Beyond Quantifier-Free Interpolation in Extensions of Presburger
... arrays (AR), using uninterpreted function symbols for read and write operations. Our interpolation procedure extracts an interpolant directly from a proof of A ⇒ C. Starting from a sound and complete proof system based on a sequent calculus, the proof rules are extended by labelled formulae and anno ...
... arrays (AR), using uninterpreted function symbols for read and write operations. Our interpolation procedure extracts an interpolant directly from a proof of A ⇒ C. Starting from a sound and complete proof system based on a sequent calculus, the proof rules are extended by labelled formulae and anno ...
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... if all of its finite subsets are. We gave three proofs for that: one using tableau proofs and König’s lemma, one giving a direct construction of a Hintikka set, and one using Lindenbaum’s construction, extending S to a maximally consistent set, which turned out to be a proof set. In first-order log ...
... if all of its finite subsets are. We gave three proofs for that: one using tableau proofs and König’s lemma, one giving a direct construction of a Hintikka set, and one using Lindenbaum’s construction, extending S to a maximally consistent set, which turned out to be a proof set. In first-order log ...
Plural Quantifiers
... The lesson to be drawn from the foregoing reflections on plurals and secondorder logic is that neither the use of plurals nor the employment of secondorder logic commits us to the existence of extra items beyond those to which we are already committed. We need not construe second-order quantifiers a ...
... The lesson to be drawn from the foregoing reflections on plurals and secondorder logic is that neither the use of plurals nor the employment of secondorder logic commits us to the existence of extra items beyond those to which we are already committed. We need not construe second-order quantifiers a ...
Modalities in the Realm of Questions: Axiomatizing Inquisitive
... of IEL, building up to a completeness result. It is shown that the standard logical features of the logical constants extend smoothly beyond the truth-conditional realm, except for double negation, which is the hallmark of truth-conditionality. In particular, while the modalities of IEL operate in a ...
... of IEL, building up to a completeness result. It is shown that the standard logical features of the logical constants extend smoothly beyond the truth-conditional realm, except for double negation, which is the hallmark of truth-conditionality. In particular, while the modalities of IEL operate in a ...
Slide 1
... 1. Lexicographically enumerate sound proofs. 2. Check each proof as it is created. If it succeeds in proving w, halt and accept. ...
... 1. Lexicographically enumerate sound proofs. 2. Check each proof as it is created. If it succeeds in proving w, halt and accept. ...
Functions, recursion and lists
... Expresses flow of data; map input values to output values No side effects or modification to variables No concept of control-flow or statements A function can be used everywhere a regular value is used Functions can take other functions as parameters and return other functions as results (higher-ord ...
... Expresses flow of data; map input values to output values No side effects or modification to variables No concept of control-flow or statements A function can be used everywhere a regular value is used Functions can take other functions as parameters and return other functions as results (higher-ord ...
Equivalence of the information structure with unawareness to the
... believe that agent j implicitly believes that p is false’. For any formula φ, denote the set of primitive propositions found in φ by Prim(φ). Certain formulas of the logic, called theorems, are later used to connect the propositional and set-based models. Any formula valid in the Kripke structure (t ...
... believe that agent j implicitly believes that p is false’. For any formula φ, denote the set of primitive propositions found in φ by Prim(φ). Certain formulas of the logic, called theorems, are later used to connect the propositional and set-based models. Any formula valid in the Kripke structure (t ...
Can Modalities Save Naive Set Theory?
... requiring only that for every condition ϕ, there is a set containing all and only the sets which are determinately ϕ. As described in the previous paragraph, this strategy might block a version of Russell’s paradox: if the Russell set does not belong to itself, it may nevertheless not be determinate ...
... requiring only that for every condition ϕ, there is a set containing all and only the sets which are determinately ϕ. As described in the previous paragraph, this strategy might block a version of Russell’s paradox: if the Russell set does not belong to itself, it may nevertheless not be determinate ...
KnotandTonk 1 Preliminaries
... This raises a further parallel between inferentialist reactions to Knot and semanticist reactions to Tonk. Semanticists sometimes allege that the natural deduction rules for Tonk fail even to define a meaningful connective, on the grounds that Tonk cannot be given semantic conditions. By exactly the ...
... This raises a further parallel between inferentialist reactions to Knot and semanticist reactions to Tonk. Semanticists sometimes allege that the natural deduction rules for Tonk fail even to define a meaningful connective, on the grounds that Tonk cannot be given semantic conditions. By exactly the ...
ICS 353: Design and Analysis of Algorithms
... • The quantifiers and have higher precedence than all logical operators from propositional calculus. • E.g., x P(x) Q(x) • means……………………….. • does not mean …………………… ...
... • The quantifiers and have higher precedence than all logical operators from propositional calculus. • E.g., x P(x) Q(x) • means……………………….. • does not mean …………………… ...
Basic Metatheory for Propositional, Predicate, and Modal Logic
... whether every truth function is expressed by some formula of L P . The issue here hinges on the connectives of L P . A set of connectives in an interpreted language (i.e., a language together with its semantics) for propositional logic is said to be adequate iff every truth function can be expressed ...
... whether every truth function is expressed by some formula of L P . The issue here hinges on the connectives of L P . A set of connectives in an interpreted language (i.e., a language together with its semantics) for propositional logic is said to be adequate iff every truth function can be expressed ...
Logic programming slides
... (So in this sense SLD-resolution is complete.) Counterexamples for arbitrary sets of predicate logical sentences = {Pa, x Px} has a model but no minimal Herbrand model. The Herbrand universe of is {a}, but no model on this domain satisfies . ' = {Pa Qa} has two minimal Herbrand models ...
... (So in this sense SLD-resolution is complete.) Counterexamples for arbitrary sets of predicate logical sentences = {Pa, x Px} has a model but no minimal Herbrand model. The Herbrand universe of is {a}, but no model on this domain satisfies . ' = {Pa Qa} has two minimal Herbrand models ...
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.