OpenLLM-France/wikimedia huggingface dataset:
# Introspector/GccCpp/tree-dump.c/char class switch

If we look at the assembly the switch for the node class, we will see the following :

### Block L5

L5:
Jump to #Block L32 if we are equal to a "e"
Jump to #Block L30 if we are greater than a "e"
Jump to block #Block L25 if we are equal to a "2"
Jump to block #Block L31 if we are greater than a "2"
Jump to block #Block L29 if we have a "1"

### Block L31

Jump to #Block L25 if we have a "<" else jump to #Block L29

### Block L30

Subtract "r" from the eax
Jump to #Block L29 Jump Above
Jump to #Block L32 if we are equal to a "e"
# Introspector/GccCpp/tree-dump.c/test rtl

here is something :
# Introspector/KifTutorial

This is a short example based tutorial of Knowledge Interchange Format. It's not complete nor very correct, but it should give you an idea about what you can do with KIF.
The knowledge base I'm using here is a simple representation of human relations. Basically two types of relation exist: family and friends. There are three kinds of family: father, mother, child. There is only one kind of friend. For our purposes partners are also friends. Let's start by entering some data:
Fred and John are males, Martha, Joan, Betty and Alice are females.
John is the father of Fred
Martha is the mother of Fred
Fred is the father of Pete
Joan is the mother of Pete
Betty is a friend of Pete
Martha is the mother of Alice
Alice is the mother of Betty
Now it's nice if we could get some information from these relations. For example _we_ know Fred is the child of Pete, but the computer doesn't. Let's tell him that.
Know we say that somebody, called ?c for now, is a child of somebody, called ?p for now, if ?p is the mother of ?c or if ?p is the father of ?c.
Let's define some other relations:
A son is a male child. A daughter is a female child.
Now to querying, getting information from the knowledge base. Here are a few queries with their result behind the =>.
That were simple queries that only return true or false. Note that your implementation may display the results in a different way (since I'm not using an interpreter at all (except my brains) while writing this it's kinda logical actually).
Here we ask the system: for each object (known as ?x for now) in the universe of discourse the set which contains every object that exists) that is a male ((male ?x) => true) tell me what the value of ?w is.
Next example, querying with two variables:
As you can see using two variables also yields the correct result.
Now let's select in queries. Say we want the sister of Fred.
As you can imagine we can program relations out of this:
Now to 'bottom'. Sometimes you want to say: this can be anything, but I don't care what it is. KIF supports this through bottom. If you write bottom you're saying: this can be anything, but you will not be informed of what it is. For example:
In this query we asked for all sons, but not about their parents.
More to follow, when I update this wiki :-).
# Introspector/GccCpp/rtl.h

here is my start
# Korean/Lesson I8

* Other languages...
* Learn Korean (Introduction)
* — Reading and writing •
* Conversation
* 1급: Beginner —
* 1. Greetings •
* 2. Forming sentences •
* 3. Connective forms and negation •
* 4. Colors •
* 5. Recreation / In a taxi •
* 6. Family •
* 7. Around the house •
* 8. Using the telephone •
* 9. School •
* 10. Shopping •
* 11. Onomatopoeia
* 2단계: High beginner •
* 3단계: Low intermediate •
* 4단계: High intermediate •
* 5단계: Low advanced •
* 6단계: Advanced
* Grammar

## Using the Telephone

* 여보세요? Yeoboseyo? Hello? (used only in the context of a telephone call)
* 안녕하십니까? Anyeong hashimnikka? Hello? (literally "Are you at peace?"), used in more formal (i.e. working relationships) situations.
* 존 계십니까? John gyesimnikka? Is John there?
* 누구십니까? Nugusipnikka? Who's calling?
# Korean/Lesson I11

