No Syllogisms for the Numerical Syllogistic
... avoid cumbersome circumlocutions, we henceforth ignore the distinction between natural numbers and the decimal strings representing them. An N -formula is an N † -formula at least one of whose literals is positive. We denote the set of N † -formulas by N † ; and similarly for N . A subset P ⊆ P is a ...
... avoid cumbersome circumlocutions, we henceforth ignore the distinction between natural numbers and the decimal strings representing them. An N -formula is an N † -formula at least one of whose literals is positive. We denote the set of N † -formulas by N † ; and similarly for N . A subset P ⊆ P is a ...
Linear Contextual Modal Type Theory
... proof theoretical account of availability, truth, and contextual validity in form of a sequent calculus. Next we prove the admissibility of cut, which guarantees the existence of canonical proofs in linear contextual modal logic. The cutelimination result of this section is formalized and machineche ...
... proof theoretical account of availability, truth, and contextual validity in form of a sequent calculus. Next we prove the admissibility of cut, which guarantees the existence of canonical proofs in linear contextual modal logic. The cutelimination result of this section is formalized and machineche ...
Recursive Predicates And Quantifiers
... of the results stands out more clearly than before. The general theorem asserts that to each of an enumeration of predicate forms, there is a predicate not expressible in that form. The predicates considered belong to elementary number theory. The possibility that this theorem may apply appears when ...
... of the results stands out more clearly than before. The general theorem asserts that to each of an enumeration of predicate forms, there is a predicate not expressible in that form. The predicates considered belong to elementary number theory. The possibility that this theorem may apply appears when ...
Foundations for Knowledge
... quantifying-in (“knowing what”), which cannot be expressed in Reiter’s approach. There are at least two reasons for this: for one, tests for Reiter are situation-suppressed formulas and hence cannot refer to future situations; for another, in order to make inferences about what the agent does not kn ...
... quantifying-in (“knowing what”), which cannot be expressed in Reiter’s approach. There are at least two reasons for this: for one, tests for Reiter are situation-suppressed formulas and hence cannot refer to future situations; for another, in order to make inferences about what the agent does not kn ...
THE SEMANTICS OF MODAL PREDICATE LOGIC II. MODAL
... more sophisticated notion of a modal individual and identity-at-a-world. It remains unsatisfactory having to choose between these competing semantics. Moreover, it would be nice if the difference between these semantics was better understood. Certainly, much research has been done into standard sema ...
... more sophisticated notion of a modal individual and identity-at-a-world. It remains unsatisfactory having to choose between these competing semantics. Moreover, it would be nice if the difference between these semantics was better understood. Certainly, much research has been done into standard sema ...
Mathematical Logic
... Any of these assumptions carries a marker . As markers we use assumption variables ¤0 , ¤1 , . . . , denoted by u, v, w, u0 , u1 , . . . . The (previous) variables will now often be called object variables, to distinguish them from assumption variables. If at a later stage (i.e. at a node below an a ...
... Any of these assumptions carries a marker . As markers we use assumption variables ¤0 , ¤1 , . . . , denoted by u, v, w, u0 , u1 , . . . . The (previous) variables will now often be called object variables, to distinguish them from assumption variables. If at a later stage (i.e. at a node below an a ...
An argumentation framework in default logic
... Abstract This article presents a formal theory about nontrivial reasoning with inconsistent information, applicable, among other things, to defeasible reasoning. The theory, which is inspired by a formal analysis of legal argument, is based on the idea that inconsistency tolerant reasoning is more t ...
... Abstract This article presents a formal theory about nontrivial reasoning with inconsistent information, applicable, among other things, to defeasible reasoning. The theory, which is inspired by a formal analysis of legal argument, is based on the idea that inconsistency tolerant reasoning is more t ...
5 model theory of modal logic
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related t ...
... between the (first-order) Kripke structure semantics and the (second-order) frame semantics, give rise to very distinct model theoretic flavours, each with their own tradition in the model theory of modal logic. Still, these two semantics meet through the notion of a general frame (closely related t ...
Strong Completeness for Iteration
... T X. We formalise such constructs using natural operations on functors. We also note that PDL and GL are usually interpreted over so-called standard models, in which the program/game constructs have a certain intended meaning. In our general framework this leads to the notion of a standard model rel ...
