Self-Referential Probability

... on a supervaluational evaluation scheme. This variation is particularly interesting because it bears a close relationship to imprecise probabilities where agents’ credal states are taken to be sets of probability functions. In this chapter, we will also consider how to use this language to describe ...

... on a supervaluational evaluation scheme. This variation is particularly interesting because it bears a close relationship to imprecise probabilities where agents’ credal states are taken to be sets of probability functions. In this chapter, we will also consider how to use this language to describe ...

The Liar Paradox: A Consistent and Semantically Closed Solution

... are often characterised by discussions of Liar Sentences. While there are sentences which unquestionably trigger the Paradox, Kripke showed that it would be fruitless to look for an intrinsic criterion that will enable us to sieve out ... those sentences which lead to paradox. ...

... are often characterised by discussions of Liar Sentences. While there are sentences which unquestionably trigger the Paradox, Kripke showed that it would be fruitless to look for an intrinsic criterion that will enable us to sieve out ... those sentences which lead to paradox. ...

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 ...

Full Text - Institute for Logic, Language and Computation

... viewing syntactical and philosophical considerations. The existence of several kinds of conditional sentences is recognized in the current literature but the consequences are not sufficiently shown. We will investigate here the criteria which allow such a division and illustrate these differences by ...

... viewing syntactical and philosophical considerations. The existence of several kinds of conditional sentences is recognized in the current literature but the consequences are not sufficiently shown. We will investigate here the criteria which allow such a division and illustrate these differences by ...

Foundations for Knowledge

... action and either learns that box1 actually is in room1 or that it is not and thus has to be in room2. Assuming that pushing box x from y to z is possible whenever x is currently located at y, then whether or not the robot afterwards pushes box1 from room1 to room2 depends on the outcome of the sen ...

... action and either learns that box1 actually is in room1 or that it is not and thus has to be in room2. Assuming that pushing box x from y to z is possible whenever x is currently located at y, then whether or not the robot afterwards pushes box1 from room1 to room2 depends on the outcome of the sen ...

Theories and uses of context in knowledge representation and

... areas. Two examples will illustrate this “family resemblance”. Sperber and Wilson, in their book on relevance (1986:15), express a similar intuition from a psycholinguistic perspective: “The set of premises used in interpreting an utterance [. . . ] constitutes what is generally known as the context ...

... areas. Two examples will illustrate this “family resemblance”. Sperber and Wilson, in their book on relevance (1986:15), express a similar intuition from a psycholinguistic perspective: “The set of premises used in interpreting an utterance [. . . ] constitutes what is generally known as the context ...

Notes on the Science of Logic

... 3. You should be in command of some natural deduction technique for constructing proofs, including conditional proof (perhaps you know it under another name), reductio ad absurdum (or indirect proof), and the four quantifier rules. 4. Under “applications” you should know how to translate between hen ...

... 3. You should be in command of some natural deduction technique for constructing proofs, including conditional proof (perhaps you know it under another name), reductio ad absurdum (or indirect proof), and the four quantifier rules. 4. Under “applications” you should know how to translate between hen ...

logic for computer science - Institute for Computing and Information

... of declarative programming as well as about the logical definitions and algorithms that the programs express. In Appendix A we give a brief introduction to the philosophy and facilities of both languages, but this is aimed to some extent at teachers and students with a considerable background in com ...

... of declarative programming as well as about the logical definitions and algorithms that the programs express. In Appendix A we give a brief introduction to the philosophy and facilities of both languages, but this is aimed to some extent at teachers and students with a considerable background in com ...

Algebraic foundations for the semantic treatment of inquisitive content

... Still, the results of our algebraic enterprise will be highly relevant for natural language semantics, since it is to be expected that natural languages generally have constructions that are used to perform the basic algebraic operations on propositions. For instance, it is natural to expect that la ...

... Still, the results of our algebraic enterprise will be highly relevant for natural language semantics, since it is to be expected that natural languages generally have constructions that are used to perform the basic algebraic operations on propositions. For instance, it is natural to expect that la ...

AN EXPOSITION ANS DEVELOPMENT OF KANGER`S EARLY

... relations made it possible to apply semantic and model-theoretic methods to the study of a variety of modal notions other than logical necessity. Although Kanger was the first to publish, other researchers, among them Hintikka and Montague, also came up with the idea of utilizing accessibility relat ...

... relations made it possible to apply semantic and model-theoretic methods to the study of a variety of modal notions other than logical necessity. Although Kanger was the first to publish, other researchers, among them Hintikka and Montague, also came up with the idea of utilizing accessibility relat ...

article - British Academy

... Then for any proposition p, Socrates believes that p if and only if Socrates knows that p. Let Socrates know that he is Socrates, so that problems of the kind discussed above do not arise. We cannot everywhere substitute ‘Socrates believes that’ for ‘Socrates knows that’, salva veritate. Socrates kn ...

... Then for any proposition p, Socrates believes that p if and only if Socrates knows that p. Let Socrates know that he is Socrates, so that problems of the kind discussed above do not arise. We cannot everywhere substitute ‘Socrates believes that’ for ‘Socrates knows that’, salva veritate. Socrates kn ...

