pdf
... 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 ...
Introduction to Mathematical Logic
... that they have relevance to the real objects –, and proves statements about what have been defined. These statements, or “theorems,” are pulled back to the real life, interpreted, explained, and compared to the expectations, do they confirm them, or do the contradict them? Mathematical logic studies ...
... that they have relevance to the real objects –, and proves statements about what have been defined. These statements, or “theorems,” are pulled back to the real life, interpreted, explained, and compared to the expectations, do they confirm them, or do the contradict them? Mathematical logic studies ...
Properties of binary transitive closure logics over trees
... Boolean connectives and quantification have their standard interpretation. Now, [[[TC x1 ,x2 φ](x, y)]]a = T iff (a(x), a(y)) ∈ TC({(b, d) | [[φ]]ab/x1d/x2 = T}) where ab/x1 d/x2 is the variable assignment that is identical to a except that x1 is assigned to b and x2 to d. If φ is a formula with fre ...
... Boolean connectives and quantification have their standard interpretation. Now, [[[TC x1 ,x2 φ](x, y)]]a = T iff (a(x), a(y)) ∈ TC({(b, d) | [[φ]]ab/x1d/x2 = T}) where ab/x1 d/x2 is the variable assignment that is identical to a except that x1 is assigned to b and x2 to d. If φ is a formula with fre ...
Constraint Propagation as a Proof System
... constraints. OBDDs possess many desirable algorithmic properties and have been used successfully in many areas, most notably in formal verification (see [Bry92,BCM 92]). We compare the strength of refutations by OBDDs with other proof systems for propositional logic. We show that OBDD-based refutati ...
... constraints. OBDDs possess many desirable algorithmic properties and have been used successfully in many areas, most notably in formal verification (see [Bry92,BCM 92]). We compare the strength of refutations by OBDDs with other proof systems for propositional logic. We show that OBDD-based refutati ...
pdf [local copy]
... the rewrite system for the Hydra battle (Moser, 2009; Fleischer, 2007), 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 elim ...
... the rewrite system for the Hydra battle (Moser, 2009; Fleischer, 2007), 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 elim ...
Safety Metric Temporal Logic is Fully Decidable
... Linear Temporal Logic in which the temporal operators are replaced by timeconstrained versions. For example, the formula [0,5] ϕ expresses that ϕ holds for the next 5 time units. Until recently, the only positive decidability results for MTL involved placing syntactic restrictions on the precision ...
... Linear Temporal Logic in which the temporal operators are replaced by timeconstrained versions. For example, the formula [0,5] ϕ expresses that ϕ holds for the next 5 time units. Until recently, the only positive decidability results for MTL involved placing syntactic restrictions on the precision ...
Programming in Logic Without Logic Programming
... isa(book, item), do not include time parameters. Temporal constraint predicates, including inequalities of the form T1 < T2 and T1 T2 between timepoints, and functional relationships among timepoints, such as max(T1, T2, T) and min(T1, T2, T) have only time parameters. In KELPS, temporal constrain ...
... isa(book, item), do not include time parameters. Temporal constraint predicates, including inequalities of the form T1 < T2 and T1 T2 between timepoints, and functional relationships among timepoints, such as max(T1, T2, T) and min(T1, T2, T) have only time parameters. In KELPS, temporal constrain ...
A Judgmental Reconstruction of Modal Logic
... reductions and expansions of proofs, respectively. Note that there are other ways to define meaning. For example, we frequently expand our language by notational definition. In intuitionistic logic negation is often given as a derived concept, where ¬A is considered a notation for A ⊃ ⊥. This means ...
... reductions and expansions of proofs, respectively. Note that there are other ways to define meaning. For example, we frequently expand our language by notational definition. In intuitionistic logic negation is often given as a derived concept, where ¬A is considered a notation for A ⊃ ⊥. This means ...
