AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY
... Such an assimilation of Kanger-type semantics to standard possible worlds semantics could, however, be misleading. Kanger’s formal semantics for modal logic does not, at least explicitly, utilize the notion of a possible world. Nor is there in his early works from 1957 any mention or discussion of p ...
... Such an assimilation of Kanger-type semantics to standard possible worlds semantics could, however, be misleading. Kanger’s formal semantics for modal logic does not, at least explicitly, utilize the notion of a possible world. Nor is there in his early works from 1957 any mention or discussion of p ...
LOGIC MAY BE SIMPLE Logic, Congruence - Jean
... However the “structuralist” approach of Bourbaki was inspired mainly by the development of abstract algebra (see [Dieudonné 1982], p. 619). It is worth noting that there was a time when “structure” was used to name what is now called “lattice” (see [Ore 1936, Glivenko 1938]). Even nowadays there is ...
... However the “structuralist” approach of Bourbaki was inspired mainly by the development of abstract algebra (see [Dieudonné 1982], p. 619). It is worth noting that there was a time when “structure” was used to name what is now called “lattice” (see [Ore 1936, Glivenko 1938]). Even nowadays there is ...
Completeness in modal logic - Lund University Publications
... We can now define some more connectives using the ones we already have. I give a list of definitions for connectives ∧, ⊃, ≡ and ◊ (meaning “and”, “if, then”, “if and only if” and “it is possible that” respectively): ...
... We can now define some more connectives using the ones we already have. I give a list of definitions for connectives ∧, ⊃, ≡ and ◊ (meaning “and”, “if, then”, “if and only if” and “it is possible that” respectively): ...
x - Loughborough University Intranet
... Objects and properties versus statements (4) • Our interpretation is that those students who do not want to declare that the statement is false as soon as a counterexample is found are not considering the closed statement. They are working with the open statement “n2-n+11 is a prime number”, in whic ...
... Objects and properties versus statements (4) • Our interpretation is that those students who do not want to declare that the statement is false as soon as a counterexample is found are not considering the closed statement. They are working with the open statement “n2-n+11 is a prime number”, in whic ...
Proof Nets Sequentialisation In Multiplicative Linear Logic
... Definition 5 (Constrainted Structure). A constrainted structure (or Cstructure) Rc is a d.a.g. obtained from a proof structure R (whose links have been given ports as in Definition 3), by adding untyped edges, called sequential edges, in such a way that each node n has the same label as in R, and ea ...
... Definition 5 (Constrainted Structure). A constrainted structure (or Cstructure) Rc is a d.a.g. obtained from a proof structure R (whose links have been given ports as in Definition 3), by adding untyped edges, called sequential edges, in such a way that each node n has the same label as in R, and ea ...
YABLO WITHOUT GODEL
... In general, if we claim that a new, more complicated proof avoids an appeal to a certain technique or assumption, we should substantiate that claim by showing that the new proof actually does us to prove the result from weaker assumptions. The proof in the previous section actually requires the addi ...
... In general, if we claim that a new, more complicated proof avoids an appeal to a certain technique or assumption, we should substantiate that claim by showing that the new proof actually does us to prove the result from weaker assumptions. The proof in the previous section actually requires the addi ...
Kripke completeness revisited
... Kripke’s proof was criticized in a review by Kaplan as lacking in rigor and as making excessive use of “intuitive” arguments on the geometry of tableau proofs. Kaplan suggested a different, more “mathematical” and more elegant approach based on an adaptation of Henkin’s completeness proof for class ...
... Kripke’s proof was criticized in a review by Kaplan as lacking in rigor and as making excessive use of “intuitive” arguments on the geometry of tableau proofs. Kaplan suggested a different, more “mathematical” and more elegant approach based on an adaptation of Henkin’s completeness proof for class ...
X - NUS School of Computing
... the resulting statement is either true or false. The set of all such elements that make the predicate true is called the truth set of the predicate. Definition 3.1.2 (Truth set) If P(x) is a predicate and x has domain D, the truth set is the set of all elements of D that make P(x) true when they are ...
... the resulting statement is either true or false. The set of all such elements that make the predicate true is called the truth set of the predicate. Definition 3.1.2 (Truth set) If P(x) is a predicate and x has domain D, the truth set is the set of all elements of D that make P(x) true when they are ...
