2.3 Weakest Preconditions
... or “executing S1 ; S2 is guaranteed to make φ true exactly when executing S1 is guaranteed to end in those circumstances, where executing S2 is guaranteed to make φ true”. • Syntactically, GCL follows the Algol 60 and Pascal tradition where ‘;’ is an operator for joining the two commands into one la ...
... or “executing S1 ; S2 is guaranteed to make φ true exactly when executing S1 is guaranteed to end in those circumstances, where executing S2 is guaranteed to make φ true”. • Syntactically, GCL follows the Algol 60 and Pascal tradition where ‘;’ is an operator for joining the two commands into one la ...
Restricted notions of provability by induction
... Proof. See Corollary 8.7 in Wilkie–Paris [25] or Theorem V.5.26 in Hájek– Pudlák [13]. As mentioned before, most results of this section are not at all specific to the induction scheme, and so are more general than stated. Here we abstract one part that may be of independent interest. This stems f ...
... Proof. See Corollary 8.7 in Wilkie–Paris [25] or Theorem V.5.26 in Hájek– Pudlák [13]. As mentioned before, most results of this section are not at all specific to the induction scheme, and so are more general than stated. Here we abstract one part that may be of independent interest. This stems f ...
Implicative Formulae in the Vroofs as Computations” Analogy
... expressive power of Petri Nets. In this respect, [MaM89] suggests that all the computations of Linear Logic which ...
... expressive power of Petri Nets. In this respect, [MaM89] suggests that all the computations of Linear Logic which ...
slides - Computer and Information Science
... The idea of a truth table for some formula is that it describes the behavior of a formula under all possible interpretations of the primitive propositions that are included in the formula. • If there are n different atomic propositions in some formula, then there are different lines in the truth tab ...
... The idea of a truth table for some formula is that it describes the behavior of a formula under all possible interpretations of the primitive propositions that are included in the formula. • If there are n different atomic propositions in some formula, then there are different lines in the truth tab ...
characterization of classes of frames in modal language
... The symmetrical relation is equal to its converse. The IM (p → GF p) derivable in Kt ∪ φ → GF φ [McArthur, 1976, pp. 34–35]. Some classes of relations are not characterized by any formula, e.g. – as it is stated in theorem 8 – the class of irreflexive times.3 In particular this concerns so called neg ...
... The symmetrical relation is equal to its converse. The IM (p → GF p) derivable in Kt ∪ φ → GF φ [McArthur, 1976, pp. 34–35]. Some classes of relations are not characterized by any formula, e.g. – as it is stated in theorem 8 – the class of irreflexive times.3 In particular this concerns so called neg ...
Object-Based Unawareness
... as in a sentence like “I was not aware that people could use this loophole to circumvent the law”, the agent’s unawareness of a certain fact can often be traced to his unawareness of a certain object referred to in the fact (here, the object is the loophole in question). The reason behind this unawa ...
... as in a sentence like “I was not aware that people could use this loophole to circumvent the law”, the agent’s unawareness of a certain fact can often be traced to his unawareness of a certain object referred to in the fact (here, the object is the loophole in question). The reason behind this unawa ...
Progress In N=2 Field Theory
... And, as realized in the 19th Century by Abel, Gauss, and Riemann, such functions (and line integrals) with branch points are properly understood in terms of surfaces with ...
... And, as realized in the 19th Century by Abel, Gauss, and Riemann, such functions (and line integrals) with branch points are properly understood in terms of surfaces with ...
A Note on Bootstrapping Intuitionistic Bounded Arithmetic
... given an alternative definition of IS21 . They also gave an improved treatment of polynomial time functionals, introduced new powerful theories using lambda calculus, strengthened the feasibility results for IS21 , and reproved the ‘main theorem’ for S21 as a corollary of their results for IS21 . Th ...
