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... dates back to the early realization of the prevalence of design errors, that is, “bugs”. While testing has once been considered a satisfying method for detecting bugs, today’s rapid development of complex and safety-critical systems requires more reliable methods. Model checking is such a more relia ...
... dates back to the early realization of the prevalence of design errors, that is, “bugs”. While testing has once been considered a satisfying method for detecting bugs, today’s rapid development of complex and safety-critical systems requires more reliable methods. Model checking is such a more relia ...
Variables In Real Life: A Jar Of Spare Change
... century before the first computers were actually developed. ...
... century before the first computers were actually developed. ...
Lecture Notes on Sequent Calculus
... Proof: From the disjunction property, either =⇒ A or =⇒ ¬A. For the first sequent, no rule applies. For the second sequent, only ⊃R applies and we would have to have a deduction of A =⇒ ⊥. But for this sequent no rule applies. ...
... Proof: From the disjunction property, either =⇒ A or =⇒ ¬A. For the first sequent, no rule applies. For the second sequent, only ⊃R applies and we would have to have a deduction of A =⇒ ⊥. But for this sequent no rule applies. ...
7 LOGICAL AGENTS
... The central component of a knowledge-based agent is its knowledge base, or KB. A knowledge base is a set of sentences. (Here “sentence” is used as a technical term. It is related but not identical to the sentences of English and other natural languages.) Each sentence is expressed in a language call ...
... The central component of a knowledge-based agent is its knowledge base, or KB. A knowledge base is a set of sentences. (Here “sentence” is used as a technical term. It is related but not identical to the sentences of English and other natural languages.) Each sentence is expressed in a language call ...
The Bang-Bang Funnel Controller (long version)
... (for example, relative degree one with stable zero dynamics). However, the price of the generality is that the input must be allowed to become arbitrarily large, which is problematic in applications. The first result concerning the funnel controller with input saturation was presented in [7] which w ...
... (for example, relative degree one with stable zero dynamics). However, the price of the generality is that the input must be allowed to become arbitrarily large, which is problematic in applications. The first result concerning the funnel controller with input saturation was presented in [7] which w ...
Lecture 2 - inst.eecs.berkeley.edu
... Intuitively, the concept of proof should already be familiar. We all like to assert things, and few of us like to say things that turn out to be false. A proof provides a means for guaranteeing such claims. Proofs in mathematics and computer science require a precisely stated proposition to be prove ...
... Intuitively, the concept of proof should already be familiar. We all like to assert things, and few of us like to say things that turn out to be false. A proof provides a means for guaranteeing such claims. Proofs in mathematics and computer science require a precisely stated proposition to be prove ...
The Relative Efficiency of Propositional Proof
... $1. Introduction. We are interested in studying the length of the shortest proof of a propositional tautology in various proof systems as a function of the length of the tautology. The smallest upper bound known for this function is exponential, no matter what the proof system. A question we would l ...
... $1. Introduction. We are interested in studying the length of the shortest proof of a propositional tautology in various proof systems as a function of the length of the tautology. The smallest upper bound known for this function is exponential, no matter what the proof system. A question we would l ...
Argumentative Approaches to Reasoning with Maximal Consistency
... Dung’s semantics for abstract argumentation frameworks. Given a framework AF (Definition 1), a key issue in its understanding is the question what combinations of arguments (called extensions) can collectively be accepted from AF. According to Dung (1995), this is determined as follows: Definition 6 ...
... Dung’s semantics for abstract argumentation frameworks. Given a framework AF (Definition 1), a key issue in its understanding is the question what combinations of arguments (called extensions) can collectively be accepted from AF. According to Dung (1995), this is determined as follows: Definition 6 ...
How to Express Self-Referential Probability and Avoid the
... These offer us two advantages. Firstly they allow for a systematic syntax once one wishes to allow for embedded probabilities. Secondly their inclusion might be fruitful, as was discussed in (Skyrms, 1980). For example we can then represent introspective abilities of an agent or the uncertainty or v ...
... These offer us two advantages. Firstly they allow for a systematic syntax once one wishes to allow for embedded probabilities. Secondly their inclusion might be fruitful, as was discussed in (Skyrms, 1980). For example we can then represent introspective abilities of an agent or the uncertainty or v ...
Intuitionistic Type Theory - The collected works of Per Martin-Löf
... In particular, the premisses and conclusion of a logical inference are judgements. The distinction between propositions and judgements was clear from Frege to Principia. These notions have later been replaced by the formalistic notions of formula and theorem (in a formal system), respectively. Contr ...
... In particular, the premisses and conclusion of a logical inference are judgements. The distinction between propositions and judgements was clear from Frege to Principia. These notions have later been replaced by the formalistic notions of formula and theorem (in a formal system), respectively. Contr ...
Intuitionistic Type Theory
... In particular, the premisses and conclusion of a logical inference are judgements. The distinction between propositions and judgements was clear from Frege to Principia. These notions have later been replaced by the formalistic notions of formula and theorem (in a formal system), respectively. Contr ...
... In particular, the premisses and conclusion of a logical inference are judgements. The distinction between propositions and judgements was clear from Frege to Principia. These notions have later been replaced by the formalistic notions of formula and theorem (in a formal system), respectively. Contr ...
finite structural axiomatization of every finite
... which is not finitely based, i.e., for every consequence C + determined by a finite set of standard rules C 6= C + . In this paper it will be proved that for every strongly finite consequence C there is a consequence C + determined ...
... which is not finitely based, i.e., for every consequence C + determined by a finite set of standard rules C 6= C + . In this paper it will be proved that for every strongly finite consequence C there is a consequence C + determined ...
