder versions of this new class of formulas are also abstract logic programming languages if the inference rules are those of either intuitionistic or minimal logic. The programming language significance of the various generalizations to firstorder Horn clauses is briefly discussed.
Logic without Model Theory
 What is a Logical System
, 1994
"... Arguably, model theory serves two main functions: (1) to explain the relationship between language and experience, and (2) to specify the notion of logical consequence. In this paper I shall propose the notion of `knowledge assimilation', the assimilation of new information into a knowledge base, as ..."
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Cited by 12 (0 self)
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Arguably, model theory serves two main functions: (1) to explain the relationship between language and experience, and (2) to specify the notion of logical consequence. In this paper I shall propose the notion of `knowledge assimilation', the assimilation of new information into a knowledge base, as an alternative understanding of the way in which a knowledge base formulated in logic relates to externally generated input sentences that describe experience. I shall argue that the notion of logical consequence can also be understood within a knowledge assimilation framework, in terms of sentences that must hold no matter what stream of input sentences might arise in the future. Classical model theory can be understood as dealing with static relationships among individuals. It leads naturally therefore to possible world semantics and modal logic, in which models are understood as related to one another by accessibility relations. I shall argue in favour of a nonmodeltheoretic alternativ...
Representing and Reasoning about Concurrent Actions with Abductive Logic Programs
, 1997
"... In this paper we extend Gelfond and Lifschitz' action description language A with concurrent actions and observation propositions to describe the predicted behaviour of domains of (concurrent) actions and actually observed behaviour, respectively, without requiring that the actually observed behavio ..."
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Cited by 6 (1 self)
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In this paper we extend Gelfond and Lifschitz' action description language A with concurrent actions and observation propositions to describe the predicted behaviour of domains of (concurrent) actions and actually observed behaviour, respectively, without requiring that the actually observed behaviour of a domain of actions be consistent with its predicted behaviour. We present a translation from domain descriptions and observations in the new action language to abductive normal logic programs. The translation is shown to be both sound and complete. From the standpoint of modelbased diagnosis, in particular, we discuss the temporal explanation of inferring actions from fluent changes at two different levels, namely, at the domain description level and at the abductive logic programming level. The method is applicable to the temporal projection problem with incomplete information, as well as to the temporal explanation of inferring actions from fluent changes. 1 Introduction There ha...
True Equality Constraints Over An Open Universe Of Terms
, 1994
"... . For a firstorder language L, the Herbrand universe consists of ground terms of L. We defined [15, 16, 17] an !Herbrand universe for L by introducing the following modification: first add to L countably many new individual constants, and then form the set of all ground terms of the resulting lan ..."
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. For a firstorder language L, the Herbrand universe consists of ground terms of L. We defined [15, 16, 17] an !Herbrand universe for L by introducing the following modification: first add to L countably many new individual constants, and then form the set of all ground terms of the resulting language. Newly added constants make this universe "open" and suitable for modeling those situations in databases where not all entities are known in advance. In this research we investigate the theory of equality determined by ! Herbrand interpretations, we give its axiomatization, and prove that it is complete and decidable. For a formula 9xB, the decision algorithm not only tells whether this formula is a consequence of our equality theory, but also computes substitutions ` such that B` is true in all !Herbrand interpretations. To put these results in a broader context, let us mention that algorithm above can be used to generate answer substitutions in a logic programming language which ...
Designing Effective Policies for Minimal Agents
"... Abstract. A policy for a minimal reactive agent is a set of conditionaction rules used to determine its response to perceived environmental stimuli. When the policy predisposes the agent to achieving a stipulated goal we call it a teleoreactive policy. This paper presents a framework for construc ..."
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Abstract. A policy for a minimal reactive agent is a set of conditionaction rules used to determine its response to perceived environmental stimuli. When the policy predisposes the agent to achieving a stipulated goal we call it a teleoreactive policy. This paper presents a framework for constructing and evaluating teleoreactive policies for one or more minimal agents, based upon discountedreward evaluation of policyrestricted subgraphs of complete situationgraphs. The main feature of the method is that it exploits explicit and definite associations of the agent’s perceptions with states. The combinatorial burden that would potentially ensue from such associations can be ameliorated by suitable use of abstractions. The framework allows one to plan for a number of agents by focusing upon the behaviour of a single representative of them. It allows for varied behaviour to be modelled, including communication between agents. Simulation results presented here indicate that the method affords a good degree of scalability and predictive power. 1