... T X. We formalise such constructs using natural operations on functors. We also note that PDL and GL are usually interpreted over so-called standard models, in which the program/game constructs have a certain intended meaning. In our general framework this leads to the notion of a standard model rel ...
PDF
... There are two natural approaches to lift the definition of vacuity in the context of model checking to a definition of inherent vacuity. In order to see the idea behind the first approach, consider specifications that are tautologies or contradictions. One need not have a context in order to see th ...
... There are two natural approaches to lift the definition of vacuity in the context of model checking to a definition of inherent vacuity. In order to see the idea behind the first approach, consider specifications that are tautologies or contradictions. One need not have a context in order to see th ...
Propositional Proof Complexity An Introduction
... remainder of πR into the segment of π2 corresponding to the occurrence of ψ in π1 . For the size analysis, let the constant K be the maximum of |πA | or |πR | over the finitely many schematic axioms and rules of F1 . The key is that for ...
... remainder of πR into the segment of π2 corresponding to the occurrence of ψ in π1 . For the size analysis, let the constant K be the maximum of |πA | or |πR | over the finitely many schematic axioms and rules of F1 . The key is that for ...
Ascribing beliefs to resource bounded agents
... model the agent in some logic and prove theorems about the agent’s behaviour in that logic. It is perhaps most natural to reason about the behaviour of the agent in an epistemic logic, and there has been a considerable amount of work in this area, for example, [15, 8, 14, 18, 21, 9, 17, 28, 25, 30]. ...
... model the agent in some logic and prove theorems about the agent’s behaviour in that logic. It is perhaps most natural to reason about the behaviour of the agent in an epistemic logic, and there has been a considerable amount of work in this area, for example, [15, 8, 14, 18, 21, 9, 17, 28, 25, 30]. ...
Logical Methods in Computer Science Vol. 8(4:19)2012, pp. 1–28 Submitted Oct. 27, 2011
... least r; similarly, Mra φ states that the rate is at most r. In this respect, our logic is similar to the Aumann’s system [Aum99b] developed for Harsanyi type spaces [Har67]. In spite of their syntactic similarities, CML and PML are very different. In the probabilistic case axiomatized by Zhou in hi ...
... least r; similarly, Mra φ states that the rate is at most r. In this respect, our logic is similar to the Aumann’s system [Aum99b] developed for Harsanyi type spaces [Har67]. In spite of their syntactic similarities, CML and PML are very different. In the probabilistic case axiomatized by Zhou in hi ...
Canonicity and representable relation algebras
... Any canonically axiomatised variety is canonical. But the converse may not hold. Canonicity might come about ‘in the limit’ — an ‘emergent property’ of a set of non-canonical axioms. Question 3 (Venema, ∼1995) Does RRA have a canonical axiomatisation – each individual axiom in it is canonical? Bit d ...
... Any canonically axiomatised variety is canonical. But the converse may not hold. Canonicity might come about ‘in the limit’ — an ‘emergent property’ of a set of non-canonical axioms. Question 3 (Venema, ∼1995) Does RRA have a canonical axiomatisation – each individual axiom in it is canonical? Bit d ...
Algebraic logic, I. Monadic boolean algebras
... is the fact that every quantifier is a closure operator. In the converse direction, the only obvious thing that can be said is that the closure operator on a discrète topological space is a quantifier. It is, in fact, a discrete quantifier; this is the reason for the use of the word "discrete" in co ...
... is the fact that every quantifier is a closure operator. In the converse direction, the only obvious thing that can be said is that the closure operator on a discrète topological space is a quantifier. It is, in fact, a discrete quantifier; this is the reason for the use of the word "discrete" in co ...
A Course in Modal Logic - Sun Yat
... differences. In this course, we will mostly study the technique part of modal logic, even if, from semantic aspect, also mostly study two types of formal semantics. Of course, different formal semantics, especially different axiomatic systems, characterize different modal concepts, whereas these dif ...
... differences. In this course, we will mostly study the technique part of modal logic, even if, from semantic aspect, also mostly study two types of formal semantics. Of course, different formal semantics, especially different axiomatic systems, characterize different modal concepts, whereas these dif ...
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 ...