Default reasoning using classical logic
... attractive and have used it widely for declarative representations of problems in a variety of areas, including diagnostic reasoning [Rei87], theory of speech acts [Per87], natural language processing [Mer88], and inheritance hierarchies with exceptions [Eth87a]. Most importantly, it has been shown ...
... attractive and have used it widely for declarative representations of problems in a variety of areas, including diagnostic reasoning [Rei87], theory of speech acts [Per87], natural language processing [Mer88], and inheritance hierarchies with exceptions [Eth87a]. Most importantly, it has been shown ...
The Project Gutenberg EBook of The Algebra of Logic, by Louis
... premises, we can, in this ideography, draw all the logical conclusions which they imply by means of rules of transformation of formulas analogous to those of algebra,in fact, in which we can replace reasoning by the almost mechanical process of calculation. This second requirement is the requireme ...
... premises, we can, in this ideography, draw all the logical conclusions which they imply by means of rules of transformation of formulas analogous to those of algebra,in fact, in which we can replace reasoning by the almost mechanical process of calculation. This second requirement is the requireme ...
LOGIC AND p-RECOGNIZABLE SETS OF INTEGERS 1
... whose p-ary expansions are recognizable by a finite automaton. Various characterizations of p-recognizability are related in Theorem 4.1 : iterated uniform morphisms, algebraic formal power series, and definability by first-order formulae. Section 4 is centered around these four models of p-recogniz ...
... whose p-ary expansions are recognizable by a finite automaton. Various characterizations of p-recognizability are related in Theorem 4.1 : iterated uniform morphisms, algebraic formal power series, and definability by first-order formulae. Section 4 is centered around these four models of p-recogniz ...
The Logic of Provability
... no trouble arises from pretending it is. Indeed, it’s common to make this interpretation concrete and write f (x̄) to represent the unique y such that F (x̄, y) holds in PA. Thus, while PA lacks an actual term for functions like 2x , it can construct p-terms for them that agree on all values and beh ...
... no trouble arises from pretending it is. Indeed, it’s common to make this interpretation concrete and write f (x̄) to represent the unique y such that F (x̄, y) holds in PA. Thus, while PA lacks an actual term for functions like 2x , it can construct p-terms for them that agree on all values and beh ...
cl-ch9
... denotations, but an interpretation must still specify a domain, and that specification makes a difference as to truth for closed formulas involving =. For instance, ∃x∃y ∼ x = y will be true if the domain has at least two distinct elements, but false if it has only one.) Closed formulas, which are a ...
... denotations, but an interpretation must still specify a domain, and that specification makes a difference as to truth for closed formulas involving =. For instance, ∃x∃y ∼ x = y will be true if the domain has at least two distinct elements, but false if it has only one.) Closed formulas, which are a ...
chapter9
... for each implication (p1 ^ … ^ pn q) in KB: for each T such that SUBST(T,p1^…^pn) = SUBST(T,p1’^…^pn’) for some p1’,…,pn’ in KB q’ SUBST(T,q) if q’ is not a renaming of a sentence already in KB or new: add q’ to new S Unify(q’,A) if S is not fail then return S add new to KB ...
... for each implication (p1 ^ … ^ pn q) in KB: for each T such that SUBST(T,p1^…^pn) = SUBST(T,p1’^…^pn’) for some p1’,…,pn’ in KB q’ SUBST(T,q) if q’ is not a renaming of a sentence already in KB or new: add q’ to new S Unify(q’,A) if S is not fail then return S add new to KB ...
Combining Paraconsistent Logic with Argumentation
... Argument C attacks D2 . Whether C defeats D2 depends on the argument ordering but plausible argument orderings are possible in which C 6≺ D2 and so C defeats D2 . This is problematic, since s can be any formula, so any defeasible argument unrelated to A2 or B2 , such as D2 , can, depending on the ar ...
... Argument C attacks D2 . Whether C defeats D2 depends on the argument ordering but plausible argument orderings are possible in which C 6≺ D2 and so C defeats D2 . This is problematic, since s can be any formula, so any defeasible argument unrelated to A2 or B2 , such as D2 , can, depending on the ar ...
