نوع مقاله : پژوهشی

نویسندگان

1 گروه علوم کامپیوتر، دانشگاه صنعتی بیرجند، بیرجند، ایران

2 گروه ریاضی محض، دانشکده ریاضی و کامپیوتر، دانشگاه شهید باهنر، کرمان، ایران

چکیده

در اوایل قرن بیستم، ایده‌هایی مبنی بر تخطی از «اصل دو ارزشی» منطق ارسطویی شکل گرفت. البته خود ارسطو نیز با اشاره به مسئله صدق یا کذبِ جملاتی که در مورد آینده اطلاعی می‌دهند، به این موضوع که بعضی جملات نه ارزش «راست» و نه ارزش «دروغ» دارند اشاره کرده بود. اما این مسئله تقریباً تا دوره رنسانس بطور کلی فراموش شد و از دوره رنسانس تا اوایل قرن بیستم، بعضی مبانی فلسفی برای آن بیان شد. تخطی از «اصل دو ارزشی» پای منطق‌های مختلفی از جمله منطق‌های چندارزشی را به حوزه منطق باز کرد. در این مقاله، پس از مرور مختصر سیر تکاملی ایده‌های مربوط به منطق‌های چند ارزشی در قرن بیستم و بررسی اهدافی که بعضاً این منطق‌ها بدنبال آن هستند، با مداقه روی مجموعه ارزش‌های درستی و عملگرهای مختلفی که نقش تعابیر رابط‌‌های منطقی را بازی می‌کنند، سعی می‌کنیم دید جامع‌تری نسبت به منطق‌های چند ارزشی کسب کنیم.

کلیدواژه‌ها

عنوان مقاله [English]

On many-valued logics

نویسندگان [English]

  • Seyed Mohammad Amin Khatami 1
  • Esfandiar Eslami 2

1 Department of Computer Science, Birjand University of Technology, Birjand, Iran

2 Shahid Bahonar University of Kerman

چکیده [English]

In the early 19th century, the ''principle of bivalence'' of the Aristotelian logic was challenged. Of course, Aristotle himself was questioned the applicability of this principle to propositions concerning future contingents, and he answered it via something like as modalities of possibility. However, Aristotle did not abandon the principle and it has not received much attention till the Renaissance. From Renaissance to the early 19th century, some philosophical considerations to this issue were developed. Rejecting the principle of bivalence implies alternative accounts of various kinds of logics such as many-valued logics in the context of logic. In this article, we first survey the development of many-valued logics by reviewing motivational ideas behind many-valued logics together with examining the aims and scopes of some of these logics. Then, we devote the rest of the paper to study various aspects of "truth value sets" and "interpretation of logical connectives" in many-valued logics to obtain a more comprehensive view on these logics.

کلیدواژه‌ها [English]

  • many-valued logic
  • fuzzy logic
  • principle of bivalence
  • principle of excluded middle
  • law of non-contradiction
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