.pdf
... tableau is infinite. We then used König’s lemma to show that this tableau has an infinite branch, which in turn must be a Hintikka set. The construction of the tableau made sure that S is a subset of that set and hence satisfiable. We will proceed in a similar way for first-order logic. First, we d ...
... tableau is infinite. We then used König’s lemma to show that this tableau has an infinite branch, which in turn must be a Hintikka set. The construction of the tableau made sure that S is a subset of that set and hence satisfiable. We will proceed in a similar way for first-order logic. First, we d ...
On presenting monotonicity and on EA=>AE (pdf file)
... But the two major books that deal with the calculational approach do a bad job of explaining how monotonicity/antimonotonicity is to be used. On page 61 of [1], Dijkstra and Scholten discuss the monotonic properties of negation and implication. But they don’t state the general theorem (5) and they d ...
... But the two major books that deal with the calculational approach do a bad job of explaining how monotonicity/antimonotonicity is to be used. On page 61 of [1], Dijkstra and Scholten discuss the monotonic properties of negation and implication. But they don’t state the general theorem (5) and they d ...
A pragmatic dialogic interpretation of bi
... involves a choice between the disjuncts. Following Girard’s classification of connectives in linear logic [27], it is the additive form of intuitionistic disjunction that makes it an unsuitable candidate as a right adjoint of subtraction. The solution advocated in [11] is to take multiplicative disj ...
... involves a choice between the disjuncts. Following Girard’s classification of connectives in linear logic [27], it is the additive form of intuitionistic disjunction that makes it an unsuitable candidate as a right adjoint of subtraction. The solution advocated in [11] is to take multiplicative disj ...
Quadripartitaratio - Revistas Científicas de la Universidad de
... into Ys” or “Xs may be regarded as Ys”. Rarely is the point made that when we are told explicitly that Xs may be regarded as Ys, there is at least the suggestion—if not a tacit admission—that Xs are not Ys. By the way, to see that ‘Some Xs are Y’ does not mean the same as ‘Some X is Y’, one may noti ...
... into Ys” or “Xs may be regarded as Ys”. Rarely is the point made that when we are told explicitly that Xs may be regarded as Ys, there is at least the suggestion—if not a tacit admission—that Xs are not Ys. By the way, to see that ‘Some Xs are Y’ does not mean the same as ‘Some X is Y’, one may noti ...
cl-ch9
... Any language will be a subset of this fixed stock. (In some contexts in later chapters where we are working with a language L we will want to be able to assume that there are infinitely many constants available that have not been used in L. This is no real difficulty, even if L itself needs to conta ...
... Any language will be a subset of this fixed stock. (In some contexts in later chapters where we are working with a language L we will want to be able to assume that there are infinitely many constants available that have not been used in L. This is no real difficulty, even if L itself needs to conta ...
Bilattices and the Semantics of Logic Programming
... any choice of truth value space, of course. M. Ginsberg has invented the elegant notion of bilattice ([14], [15]), which deals with precisely this issue. We reserve the definition till later on, but for motivation we note: Belnap’s four valued logic constitutes the simplest bilattice; a natural bila ...
... any choice of truth value space, of course. M. Ginsberg has invented the elegant notion of bilattice ([14], [15]), which deals with precisely this issue. We reserve the definition till later on, but for motivation we note: Belnap’s four valued logic constitutes the simplest bilattice; a natural bila ...
pdf
... if all of its finite subsets are. We gave three proofs for that: one using tableau proofs and König’s lemma, one giving a direct construction of a Hintikka set, and one using Lindenbaum’s construction, extending S to a maximally consistent set, which turned out to be a proof set. In first-order log ...
... if all of its finite subsets are. We gave three proofs for that: one using tableau proofs and König’s lemma, one giving a direct construction of a Hintikka set, and one using Lindenbaum’s construction, extending S to a maximally consistent set, which turned out to be a proof set. In first-order log ...
higher-order logic - University of Amsterdam
... In addition to its primitives all and some, a first-order predicate language with identity can also express such quantifiers as precisely one, all but two, at most three, etcetera, referring to specific finite quantities. What is lacking, however, is the general mathematical concept of finiteness. E ...
