Xem mã nguồn của Logic

{{1000 bài cơ bản}}{{Thanh bên triết học}}
'''Logic''' (hợp lý, hữu lý, hàm lý) hay '''luận lý học''', từ [[tiếng Hy Lạp cổ đại]] λόγος ([[logos]]), nghĩa nguyên thủy là ''[[Từ|từ ngữ]]'', hoặc ''điều đã được nói'', (nhưng trong nhiều [[ngôn ngữ]] [[châu Âu]] đã trở thành có ý nghĩa là ''suy nghĩ'' hoặc ''[[lập luận]]'' hay ''[[lý tính|lý trí]]''). Logic thường được nhắc đến như là một ngành nghiên cứu về tiêu chí đánh giá các [[luận cứ logic|luận cứ]], mặc dù định nghĩa chính xác của logic vẫn là vấn đề còn đang được bàn cãi giữa các [[triết gia]]. Tuy nhiên khi môn học được xác định, nhiệm vụ của nhà logic học vẫn như cũ: làm đẩy mạnh tiến bộ của việc phân tích các suy luận có hiệu lực và suy luận ngụy biện để người ta có thể phân biệt được [[luận cứ logic|luận cứ]] nào là hợp lý và luận cứ nào có chỗ không hợp lý.

Theo truyền thống, logic được nghiên cứu như là một nhánh của [[triết học]]. Kể từ giữa [[thế kỷ 19]] logic đã thường được nghiên cứu trong [[toán học]] và [[luật]]. Gần đây nhất logic được áp dụng vào [[khoa học máy tính]] và [[trí tuệ nhân tạo]]. Là một [[ngành khoa học hình thức]], logic nghiên cứu và phân loại cấu trúc của các khẳng định và các lý lẽ, cả hai đều thông qua việc nghiên cứu các [[hệ hình thức]] của [[việc suy luận]] và qua sự nghiên cứu lý lẽ trong ngôn ngữ tự nhiên. Tầm bao quát của logic do vậy là rất rộng, đi từ các đề tài cốt lõi như là nghiên cứu các lý lẽ [[ngụy biện]] và [[nghịch lý]], đến những phân tích chuyên gia về lập luận, chẳng hạn lập luận có [[xác suất]] đúng và các lý lẽ có liên quan đến quan hệ [[nhân quả]]. Ngày nay, logic còn được sử dụng phổ biến trong [[lý thuyết lý luận]].

Qua suốt quá trình lịch sử, đã có nhiều sự quan tâm trong việc phân biệt lập luận tốt và lập luận không tốt, và do đó logic đã được nghiên cứu trong một số dạng ít nhiều là quen thuộc đối với chúng ta. [[Logic Aristotle]] chủ yếu quan tâm đến việc dạy lý luận thế nào cho tốt, và ngày nay vẫn được dạy với mục đích đó, trong khi trong [[logic toán|logic toán học]] và [[triết học phân tích]] (''analytical philosophy'') người ta nhấn mạnh vào logic như là một đối tượng nghiên cứu riêng, và do vậy logic được nghiên cứu ở một mức độ trừu tượng hơn.

Các quan tâm về các loại logic khác nhau cho thấy rằng logic không phải là một ngành có thể nghiên cứu tách biệt. Trong khi logic thường có vẻ sự thúc đẩy chính nó, môn học này phát triển tốt nhất khi lý do mà chúng ta quan tâm đến logic được đặt ra một cách rõ ràng.

== Các lĩnh vực nghiên cứu ==
Logic được nghiên cứu bởi nhiều lĩnh vực khác nhau. Điều này thường được thực hiện bằng cách áp dụng phương pháp hình thức của nó vào các chủ đề nhất định nằm ngoài phạm vi logic, chẳng hạn như trong đạo đức học hoặc khoa học máy tính.{{sfnm|1a1=Hintikka|1y=2019|1loc=§Logic and other disciplines [Logic và các chuyên ngành khác]|2a1=Haack|2y=1978|2loc=Philosophy of logics [Triết học của logic học]|2pp=1–10}} Ngoài ra, bản thân logic cũng có thể là đối tượng nghiên cứu của các lĩnh vực khác.

