THE MODEL CHECKING PROBLEM FOR INTUITIONISTIC
... reinvestigate under an algorithmic and complexity theoretical point of view. In contrast, the formula value problem for classical propositional logic is NC1 -complete [2] independent of the number of variables. Classical propositional logic is the extension of IPC with the axiom a ∨ ¬a. Those proper ...
... reinvestigate under an algorithmic and complexity theoretical point of view. In contrast, the formula value problem for classical propositional logic is NC1 -complete [2] independent of the number of variables. Classical propositional logic is the extension of IPC with the axiom a ∨ ¬a. Those proper ...
Lecture Notes on Sequent Calculus
... The proof of contraction actually exposes an imprecision in our presentation of the sequent calculus. When there are two occurrences of a proposition A among the antecedents, we have no way to distinguish which one is being used, either as the principal formula of a left rule or in an initial sequen ...
... The proof of contraction actually exposes an imprecision in our presentation of the sequent calculus. When there are two occurrences of a proposition A among the antecedents, we have no way to distinguish which one is being used, either as the principal formula of a left rule or in an initial sequen ...
Document
... proposi:ons. All but the final proposi:on are called premises. The last statement is the conclusion. • The argument is valid if the premises imply the conclusion. An argument form is an argument that is valid no maMer what proposi:ons are subs:tuted into its proposi:onal variables. • ...
... proposi:ons. All but the final proposi:on are called premises. The last statement is the conclusion. • The argument is valid if the premises imply the conclusion. An argument form is an argument that is valid no maMer what proposi:ons are subs:tuted into its proposi:onal variables. • ...
The logic and mathematics of occasion sentences
... This problem of donkey anaphora was the primary motivation behind Discourse Representation Theory (Kamp and Reyle 1993). A solution in terms of interpretative subdomains within the framework of Discourse Semantics is found in Seuren (1998a). Both approaches use LPC and both have extended LPC with de ...
... This problem of donkey anaphora was the primary motivation behind Discourse Representation Theory (Kamp and Reyle 1993). A solution in terms of interpretative subdomains within the framework of Discourse Semantics is found in Seuren (1998a). Both approaches use LPC and both have extended LPC with de ...
Rewriting in the partial algebra of typed terms modulo AC
... λ-calculus, pushdown systems were extended to higher order pushdown systems (processes with stacks of stacks of stacks . . . ). This definition lead to a hierarchy of systems (or graphs) having a decidable monadic second order theory [8,2] as well as pushdown systems. It is natural to try to combine ...
... λ-calculus, pushdown systems were extended to higher order pushdown systems (processes with stacks of stacks of stacks . . . ). This definition lead to a hierarchy of systems (or graphs) having a decidable monadic second order theory [8,2] as well as pushdown systems. It is natural to try to combine ...
Chapter 15 Functional Programming Languages
... • Efficiency (at least at first) is the primary concern, rather than the suitability of the language for software development - The design of the functional languages is based on mathematical functions - So what…? Provides a solid theoretical basis that is also closer to the user, but relatively unc ...
... • Efficiency (at least at first) is the primary concern, rather than the suitability of the language for software development - The design of the functional languages is based on mathematical functions - So what…? Provides a solid theoretical basis that is also closer to the user, but relatively unc ...
Chapter 15 Functional Programming Languages
... • Efficiency (at least at first) is the primary concern, rather than the suitability of the language for software development - The design of the functional languages is based on mathematical functions - So what…? Provides a solid theoretical basis that is also closer to the user, but relatively unc ...
... • Efficiency (at least at first) is the primary concern, rather than the suitability of the language for software development - The design of the functional languages is based on mathematical functions - So what…? Provides a solid theoretical basis that is also closer to the user, but relatively unc ...
Lecture 11 - Nipissing University Word
... A lambda expression has the form: (lambda argument-list function-body ) In other words, a lambda expression is somewhat like defun, except that it defines an unnamed function, or it allows the user to define a function with no name. For example, ((lambda (x y) (+ x y)) 2 3) binds x and y to 2 an ...
... A lambda expression has the form: (lambda argument-list function-body ) In other words, a lambda expression is somewhat like defun, except that it defines an unnamed function, or it allows the user to define a function with no name. For example, ((lambda (x y) (+ x y)) 2 3) binds x and y to 2 an ...
A Well-Founded Semantics for Logic Programs with Abstract
... While ASP assumes that solutions are given by answer sets, well-founded models (Van Gelder, Ross, and Schlipf 1991) have been found to be very useful as well. First, computing the well-founded model of a normal logic program is tractable. This compares to the NP-completeness of computing an answer s ...
... While ASP assumes that solutions are given by answer sets, well-founded models (Van Gelder, Ross, and Schlipf 1991) have been found to be very useful as well. First, computing the well-founded model of a normal logic program is tractable. This compares to the NP-completeness of computing an answer s ...
A SHORT AND READABLE PROOF OF CUT ELIMINATION FOR
... identical recently introduced first-order extension of GL (the ML3 of [12]) differs from QGL in that its language requires that A is a sentence for all A.1 In loc. cit. a proof of cut elimination of its Gentzenisation (the GLTS defined in Section 2) is given in full detail (as well as a proof of Cr ...