X - NUS School of Computing
... the resulting statement is either true or false. The set of all such elements that make the predicate true is called the truth set of the predicate. Definition 3.1.2 (Truth set) If P(x) is a predicate and x has domain D, the truth set is the set of all elements of D that make P(x) true when they are ...
... the resulting statement is either true or false. The set of all such elements that make the predicate true is called the truth set of the predicate. Definition 3.1.2 (Truth set) If P(x) is a predicate and x has domain D, the truth set is the set of all elements of D that make P(x) true when they are ...
A Logical Framework for Default Reasoning
... syntax, semantics and a proof procedure and have theorems of soundness and completeness for this logic. 2. An alternative is to say that there is nothing wrong with classical logic; we should not expect reasoning to be just deduction from our knowledge. Circumscription [McCarthy86] can be seen in th ...
... syntax, semantics and a proof procedure and have theorems of soundness and completeness for this logic. 2. An alternative is to say that there is nothing wrong with classical logic; we should not expect reasoning to be just deduction from our knowledge. Circumscription [McCarthy86] can be seen in th ...
A Conditional Logical Framework *
... Conditional Logical Framework LFK is the same exploited in [HLL07] for the General Logical Framework GLF. However, there is an important difference between the two frameworks in the definition of predicates. On one hand, predicates in [HLL07] are used both to determine whether β-reduction fires and ...
... Conditional Logical Framework LFK is the same exploited in [HLL07] for the General Logical Framework GLF. However, there is an important difference between the two frameworks in the definition of predicates. On one hand, predicates in [HLL07] are used both to determine whether β-reduction fires and ...
Full Text - Institute for Logic, Language and Computation
... logic, like the first papers published about conditional logic. To develop it in a real mathematical form would need a lot of work. The logical and semantic framework is at best outlined, because we based our analysis primarily on what corresponds to the facts regarding the logic of natural language ...
... logic, like the first papers published about conditional logic. To develop it in a real mathematical form would need a lot of work. The logical and semantic framework is at best outlined, because we based our analysis primarily on what corresponds to the facts regarding the logic of natural language ...
Divide and congruence: From decomposition of modal formulas to preservation of branching and eta-bisimilarity
... tyft/tyxt format [22], and the ntyft/ntyxt format [21]. Bloom [5] introduced congruence formats for branching bisimilarity and for rooted branching bisimilarity. These formats include so-called patience rules for arguments i of function symbols f , which imply that a term f (p1 , . . . , pn ) inheri ...
... tyft/tyxt format [22], and the ntyft/ntyxt format [21]. Bloom [5] introduced congruence formats for branching bisimilarity and for rooted branching bisimilarity. These formats include so-called patience rules for arguments i of function symbols f , which imply that a term f (p1 , . . . , pn ) inheri ...
The Herbrand Manifesto
... weaker. In fact, it is stronger. There are more things that are true. We cannot prove them all, but we can prove everything we could prove before. Some may be disturbed by the fact that Herbrand entailment is not semi-decidable. But a similar argument could be leveled against Tarskian semantics. Sem ...
... weaker. In fact, it is stronger. There are more things that are true. We cannot prove them all, but we can prove everything we could prove before. Some may be disturbed by the fact that Herbrand entailment is not semi-decidable. But a similar argument could be leveled against Tarskian semantics. Sem ...
Document
... elements, and 2 = {}, which has one element – Induction hypothesis: k ℕ, and for every set A with k elements, 2A has 2k elements – Induction step: to show that for every set A with k+1 elements, 2A has 2k+1 elements ...
... elements, and 2 = {}, which has one element – Induction hypothesis: k ℕ, and for every set A with k elements, 2A has 2k elements – Induction step: to show that for every set A with k+1 elements, 2A has 2k+1 elements ...
Document
... elements, and 2 = {}, which has one element – Induction hypothesis: k ℕ, and for every set A with k elements, 2A has 2k elements – Induction step: to show that for every set A with k+1 elements, 2A has 2k+1 elements ...
... elements, and 2 = {}, which has one element – Induction hypothesis: k ℕ, and for every set A with k elements, 2A has 2k elements – Induction step: to show that for every set A with k+1 elements, 2A has 2k+1 elements ...
this PDF file
... Reviewed by Michel Meyer Eugene Garver's book is bound to become a classic before long, and not merely because of the amplitude of the analysis offered. It simultaneously sticks to the text and makes constant comparisons with modem authors. A full examination of Aristotle's grounding book had not be ...