=== Triết học logic và logic triết học ===
{{chính| Triết học logic | Logic triết học}}
''Triết học logic'' là lĩnh vực triết học nghiên cứu về phạm vi và bản chất của logic.{{sfnm|1a1=Hintikka|1y=2019|1loc=lead section, §Nature and varieties of logic|2a1=Audi|2loc=Philosophy of logic|2y=1999b}} Nó tra xét các tiền giả định (''presupposition'') ẩn trong logic, tìm cách xác định những khái niệm cơ bản của logic hoặc các mặc định siêu hình học có liên hệ với những khái niệm đó.{{sfn |Jacquette |2006 |loc=Introduction: Philosophy of logic today |pp=1–12}} Nó cũng quan tâm đến việc phân loại các hệ thống logic và các ràng buộc [[bản thể luận]] kéo theo những hệ thống ấy.{{sfn |Hintikka |2019 |loc=§Problems of ontology [Các vấn đề của bản thể luận]}} ''Logic triết học'' là một lĩnh vực nằm trong phạm trù triết học logic. Nó nghiên cứu ứng dụng của các phương pháp logic trong các vấn đề triết học của các ngành như siêu hình học, đạo đức học và tri thức luận.{{sfnm|1a1=Jacquette|1y=2006|1loc=Introduction: Philosophy of logic today [Dẫn nhập: Triết học logic ngày nay]|1pp=1–12|2a1=Burgess|2y=2009|2loc=1. Classical logic [Logic cổ điển]}} Những ưng dụng kiểu này thường xuất hiện dưới dạng các hệ thống logic [[#Mở rộng|mở rộng]] (''extended'') hoặc [[#Phi hình thức|phi hình thức]] (''deviant'').{{sfnm|1a1=Goble|1y=2001|1loc=Introduction|2a1=Hintikka|2a2=Sandu|2y=2006|2pp=31–32}}

=== Siêu logic học ===
{{chính|Siêu logic học}}
''Siêu logic học'' (''Metaphysics'') là ngành triết học nghiên cứu các đặc tính của các hệ thống logic hình thức. Ví dụ, khi một hệ thống hình thức mới được phát triển, các nhà siêu logic học sẽ nghiên cứu nó nhằm xác định những công thức nào có thể được chứng minh. Họ cũng sẽ tìm hiểu xem liệu có thể phát triển một [[thuật toán]] nhằm tìm ra minh chứng cho mỗi công thức hay không, đồng thời xác minh tất cả các công thức khả chứng có phải là hằng đúng (''tautology'') không. Cuối cùng, họ sẽ so sánh nó với các hệ thống logic khác để tìm ra những đặc điểm khác biệt. Một vấn đề then chốt của siêu logic học là mối liên hệ giữa cú pháp và ngữ nghĩa. Luật cú pháp của một hệ thống hình thức quy định phương cách suy đoán kết luận từ các tiền đề, tức là phương cách xây dựng minh chứng. Ngữ nghĩa của một hệ thống hình thức quyết định phát biểu nào đúng và phát biểu nào sai. Điều này quy định tính hợp lý của lý luận; sở dĩ vì, để lý luận hợp lý, không thể có chuyện tiền đề đúng mà kết luận sai. Mối quan hệ giữa cú pháp và ngữ nghĩa còn ảnh hưởng đến các vấn đề như: liệu tất cả các lý luận hợp lý có khả chứng hay không, và liệu tất cả các lý luận khả chứng có hợp lý hay không. Các nhà siêu logic cũng đánh giá xem các hệ thống logic đã hoàn thiện chưa, có vững chãi và có chặt chẽ không. Ngoài ra, họ cũng quan tâm đến [[tính khả quyết (logic)|tính khả quyết]] và [[sức biểu đạt (khoa học máy tính)|sức biểu đạt]] mà hệ thống sở hữu. Các nhà siêu logic học dựa khá nhiều vào lập luận toán học trừu tượng khi thẩm tra và xây dựng các minh chứng siêu logic học.{{sfnm|1a1=Gensler|1y=2006|1pp=xliii–xliv|2a1=Sider|2y=2010|2pp=4–6|3a1=Schagrin}}