* Other languages...
* Learn Korean (Introduction)
* — Reading and writing •
* Conversation
* 1급: Beginner —
* 1. Greetings •
* 2. Forming sentences •
* 3. Connective forms and negation •
* 4. Colors •
* 5. Recreation / In a taxi •
* 6. Family •
* 7. Around the house •
* 8. Using the telephone •
* 9. School •
* 10. Shopping •
* 11. Onomatopoeia
* 2단계: High beginner •
* 3단계: Low intermediate •
* 4단계: High intermediate •
* 5단계: Low advanced •
* 6단계: Advanced
* Grammar
Onomatopoeia 의성어 (擬聲語) ui seong eo are words used to imitate sounds.
* 빵 (ppang) - Bang!
* 아야 (a-ya) - Ouch!
* 앗 (at) - Oops!
* 음 (eum) - Um...
* 냠냠 (nyam-nyam) - sound made when chewing food
* 쾅 (kwang) - Crashing sound
* 멍멍 (meong-meong) - Dog barking
* 칙칙폭폭 (chik-chik-pok-pok) - train sound
* 꿀꿀 (kkul-kkul) - Pig noise
* 펄럭펄럭 (peol-leok-peol-leok)- flapping of cloth
* 삐약삐약 (ppi-yak-ppi-yak) - chicks chirping
* 야옹 (ya-ong) - meow of cat
<<Lesson 10 | Lesson 11
# Korean/Lesson I12

* Other languages...
* Learn Korean (Introduction)
* — Reading and writing •
* Conversation
* 1급: Beginner —
* 1. Greetings •
* 2. Forming sentences •
* 3. Connective forms and negation •
* 4. Colors •
* 5. Recreation / In a taxi •
* 6. Family •
* 7. Around the house •
* 8. Using the telephone •
* 9. School •
* 10. Shopping •
* 11. Onomatopoeia
* 2단계: High beginner •
* 3단계: Low intermediate •
* 4단계: High intermediate •
* 5단계: Low advanced •
* 6단계: Advanced
* Grammar
Onomatopoeia 의성어 (擬聲語) ui seong eo are words used to imitate sounds.
* 빵 (ppang) - Bang!
* 아야 (a-ya) - Ouch!
* 앗 (at) - Oops!
* 음 (eum) - Um...
* 냠냠 (nyam-nyam) - sound made when chewing food
* 쾅 (kwang) - Crashing sound
* 멍멍 (meong-meong) - Dog barking
* 칙칙폭폭 (chik-chik-pok-pok) - train sound
* 꿀꿀 (kkul-kkul) - Pig noise
* 펄럭펄럭 (peol-leok-peol-leok)- flapping of cloth
* 삐약삐약 (ppi-yak-ppi-yak) - chicks chirping
* 야옹 (ya-ong) - meow of cat
<<Lesson 9 | Lesson 10
# Korean/Lesson I6

* Other languages...
* Learn Korean (Introduction)
* — Reading and writing •
* Conversation
* 1급: Beginner —
* 1. Greetings •
* 2. Forming sentences •
* 3. Connective forms and negation •
* 4. Colors •
* 5. Recreation / In a taxi •
* 6. Family •
* 7. Around the house •
* 8. Using the telephone •
* 9. School •
* 10. Shopping •
* 11. Onomatopoeia
* 2단계: High beginner •
* 3단계: Low intermediate •
* 4단계: High intermediate •
* 5단계: Low advanced •
* 6단계: Advanced
* Grammar

### Vocabulary

* 할아버지 Grandfather
* 할아버님 Grandfather (formal)
* 할머니 Grandmother
* 할머님 Grandmother (formal)
* 외할아버지 Grandfather (on Mother's side)
* 외할아버님 Grandfather (on Mother's side) (formal)
* 외할머니 Grandmother (on Mother's side)
* 외할머님 Grandmother (on Mother's side) (formal)
* 아버지 Father (formal)
* 아버님 Father (very formal)
* 아빠 Father (informal)
* 어머니 Mother (formal)
* 어머님 Mother (very formal)
* 엄마 Mother (informal)
* 형 Elder brother (of a male)
* 누나 Elder sister (of a male)
* 오빠 Elder brother (of a female)
* 언니 Elder sister (of a female)
* 남동생 Younger brother
* 여동생 Younger sister
* 동생 Younger sibling
* 성함 Name (formal)
* 존함 Name (old fashioned, very formal)
* 이름 Name (Informal)
Note: -님 words such as 아버님, 어머님 are very formal.
Addressing Parents-in-Law:
As in English-speaking relationships, how one addresses one's Father-in-law and Mother-in-law varies greatly on how friendly the relationship is, as well as the customs and dialect of the geographic region, etc. Before marriage, it is common for one to call his/her girlfriend/boyfriend's parents 아버지 or 아버지님 and 어머니 or 어머님.
After marriage, the wife may address her new parents-in-law in the same way, however, a husband would call his mother-in-law 장모님, and his father-in-law 장인어른. Note that after marriage, how one speaks to one's parents-in-law becomes more formal, adding the honorific -님 suffix.