The Semantic Complexity of some Fragments of English
... Consider the familiar A-ordering defined by setting if and only if: (i) % % , (ii) Vars Vars , and (iii) % % for all Vars . (Leitsch 1997, p. 100). It is routine to show that, when -resolution is applied to the clauses , pro ...
... Consider the familiar A-ordering defined by setting if and only if: (i) % % , (ii) Vars Vars , and (iii) % % for all Vars . (Leitsch 1997, p. 100). It is routine to show that, when -resolution is applied to the clauses , pro ...
LPF and MPLω — A Logical Comparison of VDM SL and COLD-K
... definedness. For formulae formed with Kleene’s or McCarthy’s connectives and Kleene’s quantifiers, logical consequence for three-valued logics according to the second idea reduces to classical logical consequence for two-valued logics. For formulae formed with Kleene’s connectives and Kleene’s quant ...
... definedness. For formulae formed with Kleene’s or McCarthy’s connectives and Kleene’s quantifiers, logical consequence for three-valued logics according to the second idea reduces to classical logical consequence for two-valued logics. For formulae formed with Kleene’s connectives and Kleene’s quant ...
3.6 First-Order Tableau
... of the δ(c) descendant. The constant c does not occur in (φ1 , . . . , ψ, . . . , φn ), so A0 |= φ1 ∧ . . . ∧ ψ ∧ . . . ∧ φn and by construction A0 |= ψ 0 , for the δ(c) descendant ψ 0 . The case ψ = ¬∀xS .χ can be shown analogously. Completeness of a first-order calculus is more complicated than in ...
... of the δ(c) descendant. The constant c does not occur in (φ1 , . . . , ψ, . . . , φn ), so A0 |= φ1 ∧ . . . ∧ ψ ∧ . . . ∧ φn and by construction A0 |= ψ 0 , for the δ(c) descendant ψ 0 . The case ψ = ¬∀xS .χ can be shown analogously. Completeness of a first-order calculus is more complicated than in ...
No Slide Title - University of Pennsylvania
... An RSM A is an HSM, if there is a total ordering of the modules such that if a box b of a module m is mapped to madule m’ then m’ appears after m The transition system of an HSM is finite, but can be exponential in size Analysis algorithms for RSMs are typically of same complexity as those of ...
... An RSM A is an HSM, if there is a total ordering of the modules such that if a box b of a module m is mapped to madule m’ then m’ appears after m The transition system of an HSM is finite, but can be exponential in size Analysis algorithms for RSMs are typically of same complexity as those of ...
Combinaison des logiques temporelle et déontique pour la
... a resource for a certain period, the obligation to release a resource before a deadline, or the prohibition to execute a task for a too long period. Temporal and deontic logics seem well suited to specify such concepts. In this thesis, we study how to combine these logics. Firstly, we study the prod ...
... a resource for a certain period, the obligation to release a resource before a deadline, or the prohibition to execute a task for a too long period. Temporal and deontic logics seem well suited to specify such concepts. In this thesis, we study how to combine these logics. Firstly, we study the prod ...
On Herbrand`s Theorem - UCSD Mathematics
... single sequent in P2 . Thirdly, from P2 we can construct a prenexification A∗ of A0 together with a witnessing substitution, thereby obtaining a Herbrand proof of A. To do this, we iterate the following procedure for pulling quantifiers to the front of the proved formula. Find any lowest quantifier ...
... single sequent in P2 . Thirdly, from P2 we can construct a prenexification A∗ of A0 together with a witnessing substitution, thereby obtaining a Herbrand proof of A. To do this, we iterate the following procedure for pulling quantifiers to the front of the proved formula. Find any lowest quantifier ...
The Pure Calculus of Entailment Author(s): Alan Ross Anderson and
... many people; we shall refer to it as the Official view. We agree with the Official view that there are no paradoxes of implication, but for reasons which are quite different from those ordinarily given. To be sure there is a misunderstanding involved, but it does not consist in the fact that the str ...
... many people; we shall refer to it as the Official view. We agree with the Official view that there are no paradoxes of implication, but for reasons which are quite different from those ordinarily given. To be sure there is a misunderstanding involved, but it does not consist in the fact that the str ...
Extracting Proofs from Tabled Proof Search
... II History atoms are not tabled; the table uses theories to infer additional atoms. III History atoms can be tabled; the table only infers its members. IV History atoms can be tabled; the table uses theories to infer additional atoms. The first two strategies yield proof certificates that simply us ...
... II History atoms are not tabled; the table uses theories to infer additional atoms. III History atoms can be tabled; the table only infers its members. IV History atoms can be tabled; the table uses theories to infer additional atoms. The first two strategies yield proof certificates that simply us ...
Topological aspects of real-valued logic
... compactness theorem. A version of Lω1 ,ω for metric structures, which extends continuous first-order logic, was introduced by Ben Yaacov and Iovino [14]. In their logic formulas of the form supi<ω ϕi and inf i<ω ϕi are permitted, provided that the total number of free variables remains finite, and t ...
... compactness theorem. A version of Lω1 ,ω for metric structures, which extends continuous first-order logic, was introduced by Ben Yaacov and Iovino [14]. In their logic formulas of the form supi<ω ϕi and inf i<ω ϕi are permitted, provided that the total number of free variables remains finite, and t ...
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... e.g. for the rewrite system for the Hydra battle [Mos09, Fle07], since the terms one obtains are simpler in some specifiable sense. It turns out that in the present situation the crux is, as becomes clear from Kripke’s further remarks, that he considers the case where one chooses at each elimination ...
... e.g. for the rewrite system for the Hydra battle [Mos09, Fle07], since the terms one obtains are simpler in some specifiable sense. It turns out that in the present situation the crux is, as becomes clear from Kripke’s further remarks, that he considers the case where one chooses at each elimination ...