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Refining Gelfond Rationality Principle: Towards More Comprehensive Foundational Principles for Answer Set Semantics

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Yi-Dong Shen, Thomas Eiter

๐Ÿ’ก ๊ฐœ์š”

๋ณธ ๋…ผ๋ฌธ์€ ๋น„๋‹จ์กฐ ๋…ผ๋ฆฌ ํ”„๋กœ๊ทธ๋ž˜๋ฐ์˜ ํ•ต์‹ฌ์ธ Answer Set Programming(ASP)์˜ ๊ธฐ๋ฐ˜ ์›๋ฆฌ๋ฅผ ์žฌ์ •๋ฆฝํ•˜๊ณ ์ž ํ•ฉ๋‹ˆ๋‹ค. ๊ธฐ์กด์˜ Gelfond-Lifschitz ์ •์˜์—์„œ ์ถœ๋ฐœํ•˜์—ฌ, ๋ชจ๋“  ASP ์˜๋ฏธ๋ก ์— ๋ณดํŽธ์ ์œผ๋กœ ์ ์šฉ๋  ์ˆ˜ ์žˆ๋Š” ์ƒˆ๋กœ์šด ์›๋ฆฌ๋“ค์„ ์ œ์•ˆํ•˜๊ณ , ์ด๋ฅผ ๋ฐ”ํƒ•์œผ๋กœ ๊ธฐ์กด ์˜๋ฏธ๋ก ๋“ค์„ ํ‰๊ฐ€ํ•ฉ๋‹ˆ๋‹ค. ์ œ์•ˆ๋œ ์›๋ฆฌ๋“ค์€ well-supportedness, negation by default์— ๋Œ€ํ•œ ์ตœ์†Œ์„ฑ, epistemic negation์— ๋Œ€ํ•œ ์ตœ์†Œ์„ฑ์„ ํฌํ•จํ•˜๋ฉฐ, ์ด๋Š” ๋ณด๋‹ค ํฌ๊ด„์ ์ด๊ณ  ์ง๊ด€์ ์ธ Answer Set(AS) ๊ตฌ์„ฑ ๋ฐ ํ‰๊ฐ€๋ฅผ ๋ชฉํ‘œ๋กœ ํ•ฉ๋‹ˆ๋‹ค.

๐Ÿ”‘ ์‹œ์‚ฌ์  ๋ฐ ํ•œ๊ณ„

โ€ข
๊ธฐ์กด์˜ Answer Set(AS) ์˜๋ฏธ๋ก ์—์„œ ์š”๊ตฌํ•˜๋Š” ์ตœ์†Œ ๋ชจ๋ธ ์†์„ฑ, ์ œ์•ฝ ์กฐ๊ฑด ๋‹จ์กฐ์„ฑ, ์ฐฝ๋ฆฝ์„ฑ(foundedness)์ด ๋•Œ๋กœ๋Š” ๋„ˆ๋ฌด ์—„๊ฒฉํ•˜์—ฌ ๊ธฐ๋Œ€๋˜๋Š” AS๋ฅผ ๋ฐฐ์ œํ•  ์ˆ˜ ์žˆ์Œ์„ ๋ณด์—ฌ์ค๋‹ˆ๋‹ค.
โ€ข
Gelfond์˜ ํ•ฉ๋ฆฌ์„ฑ ์›๋ฆฌ๋ฅผ ๋ฐœ์ „์‹œํ‚จ well-supportedness, negation by default์— ๋Œ€ํ•œ ์ตœ์†Œ์„ฑ, epistemic negation์— ๋Œ€ํ•œ ์ตœ์†Œ์„ฑ์ด๋ผ๋Š” ์ƒˆ๋กœ์šด ๊ธฐ๋ณธ ์›๋ฆฌ๋ฅผ ์ œ์‹œํ•˜์—ฌ, AS์˜ ๊ตฌ์„ฑ๊ณผ ํ‰๊ฐ€๋ฅผ ์œ„ํ•œ ๋ณด๋‹ค ์œ ์—ฐํ•˜๊ณ  ํฌ๊ด„์ ์ธ ํ‹€์„ ์ œ๊ณตํ•ฉ๋‹ˆ๋‹ค.
โ€ข
์ œ์•ˆ๋œ ์›๋ฆฌ๋ฅผ ํ†ตํ•ด ์ƒˆ๋กœ์šด AS ์˜๋ฏธ๋ก ์„ ์ •์˜ํ•˜๊ณ , ๊ธฐ์กด AS ์˜๋ฏธ๋ก ๋“ค์„ ๋Œ€์•ˆ์ ์ธ ๊ธฐ์ค€์œผ๋กœ ํ‰๊ฐ€ํ•จ์œผ๋กœ์จ ASP ์—ฐ๊ตฌ์— ์ค‘์š”ํ•œ ํ† ๋Œ€๋ฅผ ๋งˆ๋ จํ•ฉ๋‹ˆ๋‹ค.
โ€ข
๋…ผ๋ฌธ์—์„œ ์ œ์•ˆ๋œ ์ƒˆ๋กœ์šด AS ์˜๋ฏธ๋ก ์˜ ์‹ค์ œ ์‘์šฉ์—์„œ์˜ ํšจ์œจ์„ฑ๊ณผ ๋ณต์žก์„ฑ์— ๋Œ€ํ•œ ์ถ”๊ฐ€์ ์ธ ๋ถ„์„์ด ํ•„์š”ํ•ฉ๋‹ˆ๋‹ค.
๐Ÿ‘
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