## Conversation

Kim: 안녕하세요.
John: 안녕하세요.
Kim: 성함이 어떻게 되세요?
John: John이에요. 저는 선생님이에요. 그쪽은 성함이 어떻게 되시나요?
Kim: 김이에요.
John: 만나서 반갑습니다.
Kim: 미국 사람이세요?
John: 네, 미국에서 왔어요.
Kim: 가족은 몇 분이세요?
John: 다섯 명 있어요. 형과 여동생이 있어요. 형은 의사예요. 여동생은 대학생이에요. 김씨는 형제가 있으신가요?
Kim: 없어요. 저희 다시 봐요.
John: 안녕히 가세요.

## Translation

Kim: Hello.
John: Hello.
Kim: What's your name.
John: I'm John. I'm a teacher. What's your name?
Kim: I'm Kim.
John: Nice to meet you.
Kim: Are you American?
John: Yes, I came from America.
Kim: How many people are in your family?
John: There are 5 people. I have an older brother and a younger sister. My brother is a doctor. My sister is a University student. Do you have siblings?
Kim: I don't. Let's meet again.
John: Good Bye.
<<Lesson 5 | Lesson 6 | Lesson 7>>
# Korean/Lesson I5

* Other languages...
* Learn Korean (Introduction)
* — Reading and writing •
* Conversation
* 1급: Beginner —
* 1. Greetings •
* 2. Forming sentences •
* 3. Connective forms and negation •
* 4. Colors •
* 5. Recreation / In a taxi •
* 6. Family •
* 7. Around the house •
* 8. Using the telephone •
* 9. School •
* 10. Shopping •
* 11. Onomatopoeia
* 2단계: High beginner •
* 3단계: Low intermediate •
* 4단계: High intermediate •
* 5단계: Low advanced •
* 6단계: Advanced
* Grammar

### Vocabulary

* Taxi 택시
* Hour 시간
* Minute 분
* Won (Korean currency) 원
* Around, About ~ 정도

### Conversation

Joie: 강남역까지 가고 싶습니다. / I want to go to Kang-nam station
Taxi driver: 네 강남역까지 가겠습니다. / Yes I will drive to Kang-nam station
Joie: (시간이) 얼마나 걸립니까? / How long does it take?
Taxi driver: 20분 정도 걸립니다. / It takes around 20 minutes
Joie: 얼마입니까? / How much is it?
Taxi driver: 5000원 입니다. / It is 5000 wons
Joie: 감사합니다. / Thank you
* How far is it there? (거리가) 얼마나 멉니까?
* How long does it take? (거리가) 얼마나 걸립니까?
* Turn left 왼쪽으로 돌으십시오.
* Turn right 오른쪽으로 돌으십시오.
* Go straight 직진 하십시오.
<<Lesson 4 | Lesson 5 | Lesson 6>>
# Korean/Lesson I9

* Other languages...
* Learn Korean (Introduction)
* — Reading and writing •
* Conversation
* 1급: Beginner —
* 1. Greetings •
* 2. Forming sentences •
* 3. Connective forms and negation •
* 4. Colors •
* 5. Recreation / In a taxi •
* 6. Family •
* 7. Around the house •
* 8. Using the telephone •
* 9. School •
* 10. Shopping •
* 11. Onomatopoeia
* 2단계: High beginner •
* 3단계: Low intermediate •
* 4단계: High intermediate •
* 5단계: Low advanced •
* 6단계: Advanced
* Grammar
* Kindergarten 유치원 (yu chi won)
* Elementary school 초등학교 (cho deng hak gyo)
* Middle school 중 학 교 (jung hak gyo)
* High school 고등학교 (go deng hak gyo)
* University 대 학교 (dae hak gyo)
* Graduate School 대 학원 (dae hak won)
* After-school institute, providing instruction on a particular subject 학원 (hak won)
* Major 전 공 (jeon gong)
* Minor 부 전 공 (bu jeon gong)
* Study 공 부 (gong bu)
* Dorm 기 숙 사 (gi suk sa)
* School 학 교 (hak gyo)
* College 대 학 (dae hak)
* Philosophy 철 학 (cheol hak)
<<Lesson 8 | Lesson 9 | Lesson 10>>
# Korean/Lesson I4

