The Emergence of First
... ratiocinator (a formal calculus of reasoning) and a lingua characteristica (a universal language). As a step in this direction, Frege introduced a formal language on which to found arithmetic. Frege's formal language was two-dimensional, unlike the linear languages used earlier by Boole and later by ...
... ratiocinator (a formal calculus of reasoning) and a lingua characteristica (a universal language). As a step in this direction, Frege introduced a formal language on which to found arithmetic. Frege's formal language was two-dimensional, unlike the linear languages used earlier by Boole and later by ...
A pragmatic dialogic interpretation of bi
... identify, among the mathematical models of bi-intuitionism, those which may be regarded as its intended interpretations. The quest for an intended interpretation of a formal system often arises when several mathematical structures have been proposed to characterise an informal, perhaps vague notion ...
... identify, among the mathematical models of bi-intuitionism, those which may be regarded as its intended interpretations. The quest for an intended interpretation of a formal system often arises when several mathematical structures have been proposed to characterise an informal, perhaps vague notion ...
Linear Contextual Modal Type Theory
... functional abstraction and hi for the proof term of >. This little example illustrates the complex nature of logic variables in linear logic and their role in higher-order linear unification. In the >-free case, every linear resource needs to be consumed by the same term on either side of the equati ...
... functional abstraction and hi for the proof term of >. This little example illustrates the complex nature of logic variables in linear logic and their role in higher-order linear unification. In the >-free case, every linear resource needs to be consumed by the same term on either side of the equati ...
propositional logic extended with a pedagogically useful relevant
... deemed correct by PC, even the slowest students start complaining after a while. Having described the paradoxes, textbooks and logic teachers sometimes try to reason them away. Two types of moves are invoked in this connection. The first move is legitimate but insufficient: one shows that it is corr ...
... deemed correct by PC, even the slowest students start complaining after a while. Having described the paradoxes, textbooks and logic teachers sometimes try to reason them away. Two types of moves are invoked in this connection. The first move is legitimate but insufficient: one shows that it is corr ...
Introduction to Discrete Structures Introduction
... • Definition: Let A and B be two sets. The Cartesian product of A and B, denoted AxB, is the set of all ordered pairs (a,b) where aA and bB AxB={ (a,b) | (aA) (b B) } • The Cartesian product is also known as the cross product • Definition: A subset of a Cartesian product, R AxB is called a ...
... • Definition: Let A and B be two sets. The Cartesian product of A and B, denoted AxB, is the set of all ordered pairs (a,b) where aA and bB AxB={ (a,b) | (aA) (b B) } • The Cartesian product is also known as the cross product • Definition: A subset of a Cartesian product, R AxB is called a ...
page 135 LOGIC IN WHITEHEAD`S UNIVERSAL ALGEBRA
... At the time of Moore’s writings, various sets of independent properties or postulates for various mathematical theories like groups, fields, and geometry had already been found. Moore demanded not only to provide their existential theories, that is, an interpretation of their postulates, but also to ...
... At the time of Moore’s writings, various sets of independent properties or postulates for various mathematical theories like groups, fields, and geometry had already been found. Moore demanded not only to provide their existential theories, that is, an interpretation of their postulates, but also to ...
07.1-Reasoning
... • For example in the KB it will have a sentence that if an agent in 1,1 senses a stench then 1,2 or 2,1 has a wumpus in it. • If in 1,1 the agent sense nothing then it will know that 1,2 2,1 and 1,1 all have neither a wumpus nor a pit in them. ...
... • For example in the KB it will have a sentence that if an agent in 1,1 senses a stench then 1,2 or 2,1 has a wumpus in it. • If in 1,1 the agent sense nothing then it will know that 1,2 2,1 and 1,1 all have neither a wumpus nor a pit in them. ...
Introduction to Linear Logic
... The main concern of this report is to give an introduction to Linear Logic. For pedagogical purposes we shall also have a look at Classical Logic as well as Intuitionistic Logic. Linear Logic was introduced by J.-Y. Girard in 1987 and it has attracted much attention from computer scientists, as it i ...
... The main concern of this report is to give an introduction to Linear Logic. For pedagogical purposes we shall also have a look at Classical Logic as well as Intuitionistic Logic. Linear Logic was introduced by J.-Y. Girard in 1987 and it has attracted much attention from computer scientists, as it i ...
