No Slide Title - University of Pennsylvania
... Stack inspection properties (security/access control) If setuuid bit is being set, root must be in call stack ...
... Stack inspection properties (security/access control) If setuuid bit is being set, root must be in call stack ...
Notes on First Order Logic
... Induction Step Suppose that ϕ is (∀y)ψ. Since τ is substitutable for x in ϕ we have two cases: 1. x does not occur free in ψ. Then ((∀y)ψ)[x/τ ] is the same as (∀y)ψ. Furthermore s and s[x/τ ] agree on all free variables in (∀y)ψ. By Theorem ??, we have A, s |= (∀y)ψ[x/τ ] iff A, s |= (∀y)ψ iff A, ...
... Induction Step Suppose that ϕ is (∀y)ψ. Since τ is substitutable for x in ϕ we have two cases: 1. x does not occur free in ψ. Then ((∀y)ψ)[x/τ ] is the same as (∀y)ψ. Furthermore s and s[x/τ ] agree on all free variables in (∀y)ψ. By Theorem ??, we have A, s |= (∀y)ψ[x/τ ] iff A, s |= (∀y)ψ iff A, ...
Chapter X: Computational Complexity of Propositional Fuzzy Logics
... This chapter is about computational complexity of decision problems in propositional fuzzy logics and also in algebras which constitute their algebraic semantics. We investigate sets of formulas and relations thereon, with an aim to determine their complexity by ranking them alongside well-known dec ...
... This chapter is about computational complexity of decision problems in propositional fuzzy logics and also in algebras which constitute their algebraic semantics. We investigate sets of formulas and relations thereon, with an aim to determine their complexity by ranking them alongside well-known dec ...
Bounded LTL Model Checking with Stable Models∗
... Verification of asynchronous systems is typically done by enumerating the reachable states of the system. Tools based on this approach (with various enhancements) include, e.g., the Spin system (Hol97), which supports extended finite state machines communicating through FIFO queues, and the Petri ne ...
... Verification of asynchronous systems is typically done by enumerating the reachable states of the system. Tools based on this approach (with various enhancements) include, e.g., the Spin system (Hol97), which supports extended finite state machines communicating through FIFO queues, and the Petri ne ...
Keep Changing Your Beliefs, Aiming for the Truth
... reliability of the new information. Update (known as ‘‘conditioning’’ in the Belief Revision literature) corresponds to having an absolute guarantee that the newly received information is truthful; radical upgrade (known also as ‘‘lexicographic revision’’) corresponds to having a high degree of trus ...
... reliability of the new information. Update (known as ‘‘conditioning’’ in the Belief Revision literature) corresponds to having an absolute guarantee that the newly received information is truthful; radical upgrade (known also as ‘‘lexicographic revision’’) corresponds to having a high degree of trus ...
On Decidability of Intuitionistic Modal Logics
... result in [6] and uses a translation into the two variable monadic guarded fragment of first order logic. Unfortunately, the decidability proof does not give a good decision procedure since it proceeds by reduction to satisfiability of formulas of SkS (monadic second-order theory of trees with const ...
... result in [6] and uses a translation into the two variable monadic guarded fragment of first order logic. Unfortunately, the decidability proof does not give a good decision procedure since it proceeds by reduction to satisfiability of formulas of SkS (monadic second-order theory of trees with const ...
Document
... In this case, of non-strictness (p depends on q both evenly and oddly, see later), SLDNF-resolution is incomplete, since there is no successful SLDNF-derivation for P {p}. Notice that in the absence of one of the first two clauses, there would be no incompleteness, since p true would not be in c ...
... In this case, of non-strictness (p depends on q both evenly and oddly, see later), SLDNF-resolution is incomplete, since there is no successful SLDNF-derivation for P {p}. Notice that in the absence of one of the first two clauses, there would be no incompleteness, since p true would not be in c ...
A Survey on the Model Theory of Difference Fields - Library
... (7) If (K, σ) |= ACFA and m ≥ 1, then (K, σ m ) |= ACFA. Proof. (1) The left to right implication is almost immediate. For the other one, moving K2 by some E-isomorphism, we may assume that E = E alg and that K1 and K2 are linearly disjoint over E. This implies that the ring K1 ⊗E K2 is a domain. De ...
... (7) If (K, σ) |= ACFA and m ≥ 1, then (K, σ m ) |= ACFA. Proof. (1) The left to right implication is almost immediate. For the other one, moving K2 by some E-isomorphism, we may assume that E = E alg and that K1 and K2 are linearly disjoint over E. This implies that the ring K1 ⊗E K2 is a domain. De ...
full text (.pdf)
... Equational logic possesses a rich theory and is the subject of numerous papers and texts Taylor 1979]. Its power and versatility in program specication and verication are widely recognized O'Donnell 1985 Goguen and Malcolm 1996]. The equational nature of Hoare logic has been observed previously ...