* Other languages...
* Learn Korean (Introduction)
* — Reading and writing •
* Conversation
* 1급: Beginner —
* 1. Greetings •
* 2. Forming sentences •
* 3. Connective forms and negation •
* 4. Colors •
* 5. Recreation / In a taxi •
* 6. Family •
* 7. Around the house •
* 8. Using the telephone •
* 9. School •
* 10. Shopping •
* 11. Onomatopoeia
* 2단계: High beginner •
* 3단계: Low intermediate •
* 4단계: High intermediate •
* 5단계: Low advanced •
* 6단계: Advanced
* Grammar

## Colors

As well as having two sets of numbers, Korean also uses two sets of colors, one being the native Korean set, the other being derived from Chinese characters hanja 한자 (漢字).

### Native Korean set

Various like dozens of Korean words represent similar colors but express the different impression of colors. The following Korean words about color are the most neutral and normal words.
Korean colors may be followed by native word, 빛 or 빛깔, or followed by 색 (色) which is derived from Chinese characters. Each word means color.
| Name | Adjective | Verb | Translation | Notes |
| 빨강 | 빨간 | 빨갛다 | red, crimson |
| 뻘건색 | 뻘건 | 뻘겋다 | red, ruddy |
| 파랑 | 파란 | 파랗다 | blue, bluegreen |
| 퍼런색 | 퍼런 | 퍼렇다 | darkblue |
| 보라색 | 보라색 | none | violet |
| 초록(풀빛) | 푸른 | 푸르다 | darkgreen, azure | The adjectives for blue may be used with green. 풀빛 means grass-light. |
| 노랑 | 노란 | 노랗다 | yellow |
| 누런색 | 누런 | 누렇다 | yellow, sallow |
| 하양 | 하얀 or 흰 | 하얗다 | white |
| 허연색 | 허연 | 허옇다 | pure white |
| 검정 | 검은 | 검다 | black |
| 까만색 | 까만 | 까맣다 | black, ebony |

#### Examples

* 빨간 입술 red lips
* 파란 하늘 blue sky
* 푸른 초원 green grassland
* 노란 병아리 yellow chick
* 흰 눈 white snow
* 검은 눈동자 black pupil

### Chinese character set

| 적 (赤), 홍 (紅) | red |
| 청 (靑) | blue |
| 녹 (綠) | green |
| 황 (黃) | yellow |
| 주황 (硃黃) | orange |
| 남 (藍) | navy |
| 자주 (紫硃) | purple |
| 회 (灰) | gray |
| 백 (白) | white |
| 흑 (黑) | black |
* 백인 (白人) white person
* 흑인 (黑人) black person
* 흑백필름 (黑白 film) black & white film
* 적색신호 (赤色信號) red light signal
* 청바지(靑바지) blue jeans
<<Lesson 3 | Lesson 4 | Lesson 5>>
# Korean/Lesson I7

* Other languages...
* Learn Korean (Introduction)
* — Reading and writing •
* Conversation
* 1급: Beginner —
* 1. Greetings •
* 2. Forming sentences •
* 3. Connective forms and negation •
* 4. Colors •
* 5. Recreation / In a taxi •
* 6. Family •
* 7. Around the house •
* 8. Using the telephone •
* 9. School •
* 10. Shopping •
* 11. Onomatopoeia
* 2단계: High beginner •
* 3단계: Low intermediate •
* 4단계: High intermediate •
* 5단계: Low advanced •
* 6단계: Advanced
* Grammar

### Vocabulary

* house 집
* home 가정
* apartment 아파트
* bathroom 화장실 or 욕실
* kitchen 부엌 or 주방
* bedroom 침실 or 방
* living room 거실
* garden 정원
* garage 차고
* table 탁자
* dining table 식탁
* chair 의자
* toilet 변기
* sink 싱크대
* window 창문
* door 문
# Acer Aspire 1203XC
## Year of First Manufacture

* First Manufactured:

## CPU

* CPU: Intel Celeron 1.3 GHz

## Memory

* Memory: 512MB (Maximum 640MB)
* Memory Type: 144 Pin 3.3v PC133 SDRAM SoDimm

## Video Graphics Display

* Video Graphics Chipset: S3 Savage4 (Shared Memory) UMA
* Screen Size: 14.1 inch
* Maximum Screen Resolution: 1024 x 768

## Audio

* Audio Chipset: Via VT8231

## Pointing Device

* Pointing Device Type: Touchpad
# Language Acquisition/Nature or Nurture/Animal Language

