Computing Default Extensions by Reductions on OR
... the authors state a modal reduction theorem to the effect that a formula O Rϕ is logically equivalent to a disjunction Oϕ1 ∨ · · · ∨ Oϕn , where each ϕk is a propositional formula. Because each such disjunct Oϕ k has a unique model, it is possible, within the logic itself, to break down a formula O ...
... the authors state a modal reduction theorem to the effect that a formula O Rϕ is logically equivalent to a disjunction Oϕ1 ∨ · · · ∨ Oϕn , where each ϕk is a propositional formula. Because each such disjunct Oϕ k has a unique model, it is possible, within the logic itself, to break down a formula O ...
Objective Questions - vtu-nptel
... 89. The configuration of CMOS IC is in the form of a) SOIC configuration b) DIP configuration c) SOIC and DIP configurations d) None of the above 90. The drawback of CMOS over TTL is that CMOS is a) Highly expensive b) Slow c) Sensitive to electrostatic discharge d) Not widely available 91. The full ...
... 89. The configuration of CMOS IC is in the form of a) SOIC configuration b) DIP configuration c) SOIC and DIP configurations d) None of the above 90. The drawback of CMOS over TTL is that CMOS is a) Highly expensive b) Slow c) Sensitive to electrostatic discharge d) Not widely available 91. The full ...
Admissible rules in the implication-- negation fragment of intuitionistic logic
... Although a logic may not be structurally complete, there may be well-behaved sets of formulas such that for rules whose premises form such a set, admissibility coincides with derivability. Let us fix L as a logic based on a language L containing a binary connective → for which modus ponens is deriva ...
... Although a logic may not be structurally complete, there may be well-behaved sets of formulas such that for rules whose premises form such a set, admissibility coincides with derivability. Let us fix L as a logic based on a language L containing a binary connective → for which modus ponens is deriva ...
Formalizing Basic First Order Model Theory
... The most complex syntactic definition is of substitution. We have chosen a ‘name-carrying’ formalization of syntax, rather than indexing bound variables using some scheme following de Bruijn [1]. The latter is usually preferred when formalizing logical syntax precisely because substitution is simple ...
... The most complex syntactic definition is of substitution. We have chosen a ‘name-carrying’ formalization of syntax, rather than indexing bound variables using some scheme following de Bruijn [1]. The latter is usually preferred when formalizing logical syntax precisely because substitution is simple ...
A General Proof Method for ... without the Barcan Formula.*
... This paper generalizes the proof method for modal predicate logic first described in Jackson [1987] and axiomatized in Jackson & Reichgelt [1987]. As before, the inference rules are identical for each system; different systems differ only with respect to the definition of complementarity between for ...
... This paper generalizes the proof method for modal predicate logic first described in Jackson [1987] and axiomatized in Jackson & Reichgelt [1987]. As before, the inference rules are identical for each system; different systems differ only with respect to the definition of complementarity between for ...
PDF
... The first approach is axiomatic and abstract. We state logical properties of the numbers using first-order logic. It might be the case that these first-order properties describe numbers so well that they capture our intuition completely. The classical first-order theory of numbers is called Peano Ar ...
... The first approach is axiomatic and abstract. We state logical properties of the numbers using first-order logic. It might be the case that these first-order properties describe numbers so well that they capture our intuition completely. The classical first-order theory of numbers is called Peano Ar ...
full text (.pdf)
... function assigning a truth value (0 or 1) to each sentence of the form P(~) (in the vocabulary a augmented by names for the natural numbers). Then the process described informally above is defined by the product measure on the space of such functions induced by the probability measure on {0, 1 } tha ...
... function assigning a truth value (0 or 1) to each sentence of the form P(~) (in the vocabulary a augmented by names for the natural numbers). Then the process described informally above is defined by the product measure on the space of such functions induced by the probability measure on {0, 1 } tha ...
term 1 - Teaching-WIKI
... – http://en.wikipedia.org/wiki/First-order_logic#Metalogical_theorems_of_firstorder_logic for several relevant properties ...
... – http://en.wikipedia.org/wiki/First-order_logic#Metalogical_theorems_of_firstorder_logic for several relevant properties ...
Rewriting Predicate Logic Statements
... New Proof Strategy ‘Antecedent Assumption’” of the next slide set, you should be able for each proof strategy below to: (1) identify the form of statement the strategy can prove and (2) sketch the structure of a proof that uses the strategy. Strategies: constructive/non-constructive proofs of existe ...
... New Proof Strategy ‘Antecedent Assumption’” of the next slide set, you should be able for each proof strategy below to: (1) identify the form of statement the strategy can prove and (2) sketch the structure of a proof that uses the strategy. Strategies: constructive/non-constructive proofs of existe ...
ON A MINIMAL SYSTEM OF ARISTOTLE`S SYLLOGISTIC Introduction
... One of the alternative proposals was given by J. Slupecki [8]. He accepted the general idea of constructing Syllogistic as a quantifier free theory based on PL, used the same language with the same primitive symbols, but changed the content of the theory by changing the axioms. His intention was to ...
... One of the alternative proposals was given by J. Slupecki [8]. He accepted the general idea of constructing Syllogistic as a quantifier free theory based on PL, used the same language with the same primitive symbols, but changed the content of the theory by changing the axioms. His intention was to ...
Handout 10 from Models of Computation
... VI. The Lambda Calculus So far we were concerned with models of computation based on machine models. In particular, we used the Turing machine model to define the boundary between computability and non-computability, feasibility and intractability. Machine models are often rather contrived and when ...
... VI. The Lambda Calculus So far we were concerned with models of computation based on machine models. In particular, we used the Turing machine model to define the boundary between computability and non-computability, feasibility and intractability. Machine models are often rather contrived and when ...
Symbolic Logic II
... Consider Sider’s Exercise 3.7: Show that there are no Kleene-valid wffs. How would you answer this? One way to think of the validity of a wff is if it is a tautology — that is, when all the truth values of a truth table are T (or 1). But if you think about Kleene’s truth tables, you will see that w ...
... Consider Sider’s Exercise 3.7: Show that there are no Kleene-valid wffs. How would you answer this? One way to think of the validity of a wff is if it is a tautology — that is, when all the truth values of a truth table are T (or 1). But if you think about Kleene’s truth tables, you will see that w ...
proceedings version
... H (‘here’) and T (‘there’) such that H ⊆ T . The logical language to talk about such models has connectives ⊥, ∧, ∨, and ⇒. The latter is interpreted in a non-classical way and is therefore different from the material implication →: H, T |= ϕ ⇒ ψ iff H, T |= ϕ → ψ and T, T |= ϕ → ψ where → is interp ...
... H (‘here’) and T (‘there’) such that H ⊆ T . The logical language to talk about such models has connectives ⊥, ∧, ∨, and ⇒. The latter is interpreted in a non-classical way and is therefore different from the material implication →: H, T |= ϕ ⇒ ψ iff H, T |= ϕ → ψ and T, T |= ϕ → ψ where → is interp ...
Curry–Howard correspondence
In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs. It is a generalization of a syntactic analogy between systems of formal logic and computational calculi that was first discovered by the American mathematician Haskell Curry and logician William Alvin Howard. It is the link between logic and computation that is usually attributed to Curry and Howard, although the idea is related to the operational interpretation of intuitionistic logic given in various formulations by L. E. J. Brouwer, Arend Heyting and Andrey Kolmogorov (see Brouwer–Heyting–Kolmogorov interpretation) and Stephen Kleene (see Realizability). The relationship has been extended to include category theory as the three-way Curry–Howard–Lambek correspondence.