A System of Interaction and Structure
... possess. I will argue about relation webs having a broad applicability. In fact, a certain characterisation theorem for relation webs, which is crucial in our treatment, scales up to the generic case of a logic made by any number of different multiplicative logical relations. Relation webs justify t ...
... possess. I will argue about relation webs having a broad applicability. In fact, a certain characterisation theorem for relation webs, which is crucial in our treatment, scales up to the generic case of a logic made by any number of different multiplicative logical relations. Relation webs justify t ...
The Taming of the (X)OR
... BDD-packages [BRB90] has proven to be utterly ineffective when coping with fairly basics circuits such as multipliers. Parity bit problems, based on logically simple formulae, proved to be extremely hard for CNF based provers [SKM97,WvM99,JT96,Li00]. “The taming of the xor” has therefore become one ...
... BDD-packages [BRB90] has proven to be utterly ineffective when coping with fairly basics circuits such as multipliers. Parity bit problems, based on logically simple formulae, proved to be extremely hard for CNF based provers [SKM97,WvM99,JT96,Li00]. “The taming of the xor” has therefore become one ...
![CS 512, Spring 2017, Handout 05 [1ex] Semantics of Classical](http://s1.studyres.com/store/data/001902216_1-d85c63c8a0994ab9df7b1ab59a6b4141-300x300.png)
CS 512, Spring 2017, Handout 05 [1ex] Semantics of Classical
... Proof idea in [LCS] (which works if Γ is a finite set {ϕ1 , . . . , ϕn }): Establish 3 preliminary results. From ϕ1 , . . . , ϕn |= ψ , show that: 1. |= ϕ1 → (ϕ2 → (ϕ3 → (· · · (ϕn → ψ) · · · ))) holds. 2. ` ϕ1 → (ϕ2 → (ϕ3 → (· · · (ϕn → ψ) · · · ))) is a valid sequent. 3. ϕ1 , ϕ2 , . . . , ϕn ` ψ i ...
... Proof idea in [LCS] (which works if Γ is a finite set {ϕ1 , . . . , ϕn }): Establish 3 preliminary results. From ϕ1 , . . . , ϕn |= ψ , show that: 1. |= ϕ1 → (ϕ2 → (ϕ3 → (· · · (ϕn → ψ) · · · ))) holds. 2. ` ϕ1 → (ϕ2 → (ϕ3 → (· · · (ϕn → ψ) · · · ))) is a valid sequent. 3. ϕ1 , ϕ2 , . . . , ϕn ` ψ i ...
Uniform satisfiability in PSPACE for local temporal logics over
... atomic actions and declares some of them dependent and some independent. In Section 5, we obtain similar results in this setting. A question related to the uniform satisfiability problem is the general satisfiability problem. It asks whether a property (expressed by some formula) can occur at all, i ...
... atomic actions and declares some of them dependent and some independent. In Section 5, we obtain similar results in this setting. A question related to the uniform satisfiability problem is the general satisfiability problem. It asks whether a property (expressed by some formula) can occur at all, i ...
full text (.pdf)
... A third alternative would show that the relation {(σ, τ) | ∃ρ σ 6lex ρ 6lex τ} satisfies Property 1, therefore is contained in the maximal such relation 6lex . The details of this argument, written out, would contain all the same ingredients as our other two proofs. Here is another example involving ...
... A third alternative would show that the relation {(σ, τ) | ∃ρ σ 6lex ρ 6lex τ} satisfies Property 1, therefore is contained in the maximal such relation 6lex . The details of this argument, written out, would contain all the same ingredients as our other two proofs. Here is another example involving ...
Computability and Incompleteness
... ization of pornography, “it may be hard to define precisely, but I know it when I see it.” Why, then, is such a definition desirable? In 1900 the great mathematician David Hilbert addressed the international congress of mathematicians in Paris, and presented a list of 23 problems that he hoped would ...
... ization of pornography, “it may be hard to define precisely, but I know it when I see it.” Why, then, is such a definition desirable? In 1900 the great mathematician David Hilbert addressed the international congress of mathematicians in Paris, and presented a list of 23 problems that he hoped would ...
Martin-Löf`s Type Theory
... proof that type theory can be used as a programming language; and since the program is obtained from a proof of its specification, type theory can be used as a programming logic. The relevance of constructive mathematics for computer science was pointed out already by Bishop [4]. Recently, several i ...
... proof that type theory can be used as a programming language; and since the program is obtained from a proof of its specification, type theory can be used as a programming logic. The relevance of constructive mathematics for computer science was pointed out already by Bishop [4]. Recently, several i ...
Default Logic (Reiter) - Department of Computing
... classical consequence Th, and closed under the default rules D that are applicable given E. It remains to define what ‘closed under the default rules D that are applicable given E’ means. A formal definition follows presently. ...
... classical consequence Th, and closed under the default rules D that are applicable given E. It remains to define what ‘closed under the default rules D that are applicable given E’ means. A formal definition follows presently. ...
A Conditional Logical Framework *
... matching and restricted λ-calculi. The key idea, there, is to separate two different notions that are conflated in the original LF. As already mentioned, much of the rigidity of LF arised from the fact that β-reduction can be applied always in full generality. One would like to fire a β-reduction un ...
... matching and restricted λ-calculi. The key idea, there, is to separate two different notions that are conflated in the original LF. As already mentioned, much of the rigidity of LF arised from the fact that β-reduction can be applied always in full generality. One would like to fire a β-reduction un ...
1. Propositional Logic 1.1. Basic Definitions. Definition 1.1. The
... and as a result are poorly suited to proof-theoretic work. The second major family of formal systems are natural deduction systems. These were introduced by Gentzen in part to more closely resemble ordinary mathematical reasoning. These systems typically have relatively few axioms, and more rules, a ...
... and as a result are poorly suited to proof-theoretic work. The second major family of formal systems are natural deduction systems. These were introduced by Gentzen in part to more closely resemble ordinary mathematical reasoning. These systems typically have relatively few axioms, and more rules, a ...
2 - Set Theory
... What we want: S ∪ (T ∩ R) = (S ∪ T ) ∩ (S ∪ R). Thus, we want to show the following two subset inclusions: S ∪ (T ∩ R) ⊂ (S ∪ T ) ∩ (S ∪ R) and (S ∪ T ) ∩ (S ∪ R) ⊂ S ∪ (T ∩ R). What we’ll do: For the first inclusion S ∪ (T ∩ R) ⊂ (S ∪ T ) ∩ (S ∪ R), we will assume that x ∈ S ∪ (T ∩ R). Thus, becaus ...
... What we want: S ∪ (T ∩ R) = (S ∪ T ) ∩ (S ∪ R). Thus, we want to show the following two subset inclusions: S ∪ (T ∩ R) ⊂ (S ∪ T ) ∩ (S ∪ R) and (S ∪ T ) ∩ (S ∪ R) ⊂ S ∪ (T ∩ R). What we’ll do: For the first inclusion S ∪ (T ∩ R) ⊂ (S ∪ T ) ∩ (S ∪ R), we will assume that x ∈ S ∪ (T ∩ R). Thus, becaus ...