... given an alternative definition of IS21 . They also gave an improved treatment of polynomial time functionals, introduced new powerful theories using lambda calculus, strengthened the feasibility results for IS21 , and reproved the ‘main theorem’ for S21 as a corollary of their results for IS21 . Th ...
New Methods in Computational Quantum Field Theory
... Goncharov, Spradlin, Vergu, & Volovich; Duhr, Gangl, & Rhodes ...
... Goncharov, Spradlin, Vergu, & Volovich; Duhr, Gangl, & Rhodes ...
Logic - Decision Procedures
... ... Sophism generally refers to a particularly confusing, illogical and/or insincere argument used by someone to make a point, or, perhaps, not to make a point. Sophistry refers to [...] rhetoric that is designed to appeal to the listener on grounds other than the strict logical cogency of the state ...
... ... Sophism generally refers to a particularly confusing, illogical and/or insincere argument used by someone to make a point, or, perhaps, not to make a point. Sophistry refers to [...] rhetoric that is designed to appeal to the listener on grounds other than the strict logical cogency of the state ...
Quantification - Rutgers Philosophy
... its infinite varieties, is marked by its penetration to a sentence’s sub-atomic level, a level from which sub-sentential elements that are common to multiplicities of sentences can be discerned and exploited. It has been found, specifically, that just by isolating those aspects of propositions that ...
... its infinite varieties, is marked by its penetration to a sentence’s sub-atomic level, a level from which sub-sentential elements that are common to multiplicities of sentences can be discerned and exploited. It has been found, specifically, that just by isolating those aspects of propositions that ...
A Simple Exposition of Gödel`s Theorem
... against materialism. Nine years later I was able to go to Princeton to study mathematical logic properly, and on my return tried out my argument on colleagues at Cambridge, then in a paper in 1959 to the Oxford Philosophical Society, which was finally published in 1961. G del's argument is self-refe ...
... against materialism. Nine years later I was able to go to Princeton to study mathematical logic properly, and on my return tried out my argument on colleagues at Cambridge, then in a paper in 1959 to the Oxford Philosophical Society, which was finally published in 1961. G del's argument is self-refe ...
Completeness of calculii for axiomatically defined classes of algebras
... Section 6 at the end of this paper gives an algebraic characterization of axiomatically defined classes of algebras which are definable by axioms of the latter form. In Section 2 a formal system for equation implications is described and the precise statement of our first result (Theorem 1) ...
... Section 6 at the end of this paper gives an algebraic characterization of axiomatically defined classes of algebras which are definable by axioms of the latter form. In Section 2 a formal system for equation implications is described and the precise statement of our first result (Theorem 1) ...
Modal Logics Definable by Universal Three
... frames, in particular all the classes we mentioned above, can be defined by simple first-order formulas. For a given first-order sentence Φ over the signature consisting of a single binary symbol R we define KΦ to be the set of those frames which satisfy Φ. In this paper we are interested in the sat ...
... frames, in particular all the classes we mentioned above, can be defined by simple first-order formulas. For a given first-order sentence Φ over the signature consisting of a single binary symbol R we define KΦ to be the set of those frames which satisfy Φ. In this paper we are interested in the sat ...
BernTalk
... numerator factor • Numerator violates one-loop “no-triangle” property. • Too many powers of loop momentum in one-loop subamplitude. • After cancellations behavior must be same as N = 4 Yang-Mills! ...
... numerator factor • Numerator violates one-loop “no-triangle” property. • Too many powers of loop momentum in one-loop subamplitude. • After cancellations behavior must be same as N = 4 Yang-Mills! ...
The Closed World Assumption
... A theory T in predicate logic is a set of sentences. (We do not insist that T contain only definite clauses.) A theory T is said to be complete for ground atomic formulas if, for every ground atomic formula A, either T |= A or T |= ¬A. Let T be any theory (it does not have to be complete for ground ...
... A theory T in predicate logic is a set of sentences. (We do not insist that T contain only definite clauses.) A theory T is said to be complete for ground atomic formulas if, for every ground atomic formula A, either T |= A or T |= ¬A. Let T be any theory (it does not have to be complete for ground ...