... Equational logic possesses a rich theory and is the subject of numerous papers and texts Taylor 1979]. Its power and versatility in program specication and verication are widely recognized O'Donnell 1985 Goguen and Malcolm 1996]. The equational nature of Hoare logic has been observed previously ...
On Natural Deduction in Classical First-Order Logic: Curry
... part), then the normal form u0 of u is independent from ∀α P and we found some u0 : C. If instead some assumption of ∀α P is left in u, one may encounter some instance P[n/α] which is false, and thus refute the assumption ∀α P. In this case the attempt of proving C from ∀αP fails, one obtains ¬P[n/α ...
... part), then the normal form u0 of u is independent from ∀α P and we found some u0 : C. If instead some assumption of ∀α P is left in u, one may encounter some instance P[n/α] which is false, and thus refute the assumption ∀α P. In this case the attempt of proving C from ∀αP fails, one obtains ¬P[n/α ...
The Emergence of First
... Skolem argued that set theory should be based on first-order logic, it was a radical and unprecedented proposal. The radical nature of what Skolem proposed resulted, above all, from its effect on the notion of categoricity. During the 1870s, as part of what became known as the arithmetization of ana ...
... Skolem argued that set theory should be based on first-order logic, it was a radical and unprecedented proposal. The radical nature of what Skolem proposed resulted, above all, from its effect on the notion of categoricity. During the 1870s, as part of what became known as the arithmetization of ana ...
Weak MSO+U over infinite trees
... Then the expression B[A1 , . . . , An ] defines a nested limsup automaton. This new automaton has nesting depth k + 1 and input alphabet A. When does it accept a tree t? Consider the tree t̂ over alphabet {0, 1}n , where the label of a node x is a bit-vector, which has 1 on coordinate i ∈ {1, . . . ...
... Then the expression B[A1 , . . . , An ] defines a nested limsup automaton. This new automaton has nesting depth k + 1 and input alphabet A. When does it accept a tree t? Consider the tree t̂ over alphabet {0, 1}n , where the label of a node x is a bit-vector, which has 1 on coordinate i ∈ {1, . . . ...
The Development of Mathematical Logic from Russell to Tarski
... Padoa lists a number of notions that he considers as belonging to general logic such as class (“which corresponds to the words: terminus of the scholastics, set of the mathematicians, common noun of ordinary language”). The notion of class is not defined but assumed with its informal meaning. Extens ...
... Padoa lists a number of notions that he considers as belonging to general logic such as class (“which corresponds to the words: terminus of the scholastics, set of the mathematicians, common noun of ordinary language”). The notion of class is not defined but assumed with its informal meaning. Extens ...
On the computational content of intuitionistic propositional proofs
... B is intuitionistically valid. A classical result of Harrop generalizes this result to sequents Γ→A ∨ B where Γ is a set of so called Harrop formulas. These are defined by: 1. every atomic formula is Harrop, ⊥ is Harrop; 2. if A and B are Harrop, then A ∧ B is Harrop; 3. if A is arbitrary and B is H ...
... B is intuitionistically valid. A classical result of Harrop generalizes this result to sequents Γ→A ∨ B where Γ is a set of so called Harrop formulas. These are defined by: 1. every atomic formula is Harrop, ⊥ is Harrop; 2. if A and B are Harrop, then A ∧ B is Harrop; 3. if A is arbitrary and B is H ...
Belief Revision in non
... In this section, we describe our approach for defining belief revision operators for non-classical logics. This is based on the following components: i) a sound and complete classical logic axiomatisation of the semantics of the object logic L, ii) a domain-dependent notion of “acceptability” for th ...
... In this section, we describe our approach for defining belief revision operators for non-classical logics. This is based on the following components: i) a sound and complete classical logic axiomatisation of the semantics of the object logic L, ii) a domain-dependent notion of “acceptability” for th ...
On the Complexity of the Equational Theory of Relational Action
... formulas appearing in this sequent. In particular, ACTω is a conservative extension of all its fragments, obtained by a restriction of the language, e.g. L, FL, the ∨−free fragment, the ∧−free fragment, and so on. All *-free fragments are finitary cut-free systems, admitting a standard proof-search ...
... formulas appearing in this sequent. In particular, ACTω is a conservative extension of all its fragments, obtained by a restriction of the language, e.g. L, FL, the ∨−free fragment, the ∧−free fragment, and so on. All *-free fragments are finitary cut-free systems, admitting a standard proof-search ...
