Evolutionary Psychology and the Unity of Sciences – towards an
... • Epistemology will acquire the ability to be shared: with robots, aliens or any other entity that needs cognition to survive and program its future. • Creating situated robots means carrying out our own cognitive evolution by new means, thereby engendering symbiotic, co-evolving, and selfaccelerati ...
... • Epistemology will acquire the ability to be shared: with robots, aliens or any other entity that needs cognition to survive and program its future. • Creating situated robots means carrying out our own cognitive evolution by new means, thereby engendering symbiotic, co-evolving, and selfaccelerati ...
Knowledge Representation
... • X P(X) means that P(X) must be true for every object X in the domain of interest. • X P(X) means that P(X) must be true for at least one object X in the domain of interest. • So if we have a domain of interest consisting of just two people, john and mary, and we know that tall(mary) and tall(j ...
... • X P(X) means that P(X) must be true for every object X in the domain of interest. • X P(X) means that P(X) must be true for at least one object X in the domain of interest. • So if we have a domain of interest consisting of just two people, john and mary, and we know that tall(mary) and tall(j ...
HISTORY OF LOGIC
... – Human reasoning could be reduced to calculations of a sort, and that such calculations could resolve many differences of opinion. – Leibniz enunciated the principal properties of what we now call conjunction, disjunction and negation. – All our complex ideas are compounded from a small number of s ...
... – Human reasoning could be reduced to calculations of a sort, and that such calculations could resolve many differences of opinion. – Leibniz enunciated the principal properties of what we now call conjunction, disjunction and negation. – All our complex ideas are compounded from a small number of s ...
Propositional Logic Predicate Logic
... “There exists x s.t. A” B is true for some individual x. We also use individual constant a, b, c, etc. For some specific theories, we may write ∀x ∈ X.A or ∃x ∈ X.A to specify the set that x ranges over. Note. Nullary predicates (or, predicates with zero variables) are propositions. ...
... “There exists x s.t. A” B is true for some individual x. We also use individual constant a, b, c, etc. For some specific theories, we may write ∀x ∈ X.A or ∃x ∈ X.A to specify the set that x ranges over. Note. Nullary predicates (or, predicates with zero variables) are propositions. ...
Definition - Rogelio Davila
... Definition. A set of wffs is consistent, sound, or satisfiable, if all their elements admit the same model. Otherwise it is said to be inconsistent. Definition. Let be a set of wffs and a wff, we say that entails , or that is a logical consequence of , , iff every model of is a mode ...
... Definition. A set of wffs is consistent, sound, or satisfiable, if all their elements admit the same model. Otherwise it is said to be inconsistent. Definition. Let be a set of wffs and a wff, we say that entails , or that is a logical consequence of , , iff every model of is a mode ...
Natural Deduction Proof System
... • Natural Deduction tries to follow the natural style of reasoning. Most of the proof consists of forward reasoning, i.e. deriving conclusions, deriving new conclusions from these conclusions, etc. Occasionally hypotheses are introduced or dropped. • A derivation is a tree where the nodes are the ru ...
... • Natural Deduction tries to follow the natural style of reasoning. Most of the proof consists of forward reasoning, i.e. deriving conclusions, deriving new conclusions from these conclusions, etc. Occasionally hypotheses are introduced or dropped. • A derivation is a tree where the nodes are the ru ...
Creativity and Artificial Intelligence
... techniques. Since the author sees planning as just one among a number of aspects for achieving artificial intelligence, the case for deductive planning is presented in this paper in form of a paradigm case for achieving the grander goal of artificial intelligence. The paper will therefore not only p ...
... techniques. Since the author sees planning as just one among a number of aspects for achieving artificial intelligence, the case for deductive planning is presented in this paper in form of a paradigm case for achieving the grander goal of artificial intelligence. The paper will therefore not only p ...
Logic and Proof - Collaboratory for Advanced Computing and
... “it is not the case that P(x) is T for all x” ≡ “there exists x such that P(x) is F” (Example) Negation of “all Americans eat cheeseburgers” “there is an American who do not eat cheeseburgers” ¬∃xP(x) ≡ ∀x¬P(x) “it is not the case that there exists x such that P(x) is T” ≡ “P(x) is F for all ...