=== Logic toán học ===
{{chính|Logic toán học}}
[[Tập tin:Bertrand Russell 1949.jpg|thumb|left|Nhà triết học và toán học Bertrand Russell đã có nhiều đóng góp lớn lao cho ngành logic toán học.{{sfn|Irvine|2022}}]]
Thuật ngữ "logic toán học" (''mathematical logic'') đôi khi được dùng đồng nghĩa với "logic hình thức". Tuy nhiên, nếu giải nghĩa hẹp hơn, thuật ngữ này chỉ đến sự nghiên cứu logic trong toán học. Các phân ngành lớn của nó bao gồm lý thuyết mô hình (''model theory''), [[lý thuyết chứng minh]] (''proof theory''), [[lý thuyết tập hợp]], và [[lý thuyết tính toán]].{{sfnm|1a1=Li|1y=2010|1p=ix|2a1=Rautenberg|2y=2010|2p=15|3a1=Quine|3y=1981|3p=1|4a1=Stolyar|4y=1984|4p=2}} Nghiên cứu logic toán học chủ yếu xoay quanh các đặc tính toán học của các hệ thống logic hình thức. Tuy nhiên, nó cũng bao gồm các nỗ lực để vận dụng logic vào việc phân tích các suy luận toán học, hoặc để thiết định [[nền tảng của toán học]] dựa trên logic.{{sfn|Stolyar|1984|pp=3–6}} Chủ đề "nền tảng của toán học" từng là mối bận tâm lớn đối với ngành logic toán học hồi đầu thế kỷ thứ 20, chủ trương theo đuổi cái gọi là [[chủ nghĩa duy logic]] tiên phong bởi các triết gia-logic gia tiền bối như [[Gottlob Frege]], [[Alfred North Whitehead]] và [[Bertrand Russell]]. Đối với những học giả duy logic chủ nghĩa, các lý thuyết toán học ắt phải [[hàm đúng|luôn đúng]] về mặt logic, và họ muốn chứng tỏ điều này bằng cách rút gọn toàn bộ toán học thành logic. Nhiều người đã dốc công sức để hiện thực hóa giả định này nhưng đều thất bại, từ sự sụp đổ của cơ đồ logic học Frege trong ''Grundgesetze'' trước [[nghịch lý Russell]], đến sự lụn bại của [[chương trình Hilbert]] trước [[các định lý bất toàn của Gödel]].{{sfnm|1a1=Hintikka|1a2=Spade|1loc=[https://www.britannica.com/topic/history-of-logic/Godels-incompleteness-theorems Các định lý bất toàn của Gödel]|2a1=Linsky|2y=2011|2p=4|3a1=Richardson|3y=1998|3p=15}}

Lý thuyết tập hợp vốn bắt nguồn từ nghiên cứu vô hạn của [[Georg Cantor]], và nó bấy lâu đã là ngọn nguồn của các vấn đề logic toán học đầy thử thách và quan trọng. Một số ví dụ có thể kể đến là [[định lý đường chéo Cantor]], tình trạng của [[tiên đề chọn]], nghi vấn về sự độc lập trong [[giả thuyết continuum]] và các tranh cãi đương đại xoay quanh các tiên đề [[số đếm lớn]].{{sfnm|1a1=Bagaria|1y=2021|2a1=Cunningham}}

Lý thuyết tính toán là phân ngành logic toán học nghiên cứu về các quy trình hiệu quả nhằm giải quyết các vấn đề tính toán. Đơn cử như liệu ta có thể kiếm tìm một quy trình cơ học mà có khả năng xác định một số nguyên dương là [[số nguyên tố]] hay không. Một trong những mục tiêu chính của nó là tìm hiểu xem một vấn đề toán học có thể được giải quyết bằng thuật toán hay không. Lý thuyết tính toán vận dụng đa dạng các công cụ và mô hình lý thuyết, ví dụ như [[máy Turing]], để khám phá điều này.{{sfnm|1a1=Borchert|1y=2006a|1loc=Computability Theory|2a1=Leary|2a2=Kristiansen|2y=2015|2p=195}}

