Download Correct Reasoning: Essays on Logic-Based AI in Honour of by Jack Minker (auth.), Esra Erdem, Joohyung Lee, Yuliya PDF

By Jack Minker (auth.), Esra Erdem, Joohyung Lee, Yuliya Lierler, David Pearce (eds.)

This Festschrift released in honor of Vladimir Lifschitz at the party of his sixty fifth birthday offers 39 articles by means of colleagues from worldwide with whom Vladimir Lifschitz had cooperation in a variety of respects. The 39 contributions mirror the breadth and the intensity of the paintings of Vladimir Lifschitz in good judgment programming, circumscription, default good judgment, motion conception, causal reasoning and solution set programming.

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The equivalence of the two encodings is somewhat problematic from the point of view of the language requirements that we are seeking to satisfy in this paper. In fact, in ASP the epistemic disjunction operator ∨ denotes a non-deterministic choice between two alternatives: a statement p ∨ q in ASP means that p and q are equally acceptable alternatives. In the language of IF-programs, instead, the disjunction operator appears to express a preference for the left-hand-side expression. In this sense, the representation of disjunctive knowledge in ASP and in [10] follows two very different strategies.

In fact, we purposefully designed the new language so that (1) the representation of relations is fully retained; (2) the representation of knowledge using non-Herbrand functions follows in a natural way from the typical ASP strategies; (3) the semantics is an extension of the the semantics of ASP from [9], allowing for a comparatively simple incorporation of various extensions of ASP such as weak constraints, probabilistic constructs and consistency-restoring rules. 1 Introduction In this paper we describe an extension of Answer Set Programming (ASP) [9,13,2] called ASP{f}, and aimed at simplifying the representation of non-Herbrand functions.

We continue with the definitions for FOL typed term and FOL typed λcalculus formula. A FOL atomic term is a constant or a variable of any type a. , tn ) is also a FOL atomic term of type e. Definition 1. The elements of the set Δα of FOL typed terms of type α are inductively defined as follows: 1. For each type a, every FOL atomic term of type a belongs to Δa . 2. , tn ) is a FOL typed atomic formula that belongs to Δt . 3. For any types a and b, if α ∈ Δa→b and β ∈ Δa , then α@β ∈ Δb . 4. 1 5. If α ∈ Δt and β ∈ Δt , then α ∨ β, α ∧ β and α → β ∈ Δt .

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