Paper - Department of Computer Science and Information Systems
... S4, S4.3. The computational complexity of the admissibility problem for these logics has been investigated in [Jerabek 2007]. For example, for intuitionistic logic, S4, and GL, the problem was shown to be NExpTime-complete. For further studies on unification and admissibility of rules in intuitionis ...
... S4, S4.3. The computational complexity of the admissibility problem for these logics has been investigated in [Jerabek 2007]. For example, for intuitionistic logic, S4, and GL, the problem was shown to be NExpTime-complete. For further studies on unification and admissibility of rules in intuitionis ...
Fine`s Theorem on First-Order Complete Modal Logics
... step of allowing languages to have arbitrarily large sets of variables, from which arbitrarily large canonical frames can be built for any given logic. The above body of work by Fine can be seen as part of a second wave of research that flowed from the publication by Kripke [41] of his seminal work ...
... step of allowing languages to have arbitrarily large sets of variables, from which arbitrarily large canonical frames can be built for any given logic. The above body of work by Fine can be seen as part of a second wave of research that flowed from the publication by Kripke [41] of his seminal work ...
The Expressive Power of Modal Dependence Logic
... atoms, =(p1 , . . . , pn , q). The intuitive meaning of the formula =(p1 , . . . , pn , q) is that within a team the truth value of the proposition q is functionally determined by the truth values of the propositions p1 , . . . , pn . Modal dependence logic is a first step toward combining functiona ...
... atoms, =(p1 , . . . , pn , q). The intuitive meaning of the formula =(p1 , . . . , pn , q) is that within a team the truth value of the proposition q is functionally determined by the truth values of the propositions p1 , . . . , pn . Modal dependence logic is a first step toward combining functiona ...
Modal Logic - Web Services Overview
... modal logic, or modal logic tout court. 2. The starting point, once again, is Aristotle, who was the first to study the relationship between modal statements and their validity. 3. However, the great discussion it enjoyed in the Middle Ages. 4. The official birth date of modal logic is 1921, when Cl ...
... modal logic, or modal logic tout court. 2. The starting point, once again, is Aristotle, who was the first to study the relationship between modal statements and their validity. 3. However, the great discussion it enjoyed in the Middle Ages. 4. The official birth date of modal logic is 1921, when Cl ...
Proof theory for modal logic
... for introducing the universal quantifier. For a survey on the debate around the deduction theorem in modal logic, see Hakli and Negri (2011). ...
... for introducing the universal quantifier. For a survey on the debate around the deduction theorem in modal logic, see Hakli and Negri (2011). ...
Quadripartitaratio - Revistas Científicas de la Universidad de
... orthodoxy. Even worse than the enthusiastic orthodox logicians are those who lack a sense of logical reality and who therefore treat logic like fiction, spinning out one new artificial system after the other, all equally empty. What do I mean by logical reality? What do I mean by physical reality? W ...
... orthodoxy. Even worse than the enthusiastic orthodox logicians are those who lack a sense of logical reality and who therefore treat logic like fiction, spinning out one new artificial system after the other, all equally empty. What do I mean by logical reality? What do I mean by physical reality? W ...
Knowledge Representation and Reasoning
... The preceding argument can be explained in terms of propositional logic. A proposition is an expression of a fact. The symbols, P and Q, represent propositions and the logical symbol ‘ → ’ is called a propositional connective. Many systems of propositional logic have been developed. In this lecture ...
... The preceding argument can be explained in terms of propositional logic. A proposition is an expression of a fact. The symbols, P and Q, represent propositions and the logical symbol ‘ → ’ is called a propositional connective. Many systems of propositional logic have been developed. In this lecture ...
Elementary Logic
... A literal is an atomic proposition or its negation. A propositional formula is in Conjunctive Normal Form (CNF) if it is a conjunction of disjunctions of literals. ...
... A literal is an atomic proposition or its negation. A propositional formula is in Conjunctive Normal Form (CNF) if it is a conjunction of disjunctions of literals. ...