== Lịch sử ==
{{chính|Lịch sử logic học}}
{{multiple image|perrow= 2|total_width=330
| image1= Aristotle_Altemps_Inv8575.jpg
| alt1= Bust of Aristotle
| image2= Avicenne_-_Avicenna_-_Ibn_Sina_(980-1037)_CIPB2067.jpg
| alt2= Portrait of Avicenna
| image3= Guillaume Occam.jpg
| alt3= Portrait of William of Ockham
| image4= Wismar Marienkirche Bronzebüste Gottlob Frege (01-1).JPG
| alt4= Bust showing Gottlob Frege
| footer= Hàng trên: [[Aristoteles]], triết gia đặt nền móng cho quy điển triết học Tây phương;{{sfn|Groarke}} và [[Avicenna]], triết gia đã có công thay thế logic học Aristoteles trong [[Logic trong triết học Hồi giáo|diễn ngôn Hồi giáo]].{{sfn|Lagerlund|2018}} Hàng dưới: [[William xứ Ockham]], một trong những triết gia kinh viện nổi tiếng thời trung cổ;{{sfn|Spade|Panaccio|2019}} và [[Gottlob Frege]], một trong những người có công sáng lập logic toán học hiện đại.{{sfnm|1a1=Haaparanta|1y=2009|1pp=[https://books.google.com/books?id=0jXavKsArnIC&pg=PA4 4–6]|1loc=1. Introduction [Dẫn nhập]|2a1=Hintikka|2a2=Spade|2loc=Modern logic, Logic since 1900 [Logic hiện đại, Logic học từ 1990]|3a=Klement|3y=1995a}}
}}

Logic học đã phát triển độc lập trong nhiều nền văn hóa cổ đại khác nhau. Một trong những nhân vật có những đóng góp sớm nhất là [[Aristoteles]], người đã phát triển ''logic hạn từ'' (''term logic'') trong hai trước tác ''[[Organon]]'' và ''[[Phân tích thứ nhất]]''.{{sfnm|1a1=Kline|1y=1972|1loc="A major achievement of Aristotle was the founding of the science of logic", tr. 53|2a1=Łukasiewicz|2y=1957|2p=7|3a1=Liu|3a2=Guo|3y=2023|3p=15}} Ông đã giới thiệu các khái niệm [[tam đoạn luận giả sử]] (''hypothetical syllogism''){{sfn|Lear|1980|page=34}} và logic mốt thời gian (''temporal modal logic'').{{sfnm|1a1=Knuuttila|1y=1980|1p=71|2a1=Fisher|2a2=Gabbay|2a3=Vila|2y=2005|2p=119}} Các phát kiến của Aristoteles cũng bao gồm logic quy nạp (''inductive logic''){{sfn|Berman|2009|p=133}} cũng như đàm luận về các khái niệm mới như [[thuật ngữ|hạn từ]], vị từ, tam đoạn luận và mệnh đề. Logic Aristoteles được đánh giá rất cao ở châu Âu và Trung Đông vào thời cổ điển và trung cổ. Nó tiếp tục được sử dụng ở phương Tây cho tới đầu thế kỷ thứ 19.{{sfnm|1a1=Frede|2a1=Groarke}} Tới nay thì nhiều công trình logic đã đánh đổ thế độc tôn của logic Aristoteles, song các thấu hiểu then chốt của nó vẫn có ảnh hưởng với các hệ thống logic hiện đại.{{sfnm|1a1=Ewald|1y=2019|2a1=Smith|2y=2022|loc=1. Introduction}}

== Tham khảo ==
=== Chú thích ===
{{tham khảo|group=lower-roman}}

=== Dẫn nguồn ===
{{tham khảo|30em}}

== Thư mục ==
=== Tiếng Việt ===
{{refbegin|indent=yes|38em}}
* {{chú thích sách |author1=Lê Doãn Tá |author2=Duy Tô Hợp |author3=Vũ Trọng Dung |author4=Nguyễn Bằng Tường |author5=Vũ Văn Viên |title=Giáo trình Lôgíc học |date=2007 |publisher=NXB Chính trị quốc gia |location=Hà Nội}}
* {{chú thích sách |author=Phan Đình Nghiệm |title=Nhập môn Logic học |date=2005 |publisher=NXB Đại học Thành phố Hồ Chí Minh |location=Thành phố Hồ Chí Minh}}
{{refend}}

