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Classical first-order predicate logic This is a powerful extension of
... • ∀x(bought(Tony, x) → bought(Susan, x)) ‘Susan bought everything that Tony bought.’ • ∀x bought(Tony, x) → ∀x bought(Susan, x) ‘If Tony bought everything, so did Susan.’ Note the difference! • ∀x∃y bought(x, y) ‘Everything bought something.’ • ∃x∀y bought(x, y) ‘Something bought everything.’ You ca ...
... • ∀x(bought(Tony, x) → bought(Susan, x)) ‘Susan bought everything that Tony bought.’ • ∀x bought(Tony, x) → ∀x bought(Susan, x) ‘If Tony bought everything, so did Susan.’ Note the difference! • ∀x∃y bought(x, y) ‘Everything bought something.’ • ∃x∀y bought(x, y) ‘Something bought everything.’ You ca ...
lecture notes in logic - UCLA Department of Mathematics
... “singleton operation”, i.e., for every x, x ∈ z =⇒ {x} ∈ z. (7) Choice: for every set x whose members are all non-empty and pairwise disjoint, there exists a set z which intersects each member of x in exactly one point, i.e., if y ∈ x, then there exists exactly one u such that u ∈ y and also u ∈ z. ...
... “singleton operation”, i.e., for every x, x ∈ z =⇒ {x} ∈ z. (7) Choice: for every set x whose members are all non-empty and pairwise disjoint, there exists a set z which intersects each member of x in exactly one point, i.e., if y ∈ x, then there exists exactly one u such that u ∈ y and also u ∈ z. ...
An Introduction to Mathematical Logic
... Reconsidering the above we recognize the following three “ingredients”: 1. a theorem (which is nothing but a sentence in a formalised language) 2. the claim that this theorem is a logical consequence of other sentences (here: the group axioms) 3. the proof of the theorem ,→ Mathematical logic is the ...
... Reconsidering the above we recognize the following three “ingredients”: 1. a theorem (which is nothing but a sentence in a formalised language) 2. the claim that this theorem is a logical consequence of other sentences (here: the group axioms) 3. the proof of the theorem ,→ Mathematical logic is the ...
PPT
... not faster than itself for problem size n.” i N, n N, n > i ~Faster(a, a, n) Consider an arbitrary (positive integer) i. Let n = ??. (Must be > i; so, at least i+1.) So, we need to prove: “a is not faster than itself for problem size ?? (for an arbitrary positive integer i)” ...
... not faster than itself for problem size n.” i N, n N, n > i ~Faster(a, a, n) Consider an arbitrary (positive integer) i. Let n = ??. (Must be > i; so, at least i+1.) So, we need to prove: “a is not faster than itself for problem size ?? (for an arbitrary positive integer i)” ...
PPT - UBC Department of CPSC Undergraduates
... not faster than itself for problem size n.” i N, n N, n > i ~Faster(a, a, n) Consider an arbitrary (positive integer) i. Let n = ??. (Must be > i; so, at least i+1.) So, we need to prove: “a is not faster than itself for problem size ?? (for an arbitrary positive integer i)” ...
... not faster than itself for problem size n.” i N, n N, n > i ~Faster(a, a, n) Consider an arbitrary (positive integer) i. Let n = ??. (Must be > i; so, at least i+1.) So, we need to prove: “a is not faster than itself for problem size ?? (for an arbitrary positive integer i)” ...
Classical first-order predicate logic This is a powerful extension
... • ∀x(bought(Tony, x) → bought(Susan, x)) ‘Susan bought everything that Tony bought.’ • ∀x bought(Tony, x) → ∀x bought(Susan, x) ‘If Tony bought everything, so did Susan.’ Note the difference! • ∀x∃y bought(x, y) ‘Everything bought something.’ • ∃x∀y bought(x, y) ‘Something bought everything.’ You ca ...
... • ∀x(bought(Tony, x) → bought(Susan, x)) ‘Susan bought everything that Tony bought.’ • ∀x bought(Tony, x) → ∀x bought(Susan, x) ‘If Tony bought everything, so did Susan.’ Note the difference! • ∀x∃y bought(x, y) ‘Everything bought something.’ • ∃x∀y bought(x, y) ‘Something bought everything.’ You ca ...
thèse - IRIT
... Here-and-there (HT) logic is a three-valued monotonic logic which is intermediate between classical logic and intuitionistic logic. Equilibrium logic is a nonmonotonic formalism whose semantics is given through a minimisation criterion over HT models. It is closely aligned with answer set programmin ...
... Here-and-there (HT) logic is a three-valued monotonic logic which is intermediate between classical logic and intuitionistic logic. Equilibrium logic is a nonmonotonic formalism whose semantics is given through a minimisation criterion over HT models. It is closely aligned with answer set programmin ...
Mathematical Logic
... are represented corresponds very much to the way a careful mathematician writing out all details of an argument would go anyway. Second, formal proofs in natural deduction are closely related (via the so-called CurryHoward correspondence) to terms in typed lambda calculus. This provides us not only ...
... are represented corresponds very much to the way a careful mathematician writing out all details of an argument would go anyway. Second, formal proofs in natural deduction are closely related (via the so-called CurryHoward correspondence) to terms in typed lambda calculus. This provides us not only ...
LPF and MPLω — A Logical Comparison of VDM SL and COLD-K
... In Section 2, these logics are described in broad outline. Some other logics which handle partial functions are discussed in Section 3. Sections 4–8 constitute the body of this paper. In Section 4 we present ML= , many-sorted classical logic with equality, by giving definitions of the language, the ...
... In Section 2, these logics are described in broad outline. Some other logics which handle partial functions are discussed in Section 3. Sections 4–8 constitute the body of this paper. In Section 4 we present ML= , many-sorted classical logic with equality, by giving definitions of the language, the ...
CS 208: Automata Theory and Logic
... – Introduced by Alan Turing as a simple model capable of expressing any imaginable computation – Turing machines are widely accepted as a synonyms for algorithmic computability (Church-Turing thesis) – Using these conceptual machines Turing showed that first-order logic validity problem a is non-com ...
... – Introduced by Alan Turing as a simple model capable of expressing any imaginable computation – Turing machines are widely accepted as a synonyms for algorithmic computability (Church-Turing thesis) – Using these conceptual machines Turing showed that first-order logic validity problem a is non-com ...
Document
... – If we can enumerate all of the possible cases, and prove that the statement is true in each case, then we have proven the statement – For example, if we want to prove that one proposition P implies another proposition Q, then looking at the truth tables for P and Q gives us one way of enumerating ...
... – If we can enumerate all of the possible cases, and prove that the statement is true in each case, then we have proven the statement – For example, if we want to prove that one proposition P implies another proposition Q, then looking at the truth tables for P and Q gives us one way of enumerating ...
Section 1: Propositional Logic
... • The first is the depth to which we explore the structure of statements. The study of the basic level of structure is called propositional logic. First order predicate logic, which is often called just predicate logic, studies structure on a deeper level. • The second direction is the nature of tru ...
... • The first is the depth to which we explore the structure of statements. The study of the basic level of structure is called propositional logic. First order predicate logic, which is often called just predicate logic, studies structure on a deeper level. • The second direction is the nature of tru ...
