07.1-Reasoning
... • Our agent starts in 1,1 and feels no stench. By the rule Modus Ponens and the built in knowledge in it’s KB, it can conclude that 1,2 and 2,1 do not have a wumpus. • Now by the rule And-Elimination we can see that 1,2 doesn’t contain a wumpus and neither does 2,1. • If our agent now moves to 2,1 i ...
... • Our agent starts in 1,1 and feels no stench. By the rule Modus Ponens and the built in knowledge in it’s KB, it can conclude that 1,2 and 2,1 do not have a wumpus. • Now by the rule And-Elimination we can see that 1,2 doesn’t contain a wumpus and neither does 2,1. • If our agent now moves to 2,1 i ...
relevant reasoning as the logical basis of
... With the above definition of material implication and the inference rule of Modus Ponens for material implication (from A and A→B to infer B), any valid reasoning based on CML must be truth-preserving, i.e., the conclusion of a valid reasoning must be true if all premises are true. However, as a res ...
... With the above definition of material implication and the inference rule of Modus Ponens for material implication (from A and A→B to infer B), any valid reasoning based on CML must be truth-preserving, i.e., the conclusion of a valid reasoning must be true if all premises are true. However, as a res ...
Propositional Logic and Methods of Inference
... systems in which the inference engine reasons from facts to conclusions. A descriptive term for logic programming and expert systems is automated reasoning systems. ...
... systems in which the inference engine reasons from facts to conclusions. A descriptive term for logic programming and expert systems is automated reasoning systems. ...
Phil 2302 Intro to Logic
... Rather, this kind of syllogism must be constructed of a conditional major premise, and an unconditional minor premise leading to an unconditional conclusion. 1. A conditional major premise. 2. An unconditional minor premise. 3. An unconditional conclusion. Rather than having three terms as categoric ...
... Rather, this kind of syllogism must be constructed of a conditional major premise, and an unconditional minor premise leading to an unconditional conclusion. 1. A conditional major premise. 2. An unconditional minor premise. 3. An unconditional conclusion. Rather than having three terms as categoric ...
Lecture 4 - Michael De
... Assume that instead of interpreting i as a gap, we interpret it as a glut. But then taking the value i means being both true and false, and hence true, and hence designated. So we need to add i to D. The resulting logic is called LP, or the Logic of Paradox, as Priest originally called it. It is the ...
... Assume that instead of interpreting i as a gap, we interpret it as a glut. But then taking the value i means being both true and false, and hence true, and hence designated. So we need to add i to D. The resulting logic is called LP, or the Logic of Paradox, as Priest originally called it. It is the ...
pdf
... he also allows for different subjective domains at each world. He goes further by using what is called neighborhood semantics, also called Montague-Scott structures (Fagin et al., 1995). As is well known, neighborhood semantics provide a more general approach for modeling knowledge than the standar ...
... he also allows for different subjective domains at each world. He goes further by using what is called neighborhood semantics, also called Montague-Scott structures (Fagin et al., 1995). As is well known, neighborhood semantics provide a more general approach for modeling knowledge than the standar ...
Lecture slides
... Using truth tables to test the validity of an argument is a bit slow and laborious. It would be painful for a long, complex argument? And, it is a significant departure from informal methods of presenting an argument. ...
... Using truth tables to test the validity of an argument is a bit slow and laborious. It would be painful for a long, complex argument? And, it is a significant departure from informal methods of presenting an argument. ...
Knowledge of Logical Truth Knowledge of Logical Truth
... The question is then whether those truths are derivable from any set of premises. All other possible premises imagined will be additions to E, so the question is whether adding any set of those could ruin the implication. That is, we need: For all S and p, if E├ p then E,S ├ p. So, it looks like the ...
... The question is then whether those truths are derivable from any set of premises. All other possible premises imagined will be additions to E, so the question is whether adding any set of those could ruin the implication. That is, we need: For all S and p, if E├ p then E,S ├ p. So, it looks like the ...
Semantics of PL
... first attempt at filling out ‘impossible’ was to translate the sentences into Sentential Logic and look at all possible truth-value assignments to the atomic sentences. Then since our connectives are truth-functional we can determine the value of whole sentences and look to see if there is any truth ...