=== Tiếng Anh ===
{{refbegin|indent=yes|38em}}
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* {{chú thích sách |last1=Audi |first1=Robert |author-link=Robert Audi |title=The Cambridge Dictionary of Philosophy |publisher=Cambridge University Press |url=https://philpapers.org/rec/AUDTCD-2 |chapter=Informal logic |year=1999a |access-date=29 December 2021 |archive-date=14 April 2021 |archive-url=https://web.archive.org/web/20210414132344/https://philpapers.org/rec/AUDTCD-2 |url-status=live |isbn=978-1-107-64379-6 |page=435}}
* {{chú thích sách |last1=Audi |first1=Robert |author-link=Robert Audi |title=The Cambridge Dictionary of Philosophy |publisher=Cambridge University Press |url=https://philpapers.org/rec/AUDTCD-2 |chapter=Philosophy of logic |year=1999b |access-date=29 December 2021 |archive-date=14 April 2021 |archive-url=https://web.archive.org/web/20210414132344/https://philpapers.org/rec/AUDTCD-2 |url-status=live |isbn=978-1-107-64379-6 |pages=679–681}}
* {{chú thích tạp chí |last1=Backmann |first1=Marius |title=Varieties of Justification—How (Not) to Solve the Problem of Induction |journal=Acta Analytica |date=1 June 2019 |volume=34 |issue=2 |pages=235–255 |doi=10.1007/s12136-018-0371-6 |s2cid=125767384 |language=en |issn=1874-6349 |doi-access=free }}
* {{chú thích web |last1=Bagaria |first1=Joan |title=Set Theory |url=https://plato.stanford.edu/entries/set-theory/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=23 September 2022 |year=2021}}
* {{chú thích sách |last1=Barnes |first1=Jonathan |title=Truth, etc.: Six Lectures on Ancient Logic |date=25 January 2007 |publisher=Clarendon Press |isbn=978-0-19-151574-3 |pages=274 |url=https://books.google.com/books?id=VwZREAAAQBAJ&pg=PA274 |language=en}}
* {{chú thích web |last1=Benthem |first1=Johan van |title=Modal Logic: Contemporary View: 1. Modal Notions and Reasoning Patterns: a First Pass |url=https://iep.utm.edu/modal-lo/#H1 |website=Internet Encyclopedia of Philosophy |access-date=11 March 2023}}
* {{chú thích sách |last1=Berlemann |first1=Lars |last2=Mangold |first2=Stefan |title=Cognitive Radio and Dynamic Spectrum Access |date=10 July 2009 |publisher=John Wiley & Sons |isbn=978-0-470-75443-6 |page=194 |url=https://books.google.com/books?id=XUGN9tKTIiYC&pg=PA194 |language=en}}
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* {{chú thích web |last1=Weber |first1=Zach |title=Paraconsistent Logic |url=https://iep.utm.edu/para-log/ |website=Internet Encyclopedia of Philosophy |access-date=12 December 2021}}
* {{chú thích sách |last1=Weddle |first1=Perry |title=Argumentation 3 |date= 2011 |publisher=De Gruyter Mouton |isbn=978-3-11-086771-8 |url=https://www.degruyter.com/document/doi/10.1515/9783110867718.383/html |language=en |chapter=36. Informal logic and the eductive-inductive distinction |doi=10.1515/9783110867718.383 |access-date=2 January 2022 |archive-date=31 December 2021 |archive-url=https://web.archive.org/web/20211231172343/https://www.degruyter.com/document/doi/10.1515/9783110867718.383/html |url-status=live |pages=383–388 }}