In our introductory book to linguistics, we looked at design features of human language that differentiate it from animal language:
* Reflexivity: We can use language to talk about language, e.g. Don't use a preposition at the end of a sentence!
* Displacement: We can talk about events spatially and temporally distant from us, e.g. I saw a strange guy in the pub yesterday.
* Arbitrariness: There is little connection between signifier and signified. For example, the word moon is completely random; the moon does not make a 'moo' sound like a cow or otherwise exhibit features that would justify the use of moon as a sign.
* Productivity (or creativity in Chomskyan linguistics): There is a limitless number of potential utterances in the language. The car ate the marshmallow-hating helicopter, for example, is a sentence that nobody has seen before, but any speaker of English can understand it.
* Cultural transmission: Culture is passed on from mother to child by language acquisition. This culture is not innate, unlike animal language. Cows are biologically designed to go moo, and pigs to go oink; there is no culture transmission there.
* Duality: Human language has two distinct levels, the sound and the meaning. Sounds are limited but meaning is not. We can play with the sounds in our language to produce different meanings. Consider the minimal pair made and paid. Made is broken down to the phonemes /m/, /eɪ/ and /d/, and we can swap /m/ for /p/ to produce a word with a different meaning altogether. However, animals do not have this two-level distinction. A pig may say oink, a word that means 'I'm starving', but it cannot reformulate the sounds to produce a different utterance, say, roink, replacing the glottal stop /ʔ/ at the beginning with /ɹ/. The signifier and the signified are processed on the same level, rather than two different levels.
# Language Acquisition/Nature or Nurture/Competence and Performance

To understand the notion of UG, the distinction between competence and performance is essential. Competence is inside the language user's head, while performance is what the language user actually produces.

## E-language and I-language

The notion of E-language ('externalised' language) is associated with Bloomfield's structuralist tradition of linguistics. Linguists who study E-languages collect utterances to create corpora. They then attempt to describe these data.
Chomsky believed the study of E-language was insufficient. E-language only looks at what people say. Any corpus, regardless of size, only contains a small percentage of what language users can produce. (This is because the number of sentences that can be produced is essentially limitless - we will look at this below.) Therefore, he proposed the notion of I-language, which describes the linguistic knowledge of language users. Language users know how to form sentences that conform to the grammatical rules of the language. They will not produces sentences like *Him is good very, and they can also tell that such sentences are wrong. This constitutes the linguistic intuition of language users.
# Language Acquisition/Nature or Nurture/Linguistic Nativism

Linguistic nativism is the idea that language is 'hard-wired' into our brains at birth. The hard-wired knowledge is called Universal Grammar (UG), a grammar common to all languages in the world. This unit introduces you to this idea.
It is often said that UG is like a seed. Obviously, seeds of apple trees are not trees at birth, but given nourishment, such as sunlight and water, they will grow into apple trees. They will not grow into orange trees or pear trees.
UG is the knowledge of language innate to all humans. Everyone, save for those with certain language disorders, possess UG, according to Chomsky. UG morphs into competence, which we will later see. Its distinction from performance is an important part of Chomsky's work, and will be discussed in this chapter.
UG does not claim the existence of a set of rules common to every language, say, that the subject should be the first word of every sentence. This is clearly false, since languages with word orders other than SVO and SOV do exist, uncommon as they are among the major world languages. German, for example, has V2 word order, in which the verb must come second in a sentence, but any other element - subject, object, adjunct - can be placed first. Some linguists, most notably Joseph Greenberg, have attempted to generalise sets of such rules, such as this:
(1) In conditional statements, the conditional clause precedes the conclusion as the normal order in all languages.
This is a linguistic universal, but it is not part of UG. UG does not aim at stating rules. Instead, UG attempts to generalise a set of principles that govern language. We will look into the concept of principles in this unit.

## Table of Contents

* Competence and Performance
* Principles and Parameters
* Poverty of the Stimulus
* Language Acquisition Device
# Language Acquisition

This is a book on language acquisition.

