A proof-theoretic characterization of logical languages that form suitable bases for Prolog-like 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 cut-free sequent proofs called uniform proofs. A uniform proof is one that can be found by a goal-directed 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 first-order and higher-order 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 first-order and higher-order 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 first-order Horn clauses is briefly discussed.

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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 non-model-theoretic alternativ...

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 stand-point of model-based 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...

. For a first-order 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 ...

Abstract. A policy for a minimal reactive agent is a set of condition-action rules used to determine its response to perceived environmental stimuli. When the policy pre-disposes the agent to achieving a stipulated goal we call it a teleo-reactive policy. This paper presents a framework for constructing and evaluating teleo-reactive policies for one or more minimal agents, based upon discounted-reward evaluation of policy-restricted subgraphs of complete situation-graphs. 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