... “it is not the case that P(x) is T for all x” ≡ “there exists x such that P(x) is F” (Example) Negation of “all Americans eat cheeseburgers” “there is an American who do not eat cheeseburgers” ¬∃xP(x) ≡ ∀x¬P(x) “it is not the case that there exists x such that P(x) is T” ≡ “P(x) is F for all ...
Mathematical Logic Deciding logical consequence Complexity of
... The modern notion of symbolic formal proof was developed in the 20th century by logicians and mathematicians such as Russell, Frege and Hilbert. The benefit of formal logic is that it is based on a pure syntax: a precisely defined symbolic language with procedures for transforming symbolic statement ...
... The modern notion of symbolic formal proof was developed in the 20th century by logicians and mathematicians such as Russell, Frege and Hilbert. The benefit of formal logic is that it is based on a pure syntax: a precisely defined symbolic language with procedures for transforming symbolic statement ...
Ch1 - COW :: Ceng
... Propositional logic is one of the simplest logics Propositional logic has direct applications e.g. circuit design There are efficient algorithms for reasoning in propositional logic Propositional logic is a foundation for most of the more expressive logics ...
... Propositional logic is one of the simplest logics Propositional logic has direct applications e.g. circuit design There are efficient algorithms for reasoning in propositional logic Propositional logic is a foundation for most of the more expressive logics ...
Definition: A proof is a system of reasoning or argument to convince
... true. Example: 1. All dogs are mammals. 2. Fido is a dog. 3. Therefore, Fido is a mammal. The argument is deductive. The first 2 statements are the premises. Statement 3 is the conclusion. It is valid because the logic is good (proceeds ...
... true. Example: 1. All dogs are mammals. 2. Fido is a dog. 3. Therefore, Fido is a mammal. The argument is deductive. The first 2 statements are the premises. Statement 3 is the conclusion. It is valid because the logic is good (proceeds ...
logical axiom
... 2. (a → (b → c)) → ((a → b) → (a → c)) 3. (¬a → ¬b) → (b → a) where → is a binary logical connective and ¬ is a unary logical connective, and a, b, c are any (well-formed) formulas. Let us take these formulas as axioms. Next, we pick a rule of inference. The popular choice is the rule “modus ponens ...
... 2. (a → (b → c)) → ((a → b) → (a → c)) 3. (¬a → ¬b) → (b → a) where → is a binary logical connective and ¬ is a unary logical connective, and a, b, c are any (well-formed) formulas. Let us take these formulas as axioms. Next, we pick a rule of inference. The popular choice is the rule “modus ponens ...
Propositional/First
... • A valid sentence is true in all worlds under all interpretations • If an implication sentence can be shown to be valid, then—given its premise—its consequent can be derived • Different logics make different commitments about what the world is made of and what kind of beliefs we can have regarding ...
... • A valid sentence is true in all worlds under all interpretations • If an implication sentence can be shown to be valid, then—given its premise—its consequent can be derived • Different logics make different commitments about what the world is made of and what kind of beliefs we can have regarding ...
Lecture_ai_3 - WordPress.com
... • Used to join atomic symbols to form complex structure • Valid connectives are as follows i)Not or negation Denoted by ̚ if P is true then ̚ P is false ii)Conjunction Denoted by AND/˄ P˄Q will be true if both of them is true iii)Disjunction Denoted by OR/˅ P˅Q will be true if only one of th ...
... • Used to join atomic symbols to form complex structure • Valid connectives are as follows i)Not or negation Denoted by ̚ if P is true then ̚ P is false ii)Conjunction Denoted by AND/˄ P˄Q will be true if both of them is true iii)Disjunction Denoted by OR/˅ P˅Q will be true if only one of th ...
PDF
... assume the “weaker” version and that ∆, A ` B, where ∆ is an arbitrary set of formulas. Then there is a deduction (finite sequence of formulas) A1 , . . . , An+1 = B such that each Ai (where i ≤ n) is either an axiom, A itself, a formula in ∆, or a formula obtained from an application of an inferenc ...
... assume the “weaker” version and that ∆, A ` B, where ∆ is an arbitrary set of formulas. Then there is a deduction (finite sequence of formulas) A1 , . . . , An+1 = B such that each Ai (where i ≤ n) is either an axiom, A itself, a formula in ∆, or a formula obtained from an application of an inferenc ...
Inquiry
An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.