## Contents

* Introduction

### Part I: Nature or Nurture?

* Animal Language
* Teaching Language to Animals
* Rationalism and Empricism
* Verbal Behaviour
** Chomsky's Critique
* Linguistic Nativism
** Competence and Performance
** Principles and Parameters
** Poverty of the Stimulus
** Language Acquisition Device
** Everett's Criticism
* Critical Period Hypothesis
** Feral Children

### Part II: Aspects of First Language Acquisition

* Acquiring Phonetics
* Acquiring Phonology
* Acquiring Lexicon
* Acquiring Morphology
* Acquiring Syntax
* Acquiring Semantics
* Learning to Read
* Learning to Write
* Developmental Disorders
** Specific Language Impairment

### Part III: Second Language Acquisition

* Chomskyan Approach
# Locksmithing/Tools
## Type of tool

The following is a list of tools that would be found in a commercial set. Depending on the size of the set it may contain sizes and/or designs to better fit different locks. Most all of them are made of thin steel or other hard metals.

### Tool sets

The tools for lock picking are usually different for each type of lock and can sometimes be improvised from common items.
Lock pick kits can be purchased openly via the internet. Many different selections are present. 9-piece sets and a 32-piece set equipped with a Pick Gun for example differ in value and price greatly. However, many lock pickers state that for most locking devices, a basic set of 5 picks should be enough; therefore it is unnecessary even to carry around a wide variety of professional lockpicks.

### Tension wrench

The tension wrench is used to apply tension to pins to keep pins from being pushed back down by springs after they are correctly set. Usually anywhere from 1/8th inch to 1/16th inch wide, bent into an L with a quarter twist on the long side to allow tension to be put on it (in the direction the lock is desired to be turned).

### Hook pick

The hook pick is similar to the half diamond pick, but has a hook shaped tip rather than a half diamond shape.
# Logic for Computer Science

This book discusses logic as a tool for computer science; a field that uses logic at all levels. It provides a survey of mathematical logic and its various applications. Some areas where it is particularly important include:
    Digital circuit design
    Complexity theory (NP equivalent to Existential second-order logic)
    Database Systems (SQL; roughly predicate/first-order logic)
    Computer-aided verification (Temporal logic & model checking)
    Programming languages (lambda calculus)
    AI, expert systems, inference engines
    Distributed Systems
    Logic Programming
    Computer Security
After covering basic material of propositional logic and first-order logic, the course presents the foundations of finite model theory and descriptive complexity. Other topics, including logic programming, non-monotonic reasoning, temporal logic, and reasoning about knowledge and belief, are surveyed as time allows. These notes were taken by student scribes.

## Table of Contents

* Chapter 1: Propositional Logic
* Basic concepts in logic
* Deductive systems ("Natural Deduction")
* Propositional Resolution
* Complexity of various problems
* Chapter 2: First-Order Logic (FO)
* Syntax and semantics
* A deduction calculus
* Gödel's completeness theorem
* Chapter 3: Around and about FO
* Fragments of FO
* Characteristics of FO
* Higher-Order Logics
* Chapter 4: Querying I: Expressive Power
* Query and definability
* Results for FO on popular structures
* Results for other logics and structures
* Chapter 5: Querying II: Games
* Ehrenfeucht's games and Fraisse's theorem
* Ehrenfeucht-Fraisse method
* Higher order games and 0-1 Laws
* Chapter 6: Reasoning
* Deduction
* Non-monotonic reasoning
* Uncertain and Case-based reasoning
* Chapter 7: Some Applications
* Database theory
* Complexity theory
* Expert systems

## References

You may also find the following references useful
* Mathematical Logic. H.-D. Ebbinghaus, J. Flum, and W. Thomas
* Foundations of Databases. Abiteboul, Hull, Vianu. Available here: http://www-cse.ucsd.edu/users/vianu/BOOK/book.html
* Computational Complexity. Christos H. Papadimitrou.
* Elements of Finite Model Theory. Leonid Libkin.
* Finite Model Theory and Its Applications. Grädel, Kolaitis, Libkin, Marx, Spencer, Vardi, Venema, Weinstein
* Gödels Proof. Ernest Nagel and James R. Newman
* Language, Proof, and Logic. John Barwise and John Echtermendy
* A Profile of Mathematical Logic. Howard DeLong
# Logic for Computer Science/Temporal Logic
## Modal Logic

Modal logic expands propositional logic by operators for the modalities possibility and necessity. These basic modal operators are usually written $\Box$ (or L) for necessarily and $\Diamond$ (or M) for possibly. Each can be defined from the other in the following way:
    $\Diamond P\leftrightarrow \lnot \,\Box \,\lnot \,P.$