... first attempt at filling out ‘impossible’ was to translate the sentences into Sentential Logic and look at all possible truth-value assignments to the atomic sentences. Then since our connectives are truth-functional we can determine the value of whole sentences and look to see if there is any truth ...
lecture notes
... We shall come back to it in Example 5. The above conclusions are examples of a syllogisms defined as a “deductive scheme of a formal argument consisting of a major and a minor premise and a conclusion”. Here what encyclopedia.com is to say about syllogisms: Syllogism, a mode of argument that forms t ...
... We shall come back to it in Example 5. The above conclusions are examples of a syllogisms defined as a “deductive scheme of a formal argument consisting of a major and a minor premise and a conclusion”. Here what encyclopedia.com is to say about syllogisms: Syllogism, a mode of argument that forms t ...
Query Answering for OWL-DL with Rules
... of both approaches, OWL-DL was extended with rules in [11], but this extension is undecidable [11]. Intuitively, the undecidability is due to the fact that adding rules to OWL-DL causes the loss of any form of tree model property. In a logic with such a property, every satisfiable knowledge base has ...
... of both approaches, OWL-DL was extended with rules in [11], but this extension is undecidable [11]. Intuitively, the undecidability is due to the fact that adding rules to OWL-DL causes the loss of any form of tree model property. In a logic with such a property, every satisfiable knowledge base has ...
Tableau techniques for ALC
... Theorem. (Soundness) If a FOL sentence ϕ has a tableau proof then ϕ is valid. Theorem. (Completeness) If a sentence ϕ of FOL is valid, then ϕ has a tableau proof. Because FOL is not decidable, tableau proofs may not always terminate. The source of this difficulty is the γ rule. Trivial example: Suppos ...
... Theorem. (Soundness) If a FOL sentence ϕ has a tableau proof then ϕ is valid. Theorem. (Completeness) If a sentence ϕ of FOL is valid, then ϕ has a tableau proof. Because FOL is not decidable, tableau proofs may not always terminate. The source of this difficulty is the γ rule. Trivial example: Suppos ...
Table of mathematical symbols - Wikipedia, the free
... latter; analysts, set theorists and computer scientists prefer the former. To avoid confusion, ℕ = {|a| : a ∈ ℤ} or ℕ = {|a| > 0: a ∈ ℤ} always check an author's definition of N. Set theorists often use the notation ω (for least infinite ordinal) to denote the set of natural numbers (including zero) ...
... latter; analysts, set theorists and computer scientists prefer the former. To avoid confusion, ℕ = {|a| : a ∈ ℤ} or ℕ = {|a| > 0: a ∈ ℤ} always check an author's definition of N. Set theorists often use the notation ω (for least infinite ordinal) to denote the set of natural numbers (including zero) ...
Propositional Logic What is logic? Propositions Negation
... Let F(x) be the predicate “x is female”. Let P(x) be the predicate “x is a parent”. Let M(x,y) be the predicate “x is the mother of y”. Let the universe of discourse be the set of all people. We can express the statement “If a person is female and is a parent, then this person is someone’s mother”. ...
... Let F(x) be the predicate “x is female”. Let P(x) be the predicate “x is a parent”. Let M(x,y) be the predicate “x is the mother of y”. Let the universe of discourse be the set of all people. We can express the statement “If a person is female and is a parent, then this person is someone’s mother”. ...
Default Reasoning in a Terminological Logic
... The field of TLs has lately been an active area of research, with the attention of researchers especially focusing on the investigation of their logical and computational properties. Nevertheless, few researchers have addressed the problem of extending these logics with the ability to perform defaul ...
... The field of TLs has lately been an active area of research, with the attention of researchers especially focusing on the investigation of their logical and computational properties. Nevertheless, few researchers have addressed the problem of extending these logics with the ability to perform defaul ...
Lecture Notes
... Theorem: For finite M , and φ ∈ L{K1 ,...,Kn ,CG } there exists an algorithm that solves the problem in time linear in |M | · |φ|, where |M | and |φ| are the amount of space needed to write down M and φ, ...
... Theorem: For finite M , and φ ∈ L{K1 ,...,Kn ,CG } there exists an algorithm that solves the problem in time linear in |M | · |φ|, where |M | and |φ| are the amount of space needed to write down M and φ, ...
