Relational Logic - Stanford Logic Group
... Existential Quantifiers and Functions Functions Replaced by Existential Quantifiers: loves(x,a(x)) ⇔ ∃y.loves(x,y) Existential Quantifiers Replaced by Functions: ∃y.loves(x,y) ⇔ loves(x,a(x)) Theorem: An existential sentence is satisfiable iff the corresponding functional sentence is satisfiab ...
... Existential Quantifiers and Functions Functions Replaced by Existential Quantifiers: loves(x,a(x)) ⇔ ∃y.loves(x,y) Existential Quantifiers Replaced by Functions: ∃y.loves(x,y) ⇔ loves(x,a(x)) Theorem: An existential sentence is satisfiable iff the corresponding functional sentence is satisfiab ...
Quadripartitaratio - Revistas Científicas de la Universidad de
... us cringe at the mere hint of its appearance. The transition from the feeling “it would be nice if all Xs were Ys” to the belief “certainly all Xs are Ys” is so easy it sometimes feels like an implication. And when it becomes too obvious that not all Xs are Ys, then is the time to drag out “certainl ...
... us cringe at the mere hint of its appearance. The transition from the feeling “it would be nice if all Xs were Ys” to the belief “certainly all Xs are Ys” is so easy it sometimes feels like an implication. And when it becomes too obvious that not all Xs are Ys, then is the time to drag out “certainl ...
The Omnitude Determiner and Emplacement for the Square of
... Logicists, trying to base mathematics on logic as Frege and Russell did, find their logic in natural languages like everyone else, but the portion of logic they took from it was selected and tooled for its utility in deriving mathematical statements, improving proofs, establishing relations between ...
... Logicists, trying to base mathematics on logic as Frege and Russell did, find their logic in natural languages like everyone else, but the portion of logic they took from it was selected and tooled for its utility in deriving mathematical statements, improving proofs, establishing relations between ...
Set Theory and Logic
... 1. The connective or, in logic, has an inclusive meaning. For example, Bob will play tennis or go to the movies is interpreted as follows: Bob will either play tennis, or go to the movies, or do both. 2. The connective but has an identical role as the connective and, thus the same symbol ∧ is used f ...
... 1. The connective or, in logic, has an inclusive meaning. For example, Bob will play tennis or go to the movies is interpreted as follows: Bob will either play tennis, or go to the movies, or do both. 2. The connective but has an identical role as the connective and, thus the same symbol ∧ is used f ...
Lecture 1 - Artificial Intelligence: Foundations of Computational Agents
... 1. Choose a task domain: intended interpretation. 2. Associate an atom with each proposition you want to represent. 3. Tell the system clauses that are true in the intended interpretation: axiomatizing the domain. 4. Ask questions about the intended interpretation. 5. If KB |= g , then g must be tru ...
... 1. Choose a task domain: intended interpretation. 2. Associate an atom with each proposition you want to represent. 3. Tell the system clauses that are true in the intended interpretation: axiomatizing the domain. 4. Ask questions about the intended interpretation. 5. If KB |= g , then g must be tru ...
A Well-Founded Semantics for Logic Programs with Abstract
... model semantics was first proposed for normal logic programs by Gelfond and Lifschitz in 1988, various extensions have been put forward for theoretical and/or practical reasons. These include disjunctive logic programs (Gelfond and Lifschitz 1991), nested logic programs (Lifschitz, Tang, and Turner ...
... model semantics was first proposed for normal logic programs by Gelfond and Lifschitz in 1988, various extensions have been put forward for theoretical and/or practical reasons. These include disjunctive logic programs (Gelfond and Lifschitz 1991), nested logic programs (Lifschitz, Tang, and Turner ...
Extracting Proofs from Tabled Proof Search
... be valid, i.e., proved elsewhere using (co-)inductive techniques. Actually, Strategy I collapses into Strategy II if the empty set is an allowed theory. Soundness of these two strategies is not difficult to establish and it follows the work presented in [8]. Strategy III is sound only when the table ...
... be valid, i.e., proved elsewhere using (co-)inductive techniques. Actually, Strategy I collapses into Strategy II if the empty set is an allowed theory. Soundness of these two strategies is not difficult to establish and it follows the work presented in [8]. Strategy III is sound only when the table ...
Rewriting in the partial algebra of typed terms modulo AC
... happens in each dimension of the vector is dissociated from the other components, petri nets possess subtle parallelism facilities. On the other hand the expressiveness over control flow is quiet weak (e.g. it is impossible to encode a stack). The fundamental result over petri nets is the problem of ...
... happens in each dimension of the vector is dissociated from the other components, petri nets possess subtle parallelism facilities. On the other hand the expressiveness over control flow is quiet weak (e.g. it is impossible to encode a stack). The fundamental result over petri nets is the problem of ...
Section 8.3 The Double-Angle and Half-Angle
... The half-angle formulas can be derived from the Power Reduction Formulas and taking the square root of both sides of the equation. The choice of which root (positive or negative) depends on the quadrant in which the terminal side of θ lies. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!The!Half(Angle!Formulas!f ...
... The half-angle formulas can be derived from the Power Reduction Formulas and taking the square root of both sides of the equation. The choice of which root (positive or negative) depends on the quadrant in which the terminal side of θ lies. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!The!Half(Angle!Formulas!f ...
notes
... Cook’s proof of relative completeness depends on the notion of weakest liberal preconditions. Given a command c and a postcondition Q the weakest liberal precondition is the weakest assertion P such that {P } c {Q} is a valid triple. Here, “weakest” means that any other valid precondition implies P ...
... Cook’s proof of relative completeness depends on the notion of weakest liberal preconditions. Given a command c and a postcondition Q the weakest liberal precondition is the weakest assertion P such that {P } c {Q} is a valid triple. Here, “weakest” means that any other valid precondition implies P ...
On Rosser sentences and proof predicates
... It is also clear that “the usual” ordering and “the usual” proof predicate is highly arbitrary. A change in the coding of finite sequences is likely to change the order of proofs, as is a transition between different proof systems, and even two different Gödel numberings of formulas. Standardness o ...
... It is also clear that “the usual” ordering and “the usual” proof predicate is highly arbitrary. A change in the coding of finite sequences is likely to change the order of proofs, as is a transition between different proof systems, and even two different Gödel numberings of formulas. Standardness o ...
CS389L: Automated Logical Reasoning Lecture 1
... Truth tables are completely brute-force, impractical ⇒ must list all 2n interpretations! ...
... Truth tables are completely brute-force, impractical ⇒ must list all 2n interpretations! ...
Sketch-as-proof - Norbert Preining
... The earliest systematic method used in the study of geometry was the deductive axiomatic method introduced by the Greeks. Thales (640-546 b.c.) is generally considered to be the first to treat geometry as a logical structure. In the next 300 years much geometric knowledge was developed. Then Euclid ...
... The earliest systematic method used in the study of geometry was the deductive axiomatic method introduced by the Greeks. Thales (640-546 b.c.) is generally considered to be the first to treat geometry as a logical structure. In the next 300 years much geometric knowledge was developed. Then Euclid ...