... In addition to its primitives all and some, a first-order predicate language with identity can also express such quantifiers as precisely one, all but two, at most three, etcetera, referring to specific finite quantities. What is lacking, however, is the general mathematical concept of finiteness. E ...
A Horn Clause that Implies an Undecidable Set of Horn Clauses ⋆ 1
... whether a given set of dependencies logically (finitely) implies another dependency. Many sorts of dependencies have been considered and some results concerning undecidability of finite implication have been proved. Usually the following two results have been used as tools in the proofs of undecidab ...
... whether a given set of dependencies logically (finitely) implies another dependency. Many sorts of dependencies have been considered and some results concerning undecidability of finite implication have been proved. Usually the following two results have been used as tools in the proofs of undecidab ...
Chapter 15 Slides - SRU Computer Science
... architecture of the machines on which programs will run Copyright © 2007 Addison-Wesley. All rights reserved. ...
... architecture of the machines on which programs will run Copyright © 2007 Addison-Wesley. All rights reserved. ...
ANNALS OF PURE AND APPLIED LOGIC I W
... ,f and g. Using this operator, it is possible to express a large variety of properties of computation paths. For example, c1n (skip* P skip*), where x is a program and P is a proposition, is true on a-paths that contain some P-state. Note that an h, for atomic programs expressible ...
... ,f and g. Using this operator, it is possible to express a large variety of properties of computation paths. For example, c1n (skip* P skip*), where x is a program and P is a proposition, is true on a-paths that contain some P-state. Note that an h, for atomic programs expressible ...
Ch. 15
... – Efficiency is the primary concern, rather than the suitability of the language for software development ...
... – Efficiency is the primary concern, rather than the suitability of the language for software development ...
Reasoning about Action and Change
... (1993) (see also Kautz, 1982; Morreau, 1992). In the language of firstorder dynamic logic they propose frame assertions of format A ⊃ [α]A (where α is allowed to be a compound action). We extend this idea to the intermediate states of a plan (typically a sequential composition of actions). Loosely s ...
... (1993) (see also Kautz, 1982; Morreau, 1992). In the language of firstorder dynamic logic they propose frame assertions of format A ⊃ [α]A (where α is allowed to be a compound action). We extend this idea to the intermediate states of a plan (typically a sequential composition of actions). Loosely s ...
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, ...
A Simple Tableau System for the Logic of Elsewhere
... the size of models of the satisfiable formulae) and we show that this problem becomes linear-time when the number of propositional variables is bounded. Although E and the well-known propositional modal S5 share numerous common features we show that E is strictly more expressive than S5 (in a sense ...
... the size of models of the satisfiable formulae) and we show that this problem becomes linear-time when the number of propositional variables is bounded. Although E and the well-known propositional modal S5 share numerous common features we show that E is strictly more expressive than S5 (in a sense ...
On Dummett`s Pragmatist Justification Procedure
... investigations into deduction, particularly his calculus of natural deduction, are used as a starting point for explaining the meaning of the logical constants on the basis of rules governing their use. In the standard natural deduction calculus [4, 8], the deductive use of a logical constant is gov ...
... investigations into deduction, particularly his calculus of natural deduction, are used as a starting point for explaining the meaning of the logical constants on the basis of rules governing their use. In the standard natural deduction calculus [4, 8], the deductive use of a logical constant is gov ...
Classical Propositional Logic
... The Resolution Calculus DPLL and the refined CDCL algorithm are the practically best methods for PL The resolution calculus (Robinson 1969) has been introduced as a basis for automated theorem proving in first-order logic. We will see it in detail in the first-order logic part of this lecture Refin ...
... The Resolution Calculus DPLL and the refined CDCL algorithm are the practically best methods for PL The resolution calculus (Robinson 1969) has been introduced as a basis for automated theorem proving in first-order logic. We will see it in detail in the first-order logic part of this lecture Refin ...