* {{chú thích tạp chí |last1=Westerståhl |first1=Dag |title=Aristotelian Syllogisms and Generalized Quantifiers |journal=Studia Logica |year=1989 |volume=48 |issue=4 |pages=577–585 |doi=10.1007/BF00370209 |s2cid=32089424 |url=https://philpapers.org/rec/WESASA |access-date=4 January 2022 |archive-date=4 January 2022 |archive-url=https://web.archive.org/web/20220104182746/https://philpapers.org/rec/WESASA |url-status=live }}
* {{chú thích tạp chí |last1=Wilbanks |first1=Jan J. |title=Defining Deduction, Induction, and Validity |journal=Argumentation |date=1 March 2010 |volume=24 |issue=1 |pages=107–124 |doi=10.1007/s10503-009-9131-5 |s2cid=144481717 |url=https://link.springer.com/article/10.1007/s10503-009-9131-5 |language=en |issn=1572-8374 |access-date=8 January 2022 |archive-date=8 January 2022 |archive-url=https://web.archive.org/web/20220108171721/https://link.springer.com/article/10.1007/s10503-009-9131-5 |url-status=live }}
* {{chú thích web |last1=Wilce |first1=Alexander |title=Quantum Logic and Probability Theory: 2.1 Realist Quantum Logic |url=https://plato.stanford.edu/entries/qt-quantlog/#RealQuanLogi |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=11 March 2023 |date=2021}}
* {{chú thích sách |last1=Wile |first1=Bruce |last2=Goss |first2=John |last3=Roesner |first3=Wolfgang |title=Comprehensive Functional Verification: The Complete Industry Cycle |date= 2005 |publisher=Elsevier |isbn=978-0-08-047664-3 |page=447 |url=https://books.google.com/books?id=btl_OX3kJ7MC&pg=PA447 |language=en}}
* {{chú thích web |last1=Willman |first1=Marshall D. |title=Logic and Language in Early Chinese Philosophy |url=https://plato.stanford.edu/entries/chinese-logic-language/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |access-date=11 March 2023 |at=Introduction |date=2022}}
* {{chú thích tạp chí |last1=Wolf |first1=Robert G. |title=Are Relevant Logics Deviant? |journal=Philosophia |year=1978 |volume=7 |issue=2 |pages=327–340 |doi=10.1007/BF02378819 |s2cid=143697796 |url=https://philpapers.org/rec/WOLARL |access-date=4 January 2022 |archive-date=16 December 2021 |archive-url=https://web.archive.org/web/20211216143955/https://philpapers.org/rec/WOLARL |url-status=live }}
* {{chú thích sách |last=Zegarelli |first=Mark |title=Logic For Dummies |url=https://books.google.com/books?id=xm0-0Rs2GVoC&pg=PA30 |page=30 |year=2010 |publisher=John Wiley & Sons |isbn=978-1-118-05307-2 |access-date=7 March 2015 |archive-date=14 May 2015 |archive-url=https://web.archive.org/web/20150514163900/https://books.google.com/books?id=xm0-0Rs2GVoC&pg=PA30 |url-status=live }}
{{refend}}