The History of Categorical Logic
... encodes first-order and higher-order logics (classical, intuitionistic, etc.) by categories with additional properties and structure (Boolean categories, Heyting categories and so on). Thus, from the purely technical point of view, categorical logic constitutes a generalization of the algebraic enco ...
... encodes first-order and higher-order logics (classical, intuitionistic, etc.) by categories with additional properties and structure (Boolean categories, Heyting categories and so on). Thus, from the purely technical point of view, categorical logic constitutes a generalization of the algebraic enco ...
The Dedekind Reals in Abstract Stone Duality
... example, it provides a generic way of solving equations, when this is possible. Since ASD is formulated in a type-theoretical fashion, with absolutely no recourse to set theory, it is intrinsically a computable theory. The familiar arithmetical operations +, − are × are, of course, computable algebr ...
... example, it provides a generic way of solving equations, when this is possible. Since ASD is formulated in a type-theoretical fashion, with absolutely no recourse to set theory, it is intrinsically a computable theory. The familiar arithmetical operations +, − are × are, of course, computable algebr ...
POSSIBLE WORLDS SEMANTICS AND THE LIAR Reflections on a
... intensional constructions — is an area that is thriving on paradoxes and puzzles but is also haunted by them. There are, of course, the puzzles of intensionality that started the whole enterprise and constitute its raison d’être: Frege’s puzzle about the information value of true identity statement ...
... intensional constructions — is an area that is thriving on paradoxes and puzzles but is also haunted by them. There are, of course, the puzzles of intensionality that started the whole enterprise and constitute its raison d’être: Frege’s puzzle about the information value of true identity statement ...
Proof, Sets, and Logic - Boise State University
... 4/5/2013: Considering subversive language about second-order logic. Where to put it? I added a couple of sections with musings about second order logic. They are probably not in the right places, but they might be modified to fit where they are or moved to better locations. November 30, 2012: readi ...
... 4/5/2013: Considering subversive language about second-order logic. Where to put it? I added a couple of sections with musings about second order logic. They are probably not in the right places, but they might be modified to fit where they are or moved to better locations. November 30, 2012: readi ...
Boolean Logic - Programming Systems Lab
... expression is always >, and the prime tree normal form of an unsatisfiable expressions is always ⊥. Thus an expression is satisfiable if and only if its prime tree normal form is different from ⊥. We define prime expressions inductively: 1. ⊥ and > are prime expressions. 2. Cxst is a prime expressi ...
... expression is always >, and the prime tree normal form of an unsatisfiable expressions is always ⊥. Thus an expression is satisfiable if and only if its prime tree normal form is different from ⊥. We define prime expressions inductively: 1. ⊥ and > are prime expressions. 2. Cxst is a prime expressi ...
A Well-Founded Semantics for Logic Programs with Abstract
... sets, well-founded models (Van Gelder, Ross, and Schlipf 1991) have been found to be very useful as well. First, computing the well-founded model of a normal logic program is tractable. This compares to the NP-completeness of computing an answer set. Secondly, the well-founded model of a normal logi ...
... sets, well-founded models (Van Gelder, Ross, and Schlipf 1991) have been found to be very useful as well. First, computing the well-founded model of a normal logic program is tractable. This compares to the NP-completeness of computing an answer set. Secondly, the well-founded model of a normal logi ...
page 135 LOGIC IN WHITEHEAD`S UNIVERSAL ALGEBRA
... These works of C. S. Peirce were unpublished at the time of Principia and although Whitehead may have heard of them since they appeared shortly before his [44], he does not mention them. But there is more than a new single connective behind Whitehead’s attribution to Sheffer. Continuing his introduc ...
... These works of C. S. Peirce were unpublished at the time of Principia and although Whitehead may have heard of them since they appeared shortly before his [44], he does not mention them. But there is more than a new single connective behind Whitehead’s attribution to Sheffer. Continuing his introduc ...
Logic and Discrete Mathematics for Computer Scientists
... Science curriculum. In a perhaps unsympathetic view, the standard presentations (and there are many )the material in the course is treated as a discrete collection of so many techniques that the students must master for further studies in Computer Science. Our philosophy, and the one embodied in thi ...
... Science curriculum. In a perhaps unsympathetic view, the standard presentations (and there are many )the material in the course is treated as a discrete collection of so many techniques that the students must master for further studies in Computer Science. Our philosophy, and the one embodied in thi ...