Algebraic Laws for Nondeterminism and Concurrency
... well developed in recent years [ 1, 111and applied successfullyto many nontrivial languages.Even languageswith parallel constructs have been treated in this way, using the power-domain constructions of [3], [7], and [lo]. Indeed for such languagesthere is no shortageof possibledenotational models. F ...
... well developed in recent years [ 1, 111and applied successfullyto many nontrivial languages.Even languageswith parallel constructs have been treated in this way, using the power-domain constructions of [3], [7], and [lo]. Indeed for such languagesthere is no shortageof possibledenotational models. F ...
Finite satisfiability for guarded fixpoint logic
... partial isomorphisms α : A 0 → A 1 with A i ⊆ Ai , satisfying the following back-and-forth conditions. (i) For every α : A 0 → A 1 in Z and every guarded subset B 0 of A0 there is a partial isomorphism γ : C 0 → C 1 in Z with B 0 ⊆ C 0 and α (x) = γ (x) for all x ∈ A 0 ∩ C 0 . (ii) For every α : A 0 ...
... partial isomorphisms α : A 0 → A 1 with A i ⊆ Ai , satisfying the following back-and-forth conditions. (i) For every α : A 0 → A 1 in Z and every guarded subset B 0 of A0 there is a partial isomorphism γ : C 0 → C 1 in Z with B 0 ⊆ C 0 and α (x) = γ (x) for all x ∈ A 0 ∩ C 0 . (ii) For every α : A 0 ...
CHAPTER 10 Gentzen Style Proof Systems for Classical Logic 1
... Hilbert style systems are easy to define and admit a simple proof of the Completeness Theorem but they are difficult to use. By humans, not mentioning computers. Their emphasis is on logical axioms, keeping the rules of inference at a minimum. Gentzen systems reverse this situation by emphasizing th ...
... Hilbert style systems are easy to define and admit a simple proof of the Completeness Theorem but they are difficult to use. By humans, not mentioning computers. Their emphasis is on logical axioms, keeping the rules of inference at a minimum. Gentzen systems reverse this situation by emphasizing th ...
Rich Chapter 5 Predicate Logic - Computer Science
... Logic Theorist [Newell et al., 1963] proved theorems from the first chapter of Whitehead and Russell's Principia Mathematica [1950]. Another theorem prover [Gelernter et al., 1963] proved theorems in geometry. Mathematical theorem proving is still an active area of AI research. (See, for example, Wo ...
... Logic Theorist [Newell et al., 1963] proved theorems from the first chapter of Whitehead and Russell's Principia Mathematica [1950]. Another theorem prover [Gelernter et al., 1963] proved theorems in geometry. Mathematical theorem proving is still an active area of AI research. (See, for example, Wo ...
Expressiveness of Logic Programs under the General Stable Model
... General Stable Model Semantics HENG ZHANG and YAN ZHANG ...
... General Stable Model Semantics HENG ZHANG and YAN ZHANG ...
Henkin`s Method and the Completeness Theorem
... (that is, ϕ is derivable from the axioms of L by the use of the inference rules of L); and “|= ϕ” for ϕ is valid (that is, ϕ is satisfied in every interpretation of L). The soundness theorem for L states that if ` ϕ, then |= ϕ; and the completeness theorem for L states that if |= ϕ, then ` ϕ. Put to ...
... (that is, ϕ is derivable from the axioms of L by the use of the inference rules of L); and “|= ϕ” for ϕ is valid (that is, ϕ is satisfied in every interpretation of L). The soundness theorem for L states that if ` ϕ, then |= ϕ; and the completeness theorem for L states that if |= ϕ, then ` ϕ. Put to ...
No Syllogisms for the Numerical Syllogistic
... various technical details in the ensuing presentation. Nothing of substance hinges on this decision, however; the results obtained below would not be materially altered by expanding our languages to include formulas of the form (≥ 0)[l, m]. If Θ is a set of formulas, we write A |= Θ if, for all θ ∈ ...
... various technical details in the ensuing presentation. Nothing of substance hinges on this decision, however; the results obtained below would not be materially altered by expanding our languages to include formulas of the form (≥ 0)[l, m]. If Θ is a set of formulas, we write A |= Θ if, for all θ ∈ ...
Intuitionistic Type Theory - The collected works of Per Martin-Löf
... Mathematical logic and the relation between logic and mathematics have been interpreted in at least three different ways: (1) mathematical logic as symbolic logic, or logic using mathematical symbolism; (2) mathematical logic as foundations (or philosophy) of mathematics; (3) mathematical logic as l ...
... Mathematical logic and the relation between logic and mathematics have been interpreted in at least three different ways: (1) mathematical logic as symbolic logic, or logic using mathematical symbolism; (2) mathematical logic as foundations (or philosophy) of mathematics; (3) mathematical logic as l ...
Intuitionistic Type Theory
... Mathematical logic and the relation between logic and mathematics have been interpreted in at least three different ways: (1) mathematical logic as symbolic logic, or logic using mathematical symbolism; (2) mathematical logic as foundations (or philosophy) of mathematics; (3) mathematical logic as l ...
... Mathematical logic and the relation between logic and mathematics have been interpreted in at least three different ways: (1) mathematical logic as symbolic logic, or logic using mathematical symbolism; (2) mathematical logic as foundations (or philosophy) of mathematics; (3) mathematical logic as l ...
Symbolic Execution - Harvard University
... he language that we will use for writing assertion is the set of logical formulas that include ons of arithmetic expressions, standard logical operators (and, or, implication, negation), as w ifiers (universal and existential). Assertions may use additional logical variables, different tha ...
... he language that we will use for writing assertion is the set of logical formulas that include ons of arithmetic expressions, standard logical operators (and, or, implication, negation), as w ifiers (universal and existential). Assertions may use additional logical variables, different tha ...
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 the Notion of Coherence in Fuzzy Answer Set Semantics
... negation in the context of residuated logic programming is provided in terms of the notion of coherence as a generalization in the fuzzy framework of the concept of consistence. Then, fuzzy answer sets for general residuated logic programs are defined as a suitable generalization of the Gelfond-Lifs ...
... negation in the context of residuated logic programming is provided in terms of the notion of coherence as a generalization in the fuzzy framework of the concept of consistence. Then, fuzzy answer sets for general residuated logic programs are defined as a suitable generalization of the Gelfond-Lifs ...
Classical Propositional Logic
... Tableau Systems Soundness Completeness A Henkin-style Completeness Proof for Natural Deduction Computability ...
... Tableau Systems Soundness Completeness A Henkin-style Completeness Proof for Natural Deduction Computability ...
