In mathematical logic, a formula is satisfiable if it is true under some assignment of values to its variables. For example, the formula is satisfiable because it is true when and , while the formula is not satisfiable over the integers. The dual concept to satisfiability is validity; a formula is valid if every assignment of values to its variables makes the formula true. For example, is valid over the integers, but is not. Formally, satisfiability is studied with respect to a fixed logic defining the syntax of allowed symbols, such as first-order logic, second-order logic or propositional logic. Rather than being syntactic, however, satisfiability is a semantic property because it relates to the meaning of the symbols, for example, the meaning of in a formula such as . Formally, we define an interpretation (or model) to be an assignment of values to the variables and an assignment of meaning to all other non-logical symbols, and a formula is said to be satisfiable if there is some interpretation which makes it true. While this allows non-standard interpretations of symbols such as , one can restrict their meaning by providing additional axioms. The satisfiability modulo theories problem considers satisfiability of a formula with respect to a formal theory, which is a (finite or infinite) set of axioms. Satisfiability and validity are defined for a single formula, but can be generalized to an arbitrary theory or set of formulas: a theory is satisfiable if at least one interpretation makes every formula in the theory true, and valid if every formula is true in every interpretation. For example, theories of arithmetic such as Peano arithmetic are satisfiable because they are true in the natural numbers. This concept is closely related to the consistency of a theory, and in fact is equivalent to consistency for first-order logic, a result known as Gödel's completeness theorem. The negation of satisfiability is unsatisfiability, and the negation of validity is invalidity. These four concepts are related to each other in a manner exactly analogous to Aristotle's square of opposition. The problem of determining whether a formula in propositional logic is satisfiable is decidable, and is known as the Boolean satisfiability problem, or SAT. In general, the problem of determining whether a sentence of first-order logic is satisfiable is not decidable. In universal algebra, equational theory, and automated theorem proving, the methods of term rewriting, congruence closure and unification are used to attempt to decide satisfiability. Whether a particular theory is decidable or not depends whether the theory is variable-free and on other conditions. (Wikipedia).
Irrigation Efficiencies - Part 1
From playlist TEMP 1
The idea of ‘atonement’ sounds very old-fashioned and is deeply rooted in religious tradition. To atone means, in essence, to acknowledge one’s capacity for wrongness and one’s readiness for apology and desire for change. It’s a concept that every society needs at its center. For gifts and
From playlist RELATIONSHIPS
Is There an Alternative to Political Correctness?
Political correctness aims for some very nice results, but its means have a habit of upsetting a lot of people. Might there be an alternative to it? We think there is, and it’s called Politeness. If you like our films, take a look at our shop (we ship worldwide): https://goo.gl/iVqWJ1 Joi
From playlist WORK + CAPITALISM
Proof: Supremum and Infimum are Unique | Real Analysis
If a subset of the real numbers has a supremum or infimum, then they are unique! Uniqueness is a tremendously important property, so although it is almost complete trivial as far as difficulty goes in this case, we would be ill-advised to not prove these properties! In this lesson we'll be
From playlist Real Analysis
Maximum and Minimum of a set In this video, I define the maximum and minimum of a set, and show that they don't always exist. Enjoy! Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCZggpJZvUXnUzaw7fHCtoh
From playlist Real Numbers
How to Solve Absolute Value Inequalities
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How to Solve Absolute Value Inequalities
From playlist College Algebra
Absolute Value Equations & Inequalities (1 of 4: Visualising an equation)
More resources available at www.misterwootube.com
From playlist Working with Functions
Math 101 Fall 2017 112917 Introduction to Compact Sets
Definition of an open cover. Definition of a compact set (in the real numbers). Examples and non-examples. Properties of compact sets: compact sets are bounded. Compact sets are closed. Closed subsets of compact sets are compact. Infinite subsets of compact sets have accumulation poi
From playlist Course 6: Introduction to Analysis (Fall 2017)
What is the definition of absolute value
http://www.freemathvideos.com In this video playlist you will learn how to solve and graph absolute value equations and inequalities. When working with absolute value equations and functions it is important to understand that the absolute value symbol represents the absolute distance from
From playlist Solve Absolute Value Equations
Lecture 20 - Introduction to NP-completeness
This is Lecture 20 of the CSE373 (Analysis of Algorithms) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1997. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/1997/lecture22.pdf
From playlist CSE373 - Analysis of Algorithms - 1997 SBU
CSE 373 --- Lecture 20: Satisfiability (Fall 2021)
11/23/21
From playlist CSE373 --- Analysis of Algorithms (Fall 2021)
On Approximability of CSPs on Satisfiable Instances - Subhash Khot
Computer Science/Discrete Mathematics Seminar I Topic: On Approximability of CSPs on Satisfiable Instances Speaker: Subhash Khot Affiliation: New York University Date: November 22, 2021 Constraint Satisfaction Problems (CSPs) are among the most well-studied problems in Computer Science,
From playlist Mathematics
This is Lecture 21 of the CSE373 (Analysis of Algorithms) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1997. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/1997/lecture23.pdf
From playlist CSE373 - Analysis of Algorithms - 1997 SBU
CSE 373 -- Lecture 24, Fall 2020
From playlist CSE 373 -- Fall 2020
This is Lecture 24 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www3.cs.stonybrook.edu/~skiena/] at Stony Brook University in 2016. The lecture slides are available at: https://www.cs.stonybrook.edu/~skiena/373/newlectures/lecture20.pdf More inf
From playlist CSE373 - Analysis of Algorithms 2016 SBU
Introduction to Linear Inequalities in Two Variables (L11.6)
This lesson introduces linear inequalities in two variables. Video content created by Jenifer Bohart, William Meacham, Judy Sutor, and Donna Guhse from SCC (CC-BY 4.0)
From playlist Solving Linear Inequalities in Two Variables
Yongnam Lee: Q-Gorenstein Deformations and their applications
In this talk we will discuss Q-Gorenstein schemes and Q-Gorenstein morphisms in a general setting. Based on the notion of Q-Gorenstein morphism, we define the notion of Q-Gorenstein deformations and discuss their properties. Versal properties of Q-Gorenstein deformations and their applicat
From playlist HIM Lectures: Junior Trimester Program "Algebraic Geometry"
Hall's Theorem and Condition for Bipartite Matchings | Graph Theory, Hall's Marriage Theorem
What are Hall's Theorem and Hall's Condition for bipartite matchings in graph theory? Also sometimes called Hall's marriage theorem, we'll be going it in today's video graph theory lesson! A bipartite graph with partite sets U and W, where U has as many or fewer vertices than W, satisfie
From playlist Graph Theory
CERIAS Security: An Algebra for Specifying High-level Security Policies 2/5
Clip 2/5 Speaker: Qihua Wang · Purdue University A high-level security policy states an overall requirement for a sensitive task. One example of a high-level security policy is a separation of duty policy, which requires a sensitive task to be performed by a team of at least k users.
From playlist The CERIAS Security Seminars 2006
Observability is a hot tech topic yet has also become one of the industry’s most overused buzzwords. The term means understanding the behavior, performance, and other aspects of cloud infrastructure and cloud apps based on the data they generate, such as metrics, events, logs and traces. O
From playlist Software Development