== Đọc thêm ==
{{refbegin|indent=yes|38em}}
* {{chú thích sách |last1=Barwise |first1=Jon |author-link=John Barwise |title=Handbook of Mathematical Logic. |date=1989 |publisher=Elsevier |isbn=978-0-08-093364-1}}
* {{chú thích sách |last1=Belnap |first1=Nuel |author-link=Nuel Belnap |editor1-last=Dunn |editor1-first=J. Michael |editor2-last=Epstein |editor2-first=George |title=Modern uses of multiple-valued logic: invited papers from the Fifth International Symposium on Multiple-Valued Logic, held at Indiana University, Bloomington, Indiana, May 13–16, 1975 |url=https://archive.org/details/modernusesofmult0000inte |date=1977 |publisher=Springer |isbn=978-90-277-0747-5 |chapter=A useful four-valued logic}}
* {{chú thích sách |last1=Bocheński |first1=Józef Maria |author-link=Józef Maria Bocheński |title=A Precis of Mathematical Logic |date=1959 |publisher=Springer Netherlands |url=https://books.google.com/books?id=4I8XAAAAIAAJ |language=en}}
* {{chú thích sách |last1=Bocheński |first1=Józef Maria |title=A History of Formal Logic |date=1970 |publisher=Chelsea Publishing Company |isbn=978-0-8284-0238-5 |url=https://books.google.com/books?id=cgAZAQAAIAAJ |language=en}}
* {{chú thích sách |last=Brookshear |first=J. Glenn |title=Theory of computation: formal languages, automata, and complexity |publisher=Benjamin/Cummings Pub. Co. |year=1989 |isbn=978-0-8053-0143-4 }}
* {{chú thích sách |last1=Cohen |first1=Robert S. |last2=Wartofsky |first2=Marx W. |title=Logical and Epistemological Studies in Contemporary Physics |date=2012 |publisher=Springer Science & Business Media |isbn=978-94-010-2656-7 |url=https://books.google.com/books?id=MY5qCQAAQBAJ |language=en}}
* {{chú thích sách |last1=Finkelstein |first1=David |editor1-last=Cohen |editor1-first=Robert S. |editor2-last=Wartofsky |editor2-first=Marx W. |title=Boston Studies in the Philosophy of Science: Proceedings of the Boston Colloquium for the Philosophy of Science 1966/1968 |date=2012 |publisher=Springer Science & Business Media |isbn=978-94-010-3381-7 |chapter-url=https://books.google.com/books?id=qw38CAAAQBAJ&pg=PA199 |language=en |chapter=Matter, Space, and Logic}}
* {{chú thích sách |last1=Gabbay |first1=Dov M. |author-link=Dov Gabbay |last2=Guenthner |first2=Franz |title=Handbook of Philosophical Logic: Volume I: Elements of Classical Logic |date=2011 |publisher=Springer Netherlands |isbn=978-94-009-7068-7 |url=https://books.google.com/books?id=IZI7ngEACAAJ |language=en}}
* {{chú thích web |url=http://www.etymonline.com/index.php?term=logic |title=Logic |last=Harper |first=Robert |year=2001 |website=[[Online Etymology Dictionary]] |access-date=8 May 2009 |archive-date=6 February 2009 |archive-url=https://web.archive.org/web/20090206201125/http://www.etymonline.com/index.php?term=logic |url-status=live }}
* {{chú thích sách |last1=Hilbert |first1=David |author-link=David Hilbert |last2=Ackermann |first2=Wilhelm |title=Grundzüge der theoretischen Logik |date=21 November 2013 |publisher=Springer-Verlag |isbn=978-3-662-41928-1 |url=https://books.google.com/books?id=NEiGBwAAQBAJ |language=de}}
* {{chú thích sách |last1=Hodges |first1=Wilfrid |author-link=Wilfrid Hodges |title=Logic |date=2001 |publisher=Penguin Adult |isbn=978-0-14-100314-6 |url=https://books.google.com/books?id=xIcTc2d4y_AC |language=en}}
* {{chú thích web |last1=Hofweber |first1=Thomas |title=Logic and Ontology |url=http://plato.stanford.edu/entries/logic-ontology/ |website=The Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |date=2021}}
* {{chú thích sách |last1=Hughes |first1=R. I. G. |title=A Philosophical Companion to First-order Logic |date=1993 |publisher=Hackett Publishing |isbn=978-0-87220-181-1 |url=https://books.google.com/books?id=gk1Tp_7cgiEC |language=en}}
* {{chú thích sách |last1=Mendelson |first1=Elliott |author-link=Elliott Mendelson |title=Introduction to Mathematical Logic |edition=6th |date= 2015 |publisher=Taylor & Francis |isbn=978-1-4822-3772-6 |url=https://books.google.com/books?id=5GTpngEACAAJ |language=en}}
* {{chú thích tạp chí |last1=Smith |first1=Barry |author-link=Barry Smith (ontologist) |title=Logic and the Sachverhalt |journal=The Monist |date=1989 |volume=72 |issue=1 |pages=52–69 |doi=10.5840/monist19897212 |url=https://philpapers.org/rec/SMILAT-3}}
* {{chú thích sách |last1=Whitehead |first1=Alfred North |author1-link=Alfred North Whitehead |last2=Russell |first2=Bertrand |author2-link=Bertrand Russell |title=Principia Mathematica |date=1910 |publisher=Rough Draft Printing |url=https://books.google.com/books?id=MZpJngEACAAJ |language=en}}
{{refend}}

== Liên kết ngoài ==
{{Sister project links|Logic}}
{{Library resources box}}
* {{springer|title=Logical calculus|id=p/l060690}}
* [http://somerby.net/mack/logic A Logic Calculator] Một ứng dụng web để đánh giá các khẳng định đơn giản thông qua logic tượng trưng. {{en}}
* [http://www.ontology.co/history-of-logic.htm Bản thể học và Lịch sử Logic. Một dẫn nhập] với thư mục dẫn chú. {{en}}

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