PDF
... 5. If ∆ is consistent, then at least one of ∆ ∪ {A} or ∆ ∪ {¬A} is consistent for any wff A. 6. If there is a truth-valuation v such that v(A) = 1 for all A ∈ ∆, then ∆ is consistent. 7. If 6` A, and ∆ contains the schema based on A, then ∆ is not consistent. Remark. The converse of 6 is also true; ...
... 5. If ∆ is consistent, then at least one of ∆ ∪ {A} or ∆ ∪ {¬A} is consistent for any wff A. 6. If there is a truth-valuation v such that v(A) = 1 for all A ∈ ∆, then ∆ is consistent. 7. If 6` A, and ∆ contains the schema based on A, then ∆ is not consistent. Remark. The converse of 6 is also true; ...
santhanam_ratlocc2011
... • PRGs exist non-constructively for any natural class of properties (by the probabilistic method), but when do quick PRGs exist? • Theorem [NW, IW, KvM] : There is a quick PRG against SIZEA(poly) iff there are explicit functions which are hard against A-oracle circuits of size 2o(n) ...
... • PRGs exist non-constructively for any natural class of properties (by the probabilistic method), but when do quick PRGs exist? • Theorem [NW, IW, KvM] : There is a quick PRG against SIZEA(poly) iff there are explicit functions which are hard against A-oracle circuits of size 2o(n) ...
PROPERTIES PRESERVED UNDER ALGEBRAIC
... under homomorphism ; a moment's reflection shows that this jibes with Theorem H, using the appropriate interpretation of "equivalence" of sentences. Tarski ordinarily considers more general systems that possess relations other than equality, and possibly no operations: for example, ordered groups, o ...
... under homomorphism ; a moment's reflection shows that this jibes with Theorem H, using the appropriate interpretation of "equivalence" of sentences. Tarski ordinarily considers more general systems that possess relations other than equality, and possibly no operations: for example, ordered groups, o ...
Propositional Logic
... A model of a set of sentences is an interpretation in which all the sentences are true ...
... A model of a set of sentences is an interpretation in which all the sentences are true ...
19_pl
... There are 8 interpretations (TTT, ..., FFF) The semantics (meaning) of a sentence is the set of interpretations in which the sentence evaluates to True Example: the semantics of the sentence P ( Q is the set of ...
... There are 8 interpretations (TTT, ..., FFF) The semantics (meaning) of a sentence is the set of interpretations in which the sentence evaluates to True Example: the semantics of the sentence P ( Q is the set of ...
Almost-certain eventualities and abstract probabilities in quantitative
... which we call qMµ — whose expressions are real- rather than Boolean-valued over S; the expressions denote ‘expected values’ of random variables over probabilistic distributions on the state space. The transitions exhibit probabilistic nondeterminism as well as potentially the other two kinds. As in ...
... which we call qMµ — whose expressions are real- rather than Boolean-valued over S; the expressions denote ‘expected values’ of random variables over probabilistic distributions on the state space. The transitions exhibit probabilistic nondeterminism as well as potentially the other two kinds. As in ...
Default Logic (Reiter) - Department of Computing
... where γ, α1 , . . . , αm , βm+1 , . . . , βn can be any formulas. The above would be written as a default rule like this: α1 ∧ · · · ∧ αm : ¬βm+1 , . . . , ¬βn γ Informally: ¬βi is consistent when βi is not derivable, and βi is not derivable corresponds to negation by failure not βi But consistent w ...
... where γ, α1 , . . . , αm , βm+1 , . . . , βn can be any formulas. The above would be written as a default rule like this: α1 ∧ · · · ∧ αm : ¬βm+1 , . . . , ¬βn γ Informally: ¬βi is consistent when βi is not derivable, and βi is not derivable corresponds to negation by failure not βi But consistent w ...