... Reviewed by Michel Meyer Eugene Garver's book is bound to become a classic before long, and not merely because of the amplitude of the analysis offered. It simultaneously sticks to the text and makes constant comparisons with modem authors. A full examination of Aristotle's grounding book had not be ...
Interactive Theorem Proving with Temporal Logic
... Each of the rules of this sequent calculus can be given an intuitive reading. These readings will be re ected directly in the generation of text from proofs. Most of the propositional rules are straightforward. The ^ right rule for example states that if A and B each hold from the assumptions , then ...
... Each of the rules of this sequent calculus can be given an intuitive reading. These readings will be re ected directly in the generation of text from proofs. Most of the propositional rules are straightforward. The ^ right rule for example states that if A and B each hold from the assumptions , then ...
Chapter 2
... prove that the product of two even integers is also even, we can use knowledge about number theory. In particular, we could use the fact that an even integer is divisible by 2, or that an even integer m can be rewritten as 2k for some integer k. In this example, P(x, y) : x is an even integer y is ...
... prove that the product of two even integers is also even, we can use knowledge about number theory. In particular, we could use the fact that an even integer is divisible by 2, or that an even integer m can be rewritten as 2k for some integer k. In this example, P(x, y) : x is an even integer y is ...
An Overview of Intuitionistic and Linear Logic
... Constructivism is a point of view concerning the concepts and methods used in mathematical proofs, with preference towards constructive concepts and methods. It emerged in the late 19th century, as a response to the increasing use of abstracts concepts and methods in proofs in mathematics. Kronecker ...
... Constructivism is a point of view concerning the concepts and methods used in mathematical proofs, with preference towards constructive concepts and methods. It emerged in the late 19th century, as a response to the increasing use of abstracts concepts and methods in proofs in mathematics. Kronecker ...
Structural Logical Relations
... structural logical relations follow the same line of reasoning as their informal counterparts. The central idea is to formalize the relevant part of the argument in this auxiliary logic, which we refer to as the assertion logic. Structural logical relations are therefore best employed in proof assis ...
... structural logical relations follow the same line of reasoning as their informal counterparts. The central idea is to formalize the relevant part of the argument in this auxiliary logic, which we refer to as the assertion logic. Structural logical relations are therefore best employed in proof assis ...
Admissible rules in the implication-- negation fragment of intuitionistic logic
... logics and transitive modal logics have been obtained by Citkin and Rybakov [5,26]. Bases have been provided for certain intermediate logics by Iemhoff [10] and for transitive modal logics by Jeřábek [13], and Gentzen-style proof systems have been developed for these logics by Iemhoff and Metcalfe [ ...
... logics and transitive modal logics have been obtained by Citkin and Rybakov [5,26]. Bases have been provided for certain intermediate logics by Iemhoff [10] and for transitive modal logics by Jeřábek [13], and Gentzen-style proof systems have been developed for these logics by Iemhoff and Metcalfe [ ...
Introduction to first order logic for knowledge representation
... Language, real world and mathematical structure Language In describing a phenomena or a portion of the world, we adopt a language. The phrases of this language are used to describe objects of the real worlds, their properties, and facts that holds. This language can be informal (natural language, g ...
... Language, real world and mathematical structure Language In describing a phenomena or a portion of the world, we adopt a language. The phrases of this language are used to describe objects of the real worlds, their properties, and facts that holds. This language can be informal (natural language, g ...
Predicate logic definitions
... individual terms, the atomic sentence Ft1 t2 . . . tn is true in I iff the objects assigned to each closed individual term by I, in that order, have the property assigned to the predicate F by I. 2. A sentence of the form t1 = t2 is true in I iff the object assigned to t1 by I is identical to the ob ...
... individual terms, the atomic sentence Ft1 t2 . . . tn is true in I iff the objects assigned to each closed individual term by I, in that order, have the property assigned to the predicate F by I. 2. A sentence of the form t1 = t2 is true in I iff the object assigned to t1 by I is identical to the ob ...
Mathematical Induction - Cambridge Computer Lab
... To be valid, this argument cannot go on forever: it requires an ordering; and it must terminate (see lecture 7); this is called a well-founded partial ordering. ...
... To be valid, this argument cannot go on forever: it requires an ordering; and it must terminate (see lecture 7); this is called a well-founded partial ordering. ...