7 LOGICAL AGENTS
... Humans, it seems, know things; and what they know helps them do things. These are not empty statements. They make strong claims about how the intelligence of humans is achieved—not by purely reflex mechanisms but by processes of reasoning that operate on internal representations of knowledge. In AI, ...
... Humans, it seems, know things; and what they know helps them do things. These are not empty statements. They make strong claims about how the intelligence of humans is achieved—not by purely reflex mechanisms but by processes of reasoning that operate on internal representations of knowledge. In AI, ...
Artificial Intelligence - Academic year 2016/2017
... Logic is the study of conditions under which an argumentation (reasoning) is correct. The above definition involves the following concepts: I ...
... Logic is the study of conditions under which an argumentation (reasoning) is correct. The above definition involves the following concepts: I ...
Part3
... Proving Conditional Statements: p → q Definition: The real number r is rational if there exist integers p and q where q≠0 such that r = p/q Example: Prove that the sum of two rational numbers is rational. Solution: Assume r and s are two rational numbers. Then there must be integers p, q and also t ...
... Proving Conditional Statements: p → q Definition: The real number r is rational if there exist integers p and q where q≠0 such that r = p/q Example: Prove that the sum of two rational numbers is rational. Solution: Assume r and s are two rational numbers. Then there must be integers p, q and also t ...
Lesson 1
... Examples of deductively valid arguments All agarics (mushrooms) have a strong toxic effect. This apple is an agaric. ---------------------------------------------------------------------Hence This apple has a strong toxic effect. The argument is valid. But the conclusion is evidently not true (fa ...
... Examples of deductively valid arguments All agarics (mushrooms) have a strong toxic effect. This apple is an agaric. ---------------------------------------------------------------------Hence This apple has a strong toxic effect. The argument is valid. But the conclusion is evidently not true (fa ...
Three Solutions to the Knower Paradox
... known. As we can trivially see, they do not say anything about what we really do know, whereas the assumption number two affirms knowledge of something (the reflection principle). This difference of shape could be a good sign for believing that the assumption we have to rule out is the second one. A ...
... known. As we can trivially see, they do not say anything about what we really do know, whereas the assumption number two affirms knowledge of something (the reflection principle). This difference of shape could be a good sign for believing that the assumption we have to rule out is the second one. A ...
P - Bakers Math Class
... “I will study discrete math or I will study databases.” “Therefore, I will study databases or I will study English literature.” ...
... “I will study discrete math or I will study databases.” “Therefore, I will study databases or I will study English literature.” ...
x - Koc Lab
... Let p be “I will study discrete math.” Let r be “I will study English literature.” Let q be “I will study databases.” “I will not study discrete math or I will study English literature.” “I will study discrete math or I will study databases.” “Therefore, I will study databases or I will English lite ...
... Let p be “I will study discrete math.” Let r be “I will study English literature.” Let q be “I will study databases.” “I will not study discrete math or I will study English literature.” “I will study discrete math or I will study databases.” “Therefore, I will study databases or I will English lite ...
Logic is a discipline that studies the principles and methods used in
... Predicate Logic: Existential Quantifier Suppose P(x) is a predicate on some universe of discourse. The existential quantification of P(x) is the proposition: “There exists at least one x in the universe of discourse such that P(x) is true.” ∃ x P(x) reads “for some x, P(x)” or “There exists x, P(x) ...
... Predicate Logic: Existential Quantifier Suppose P(x) is a predicate on some universe of discourse. The existential quantification of P(x) is the proposition: “There exists at least one x in the universe of discourse such that P(x) is true.” ∃ x P(x) reads “for some x, P(x)” or “There exists x, P(x) ...
Document
... The existential quantification of P(x) is the proposition: “There exists at least one x in the universe of discourse such that P(x) is true.” x P(x) reads “for some x, P(x)” or “There exists x, P(x) is True” x P(x) is TRUE means there is an x in UoD(x) for which P(x) is true. ...
... The existential quantification of P(x) is the proposition: “There exists at least one x in the universe of discourse such that P(x) is true.” x P(x) reads “for some x, P(x)” or “There exists x, P(x) is True” x P(x) is TRUE means there is an x in UoD(x) for which P(x) is true. ...