Simply Logical: Intelligent Reasoning by Example
... 1990) or Sterling and Shapiro’s The Art of Prolog (MIT Press, 1986). ...
... 1990) or Sterling and Shapiro’s The Art of Prolog (MIT Press, 1986). ...
Structural Proof Theory
... based on axiomatic systems with just one or two rules of inference. Such systems can be useful as formal representations of what is provable, but the actual finding of proofs in axiomatic systems is next to impossible. A proof begins with instances of the axioms, but there is no systematic way of fi ...
... based on axiomatic systems with just one or two rules of inference. Such systems can be useful as formal representations of what is provable, but the actual finding of proofs in axiomatic systems is next to impossible. A proof begins with instances of the axioms, but there is no systematic way of fi ...
Annals of Pure and Applied Logic Commutative integral bounded
... previous work, considered pseudocomplemented BL-algebras with an added involution. This line of research was continued in [10], where subvarieties of pseudocomplemented BL-algebras with involution were introduced, and in [14], where the more general case of MTL-algebras was considered. As Heyting al ...
... previous work, considered pseudocomplemented BL-algebras with an added involution. This line of research was continued in [10], where subvarieties of pseudocomplemented BL-algebras with involution were introduced, and in [14], where the more general case of MTL-algebras was considered. As Heyting al ...
Incompleteness
... 1. Review of First Order Logic We give a brief overview of the main concepts and results of first order logic. This is far from a complete survey, but rather a quick presentation of the central points. We first review the basic set-up of first-order logic, with an eye towards two cases of particular ...
... 1. Review of First Order Logic We give a brief overview of the main concepts and results of first order logic. This is far from a complete survey, but rather a quick presentation of the central points. We first review the basic set-up of first-order logic, with an eye towards two cases of particular ...
MATH20302 Propositional Logic
... such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). The definition above is an inductive one, with (0) being the base case an ...
... such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). The definition above is an inductive one, with (0) being the base case an ...
.pdf
... Thus, changing the environment can affect what properties a program satisfies. Programming logics usually axiomatize program behavior under certain assumptions about the environment. Logics to reason about real-time, for example, axiomatize assumptions about how time advances while the program execu ...
... Thus, changing the environment can affect what properties a program satisfies. Programming logics usually axiomatize program behavior under certain assumptions about the environment. Logics to reason about real-time, for example, axiomatize assumptions about how time advances while the program execu ...
recursion
... Consider the number N = 1 + P1, P2….. Pk N is larger than Pk Thus N is not prime. So N must be product of some primes. ...
... Consider the number N = 1 + P1, P2….. Pk N is larger than Pk Thus N is not prime. So N must be product of some primes. ...
Duplication of directed graphs and exponential blow up of
... some other building blocks, and so on. In other words, symmetry is found at repeated levels. The upper bound in Theorem 31 re ects well this idea and shows how patterns lying in cut-free proofs might be recoverable from the graph of the original proof with cuts. In Sections 5 and 13 we analyze how p ...
... some other building blocks, and so on. In other words, symmetry is found at repeated levels. The upper bound in Theorem 31 re ects well this idea and shows how patterns lying in cut-free proofs might be recoverable from the graph of the original proof with cuts. In Sections 5 and 13 we analyze how p ...
Optimal acceptors and optimal proof systems
... One proof system Πw is simulated by another one Πs if the shortest proof for every tautology in Πs is at most polynomially longer than its shortest proof in Πw . The notion of p-simulation is similar, but requires also a polynomial-time computable function for translating the proofs from Πw to Πs . ...
... One proof system Πw is simulated by another one Πs if the shortest proof for every tautology in Πs is at most polynomially longer than its shortest proof in Πw . The notion of p-simulation is similar, but requires also a polynomial-time computable function for translating the proofs from Πw to Πs . ...
JUXTAPOSITION - Brown University
... §1. Introduction. Methods of combining logics are of great interest.1 Formal systems that result from the combination of multiple logical systems into a single system have applications in mathematics, linguistics, and computer science. For example, there are many applications for logics with multipl ...
... §1. Introduction. Methods of combining logics are of great interest.1 Formal systems that result from the combination of multiple logical systems into a single system have applications in mathematics, linguistics, and computer science. For example, there are many applications for logics with multipl ...
Independence logic and tuple existence atoms
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
Chu Spaces - Stanford University
... It is convenient to view Chu spaces as organized either by rows or by columns. For the former, we define r̂ : A → (X → Σ) as r̂(a)(x) = r(a, x), and refer to the function r̂(a) : X → Σ as row a of A. Dually we define ř : X → (A → Σ) as ř(x)(a) = r(a, x) and call ř(x) : A → Σ column x of A. When r ...
... It is convenient to view Chu spaces as organized either by rows or by columns. For the former, we define r̂ : A → (X → Σ) as r̂(a)(x) = r(a, x), and refer to the function r̂(a) : X → Σ as row a of A. Dually we define ř : X → (A → Σ) as ř(x)(a) = r(a, x) and call ř(x) : A → Σ column x of A. When r ...
pdf
... The idea here is to search through sub-formulas of the given formulas that might be TRUE simultaneously. For example, if is TRUE, then must be TRUE and must be FALSE. Starting with the input formula, we build a tree of possible models based on subformulas and derive a contradiction in each br ...
... The idea here is to search through sub-formulas of the given formulas that might be TRUE simultaneously. For example, if is TRUE, then must be TRUE and must be FALSE. Starting with the input formula, we build a tree of possible models based on subformulas and derive a contradiction in each br ...
Preferences and Unrestricted Rebut
... (possibly even the last one) is defeasible. Hence, if an argument restrictedly rebuts another argument then it also unrestrictedly rebuts it, but not vice versa. Forms of unrestricted rebut are applied in the formalism of Prakken and Sartor [16], the argumentation version of Nute’s Defeasible Logic ...
... (possibly even the last one) is defeasible. Hence, if an argument restrictedly rebuts another argument then it also unrestrictedly rebuts it, but not vice versa. Forms of unrestricted rebut are applied in the formalism of Prakken and Sartor [16], the argumentation version of Nute’s Defeasible Logic ...