Belief Revision in non
... logic axiomatisation of the semantics of the object logic L, ii) a domain-dependent notion of “acceptability” for theories of L and iii) a classical AGM belief revision operation. In general, different translation mechanisms can be defined from a given object logic to classical logic, depending on t ...
... logic axiomatisation of the semantics of the object logic L, ii) a domain-dependent notion of “acceptability” for theories of L and iii) a classical AGM belief revision operation. In general, different translation mechanisms can be defined from a given object logic to classical logic, depending on t ...
Quantifiers
... validity, we should be able to make this into a test for FO invalidity as follows: Have the procedure test for validity. If it is valid, then eventually the procedure will say it is valid (e.g. it says “Yes, it’s valid”), and hence we will know (because the procedure is sound) that it is not invalid ...
... validity, we should be able to make this into a test for FO invalidity as follows: Have the procedure test for validity. If it is valid, then eventually the procedure will say it is valid (e.g. it says “Yes, it’s valid”), and hence we will know (because the procedure is sound) that it is not invalid ...
Logic Programming, Functional Programming, and Inductive
... monotone. However, perhaps the database can be partitioned into several inductive definitions, so that each negation refers to a set that has already been defined (the dependency graph must be acyclic). The database can then be interpreted as an iterated inductive definition (via some treatment of f ...
... monotone. However, perhaps the database can be partitioned into several inductive definitions, so that each negation refers to a set that has already been defined (the dependency graph must be acyclic). The database can then be interpreted as an iterated inductive definition (via some treatment of f ...
1992-Ideal Introspective Belief
... that the beliefs will be introspectively complete, but it does not constrain them to be soundly based on the premises. Moore recognized this situation in formulated autoepistemic logic; his solution was to ground the belief set by making every element derivable from the premises and some assumptions ...
... that the beliefs will be introspectively complete, but it does not constrain them to be soundly based on the premises. Moore recognized this situation in formulated autoepistemic logic; his solution was to ground the belief set by making every element derivable from the premises and some assumptions ...
Handling Exceptions in nonmonotonic reasoning
... Note that γ1 is complete because g2 is rejected and g3 is excluded by γ1 . γ2 is complete because g1 is rejected and g4 is excluded by γ2 . The Exceptions-First Principle8 captures a very important feature of reasoning with propositions subject to exceptions. Exceptions stipulate meta conditions to ...
... Note that γ1 is complete because g2 is rejected and g3 is excluded by γ1 . γ2 is complete because g1 is rejected and g4 is excluded by γ2 . The Exceptions-First Principle8 captures a very important feature of reasoning with propositions subject to exceptions. Exceptions stipulate meta conditions to ...
Complexity of Recursive Normal Default Logic 1. Introduction
... translations, [GL90, MT93, MNR93], to show that this nonmonotonic rule system can also be represented as recursive propositional or a finite predicate logic program with classical negation and a recursive propositional or finite predicate logic normal default theory. We note in passing that the tech ...
... translations, [GL90, MT93, MNR93], to show that this nonmonotonic rule system can also be represented as recursive propositional or a finite predicate logic program with classical negation and a recursive propositional or finite predicate logic normal default theory. We note in passing that the tech ...
1 LOGICAL CONSEQUENCE: A TURN IN STYLE KOSTA DO SEN
... Gentzen’s work and in the proof-theoretical tradition stemming from it. Cut is specific because, unlike all the other rules in Gentzen’s formulation of logic, it has a formula (the formula C in the formulation of cut in the previous section), called the ‘cut formula’, which is in the premises but ca ...
... Gentzen’s work and in the proof-theoretical tradition stemming from it. Cut is specific because, unlike all the other rules in Gentzen’s formulation of logic, it has a formula (the formula C in the formulation of cut in the previous section), called the ‘cut formula’, which is in the premises but ca ...
article in press - School of Computer Science
... monadic two-variable guarded fragment GF 2mon of classical first-order logic, where guard relations satisfy conditions that can be expressed as monadic second-order definable closure constraints, is decidable. Our contribution is a slight generalisation of this result to account for conditions which ...
... monadic two-variable guarded fragment GF 2mon of classical first-order logic, where guard relations satisfy conditions that can be expressed as monadic second-order definable closure constraints, is decidable. Our contribution is a slight generalisation of this result to account for conditions which ...