Beyond Quantifier-Free Interpolation in Extensions of Presburger
... The and-left rule propagates the L-label to the subformulae of the antecedent of the first sequent. By applying or-left-l to the disjunction p(c) ∨ p(d), the proof splits into two branches. The right branch can immediately be closed using close-lr. The left branch requires an application of not-left ...
... The and-left rule propagates the L-label to the subformulae of the antecedent of the first sequent. By applying or-left-l to the disjunction p(c) ∨ p(d), the proof splits into two branches. The right branch can immediately be closed using close-lr. The left branch requires an application of not-left ...
Weak MSO+U over infinite trees
... The expressive power of the logic MSO+U is still not properly understood. It is an open problem whether satisfiability is decidable over infinite words. So far, research has dealt with fragments of the logic. The paper [4] introduces two classes of automata on infinite words, called ωB- and ωS-autom ...
... The expressive power of the logic MSO+U is still not properly understood. It is an open problem whether satisfiability is decidable over infinite words. So far, research has dealt with fragments of the logic. The paper [4] introduces two classes of automata on infinite words, called ωB- and ωS-autom ...
Axiomatic Set Teory P.D.Welch.
... other such properties. Borel in particular defined a hierarchy of sets now named after him, which gave very real substance to Cantor’s efforts to build up a hiearchy of increasing complexity from simple sets.) However it was clear that although the study of such sets was rewarded with a regular pict ...
... other such properties. Borel in particular defined a hierarchy of sets now named after him, which gave very real substance to Cantor’s efforts to build up a hiearchy of increasing complexity from simple sets.) However it was clear that although the study of such sets was rewarded with a regular pict ...
A Proof Theory for Generic Judgments
... for many examples. We will present a sequent calculus which provides this local notion of prooflevel abstraction via generic judgment and a new quantifier, ∇, which explicitly manipulates such local scope. Intuitionistic logic extended with ∇ satisfies cut-elimination even when the logic is addition ...
... for many examples. We will present a sequent calculus which provides this local notion of prooflevel abstraction via generic judgment and a new quantifier, ∇, which explicitly manipulates such local scope. Intuitionistic logic extended with ∇ satisfies cut-elimination even when the logic is addition ...
PDF
... Gurevich (1988) formalized the notion of a logic capturing PTIME and conjectured a negative answer to the above question. We saw above that in the presence of a linear order, FO + IFP captures PTIME. It can also be seen that this built-in order is necessary. On arbitrary nite structures, FO + IFP c ...
... Gurevich (1988) formalized the notion of a logic capturing PTIME and conjectured a negative answer to the above question. We saw above that in the presence of a linear order, FO + IFP captures PTIME. It can also be seen that this built-in order is necessary. On arbitrary nite structures, FO + IFP c ...
REVERSE MATHEMATICS AND RECURSIVE GRAPH THEORY
... there is a sequence hPi : i ∈ Ni such that for each i, Pi is a Hamilton path through Gi . From Theorem 16, together with the fact that ω together with the hyperarithmetical sets is a model of Σ11 −AC0 [16], we can draw the following recursion theoretic conclusion. Corollary 17. If hGi : i ∈ Ni is a ...
... there is a sequence hPi : i ∈ Ni such that for each i, Pi is a Hamilton path through Gi . From Theorem 16, together with the fact that ω together with the hyperarithmetical sets is a model of Σ11 −AC0 [16], we can draw the following recursion theoretic conclusion. Corollary 17. If hGi : i ∈ Ni is a ...
Admissible rules in the implication-- negation fragment of intuitionistic logic
... It can be checked, following [23], that for any intermediate logic L and finite set of implicational formulas {ϕ1 , . . . , ϕn }, the substitution σ p = ϕ1 → (ϕ2 → (· · · → (ϕn → p) · · · ) is an L-projective unifier. So by Lemma 2.3, the implicational fragment of any intermediate logic is (heredita ...
... It can be checked, following [23], that for any intermediate logic L and finite set of implicational formulas {ϕ1 , . . . , ϕn }, the substitution σ p = ϕ1 → (ϕ2 → (· · · → (ϕn → p) · · · ) is an L-projective unifier. So by Lemma 2.3, the implicational fragment of any intermediate logic is (heredita ...
The Expressive Power of Modal Dependence Logic
... With the aim to import dependences and team semantics to modal logic Väänänen [17] introduced modal dependence logic MDL. In the context of modal logic a team is just a set of states in a Kripke model. Modal dependence logic extends standard modal logic with team semantics by modal dependence atoms, ...
... With the aim to import dependences and team semantics to modal logic Väänänen [17] introduced modal dependence logic MDL. In the context of modal logic a team is just a set of states in a Kripke model. Modal dependence logic extends standard modal logic with team semantics by modal dependence atoms, ...