Guarded fragments with constants - Institute for Logic, Language
... 1 often suffices. However, in order to explain low complexity, a more refined analysis is needed. Consider for instance the global consequence problem for modal formulas (does every model that globally satisfies φ globally satisfy ψ? ). This is an ExpTime-complete problem. To understand why this pro ...
... 1 often suffices. However, in order to explain low complexity, a more refined analysis is needed. Consider for instance the global consequence problem for modal formulas (does every model that globally satisfies φ globally satisfy ψ? ). This is an ExpTime-complete problem. To understand why this pro ...
ADVENTURES IN PHYSICS AND MATH Edward Witten From a
... I have gone into so much detail about this to try to explain what my interests were as a graduate student in the mid-1970's. In short, when I was a graduate student, the era of perpetual revolution in particle physics was still in full swing. I assumed it would go on and I was hoping to participate ...
... I have gone into so much detail about this to try to explain what my interests were as a graduate student in the mid-1970's. In short, when I was a graduate student, the era of perpetual revolution in particle physics was still in full swing. I assumed it would go on and I was hoping to participate ...
A A S x
... if A has a model then AS has a model. It also holds that AS |= A, but the two formulas are not equivalent. The non-equivalent steps are: ...
... if A has a model then AS has a model. It also holds that AS |= A, but the two formulas are not equivalent. The non-equivalent steps are: ...
Mathematische Logik - WS14/15 Iosif Petrakis, Felix Quirin Weitk¨ amper November 13, 2014
... (B) m = 0. The corresponding (∗)-condition is that φ ∈ S(L) i.e., φ is a sentence. The definitional clauses are: (G1) A |= t1 = t2 iff t1 A = t2 A . (G2) A |= Rt1 . . . tn iff RA (t1 A . . . tn A ). (G3) A |= ¬φ iff not A |= φ. (G4) A |= (φ ∨ ψ) iff A |= φ or A |= ψ. (G5s) A |= (∃x ψ) iff there exis ...
... (B) m = 0. The corresponding (∗)-condition is that φ ∈ S(L) i.e., φ is a sentence. The definitional clauses are: (G1) A |= t1 = t2 iff t1 A = t2 A . (G2) A |= Rt1 . . . tn iff RA (t1 A . . . tn A ). (G3) A |= ¬φ iff not A |= φ. (G4) A |= (φ ∨ ψ) iff A |= φ or A |= ψ. (G5s) A |= (∃x ψ) iff there exis ...
Existential Definability of Modal Frame Classes
... by a set of modal formulas if and only if K is closed under surjective bounded morphisms, disjoint unions and generated subframes, and reflects ultrafilter extensions. All of the frame constructions used in the theorem – bounded morphisms, disjoint unions, generated subframes and ultrafilter extensio ...
... by a set of modal formulas if and only if K is closed under surjective bounded morphisms, disjoint unions and generated subframes, and reflects ultrafilter extensions. All of the frame constructions used in the theorem – bounded morphisms, disjoint unions, generated subframes and ultrafilter extensio ...
On Probability of First Order Formulas in a Given Model
... This paper tries to be a positive contribution to the efforts of building up a probability apparatus over formulas of semantic logic, in order to use it then to form the base of information theory and to apply it in forming information systems theory. Nevertheless, only a few fundamental probabilist ...
... This paper tries to be a positive contribution to the efforts of building up a probability apparatus over formulas of semantic logic, in order to use it then to form the base of information theory and to apply it in forming information systems theory. Nevertheless, only a few fundamental probabilist ...
+2 - Gore High School
... http://www.youtube.com/watch?v=fNE_I9FJc20&feature=related (take care, uses Llbs) ...
... http://www.youtube.com/watch?v=fNE_I9FJc20&feature=related (take care, uses Llbs) ...