... identical recently introduced first-order extension of GL (the ML3 of [12]) differs from QGL in that its language requires that A is a sentence for all A.1 In loc. cit. a proof of cut elimination of its Gentzenisation (the GLTS defined in Section 2) is given in full detail (as well as a proof of Cr ...
Lect_8_9
... A useful library function is zip, which maps two lists to a list of pairs of their corresponding ...
... A useful library function is zip, which maps two lists to a list of pairs of their corresponding ...
Lecture 2 - cs.Virginia - University of Virginia
... keep me there I will be really annoyed and glare at you”. ...
... keep me there I will be really annoyed and glare at you”. ...
What is a Program?
... — A program (computation) is a transformation from input data to output data. ...
... — A program (computation) is a transformation from input data to output data. ...
Three Solutions to the Knower Paradox
... The Knower Paradox in the Framework of Modal Logic. If L∗ satisfies these two conditions, then L∗ is inconsistent. Proof. This result follows immediately from the inconsistency result just derived in the first-order arithmetic theory. 2. Two important points common to the three solutions The aim of ...
... The Knower Paradox in the Framework of Modal Logic. If L∗ satisfies these two conditions, then L∗ is inconsistent. Proof. This result follows immediately from the inconsistency result just derived in the first-order arithmetic theory. 2. Two important points common to the three solutions The aim of ...
Logic and Computation Lecture notes Jeremy Avigad Assistant Professor, Philosophy
... I should qualify this remark, however. In everyday life, we use different modes of reasoning in different contexts. We can reason about our experiences, and try to determine causal relations between different types of events; this forms the basis of scientific inquiry. We can reason probabilisticall ...
... I should qualify this remark, however. In everyday life, we use different modes of reasoning in different contexts. We can reason about our experiences, and try to determine causal relations between different types of events; this forms the basis of scientific inquiry. We can reason probabilisticall ...
Lambda-Lifting in Quadratic Time
... partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one f ...
... partial evaluators and that operates in cubic time. In this article, we show how to reduce this complexity to quadratic time, and we present a flow-sensitive lambda-lifter that also works in quadratic time. Lambda-lifting transforms a block-structured program into a set of recursive equations, one f ...
A Resolution-Based Proof Method for Temporal Logics of
... time’. Thus ϕ will be satisfied at some time if ϕ is satisfied at the next time. The connective means ‘until’. Thus ϕ ψ will be satisfied at some time if ψ is satisfied at that time or some time in the future, and Pϕ is satisfied at all times until the time that ψ is satisfied. P Of the derive ...
... time’. Thus ϕ will be satisfied at some time if ϕ is satisfied at the next time. The connective means ‘until’. Thus ϕ ψ will be satisfied at some time if ψ is satisfied at that time or some time in the future, and Pϕ is satisfied at all times until the time that ψ is satisfied. P Of the derive ...
From Answer Set Logic Programming to Circumscription via Logic of
... Answer Set Programming (ASP) is a new paradigm of constraint-based programming based on logic programming with answer set semantics 17,9,13]. It started out with normal logic programs, which are programs that can have negation but not disjunction. Driven by the need of applications, various extensi ...
... Answer Set Programming (ASP) is a new paradigm of constraint-based programming based on logic programming with answer set semantics 17,9,13]. It started out with normal logic programs, which are programs that can have negation but not disjunction. Driven by the need of applications, various extensi ...
3.6 First-Order Tableau
... The different versions of tableau for first-order logic differ in particular in the treatment of variables by the tableau rules. The first variant I consider is standard first-order tableau where variables are instantiated by ground terms. For this section, if not stated otherwise, all considered fo ...
... The different versions of tableau for first-order logic differ in particular in the treatment of variables by the tableau rules. The first variant I consider is standard first-order tableau where variables are instantiated by ground terms. For this section, if not stated otherwise, all considered fo ...
MoggiMonads.pdf
... was later extended, following a similar methodology, to consider other features of computations like nondeterminism (see [Sha84]), side-effects and continuations (see [FFKD86, FF89]). The calculi based only on operational considerations, like the λv -calculus, are sound and complete w.r.t. the opera ...
... was later extended, following a similar methodology, to consider other features of computations like nondeterminism (see [Sha84]), side-effects and continuations (see [FFKD86, FF89]). The calculi based only on operational considerations, like the λv -calculus, are sound and complete w.r.t. the opera ...
Propositional Logic and Methods of Inference
... For example, let p represent “you are 18 or older” and q represents “you can vote” you are 18 or older implies you can vote if you are 18 or older then you can vote you are 18 or older, only if you can vote you are 18 or older is sufficient for you can vote you can vote if you are 18 or older you ca ...
... For example, let p represent “you are 18 or older” and q represents “you can vote” you are 18 or older implies you can vote if you are 18 or older then you can vote you are 18 or older, only if you can vote you are 18 or older is sufficient for you can vote you can vote if you are 18 or older you ca ...