A Qualitative Theory of Dynamic Interactive Belief Revision

... with the agents’ prior beliefs. On the other hand, the classical AGM theory and its more recent extensions have been very successful in dealing with the problem of revising one-agent, first-level (factual) beliefs when they are contradicted by new information. So it is natural to look for a way to c ...

... with the agents’ prior beliefs. On the other hand, the classical AGM theory and its more recent extensions have been very successful in dealing with the problem of revising one-agent, first-level (factual) beliefs when they are contradicted by new information. So it is natural to look for a way to c ...

Back to Basics: Revisiting the Incompleteness

... quantifiers can either be primitive, or – e.g. in the case where T is a rich set theory – they will be defined by restricting the theory’s native quantifiers. Either way, quantifier notation in the formal sentences below should always be read as indicating such numerical quantifiers. The standard in ...

... quantifiers can either be primitive, or – e.g. in the case where T is a rich set theory – they will be defined by restricting the theory’s native quantifiers. Either way, quantifier notation in the formal sentences below should always be read as indicating such numerical quantifiers. The standard in ...

7 LOGICAL AGENTS

... bottomless pits that will trap anyone who wanders into these rooms (except for the wumpus, which is too big to fall in). The only mitigating feature of this bleak environment is the possibility of finding a heap of gold. Although the wumpus world is rather tame by modern computer game standards, it ...

... bottomless pits that will trap anyone who wanders into these rooms (except for the wumpus, which is too big to fall in). The only mitigating feature of this bleak environment is the possibility of finding a heap of gold. Although the wumpus world is rather tame by modern computer game standards, it ...

Carnap and Quine on the analytic-synthetic - Philsci

... logical/factual, logical/descriptive, a priori/a posteriori, internal/external, necessary/contingent, which in one way or another have all been equated to the general analytic/synthetic distinction. It would lead to far to analyse the differences and interplay between the various pairs. In order to ...

... logical/factual, logical/descriptive, a priori/a posteriori, internal/external, necessary/contingent, which in one way or another have all been equated to the general analytic/synthetic distinction. It would lead to far to analyse the differences and interplay between the various pairs. In order to ...

Discrete Mathematics: Chapter 2, Predicate Logic

... SL is complete. The second way relates to SL’s expressive capabilities. The logical connectives of SL form a complete set of connectives: any sentence that can be formulated by means of truth-functional connectives, regardless of the number of sentences combined or the types of connectives employed, ...

... SL is complete. The second way relates to SL’s expressive capabilities. The logical connectives of SL form a complete set of connectives: any sentence that can be formulated by means of truth-functional connectives, regardless of the number of sentences combined or the types of connectives employed, ...

x - Loughborough University Intranet

... • In our population, a large number of students face difficulties to provide negation of quantified sentences, especially in the case of the sentence involving an implication. • As the population comes from various universities, we can suspect that many fresh students in France face these difficulti ...

... • In our population, a large number of students face difficulties to provide negation of quantified sentences, especially in the case of the sentence involving an implication. • As the population comes from various universities, we can suspect that many fresh students in France face these difficulti ...

The substitutional theory of logical consequence

... truth preservation is not a sufficient condition for formal validity. It could be objected that this depends on a certain understanding of necessity: If we understand necessity as formal or logical necessity, then necessary truth preservation is a sufficient condition for formal validity. However, t ...

... truth preservation is not a sufficient condition for formal validity. It could be objected that this depends on a certain understanding of necessity: If we understand necessity as formal or logical necessity, then necessary truth preservation is a sufficient condition for formal validity. However, t ...

Soundness and Completeness for Sentence Logic Trees

... worry later about connecting this up with validity-lemma L1 assures us that we will be able to do so. For now, we will connect the semantic concept of a model with the syntactic concept of an open branch. Remember that an open branch always represents an interpretation in which all sentences on the ...

... worry later about connecting this up with validity-lemma L1 assures us that we will be able to do so. For now, we will connect the semantic concept of a model with the syntactic concept of an open branch. Remember that an open branch always represents an interpretation in which all sentences on the ...

Counterfactuals

... similarity around a world w with the set {w} representing the highest level of similarity and other spheres loosening the constraints from there. Since the centered system has nesting, the similarity ordering for two spheres of a given world is always well-defined. Lewis’ conditions are, quite obvio ...

... similarity around a world w with the set {w} representing the highest level of similarity and other spheres loosening the constraints from there. Since the centered system has nesting, the similarity ordering for two spheres of a given world is always well-defined. Lewis’ conditions are, quite obvio ...

Truth-Functional Propositional Logic

... the substitution of simple symbols for words. The examples to have in mind are the rules and operations employed in arithmetic and High School algebra. Once we learn how to add, subtract, multiply, and divide the whole numbers {0,1,2,3,...} in elementary school, we can apply these rules, say, to cal ...

... the substitution of simple symbols for words. The examples to have in mind are the rules and operations employed in arithmetic and High School algebra. Once we learn how to add, subtract, multiply, and divide the whole numbers {0,1,2,3,...} in elementary school, we can apply these rules, say, to cal ...

Hybrid, Classical, and Presuppositional Inquisitive Semantics

... • Since the interrogative ?{p , q} is to be a question, is has to be non-informative. The disjunct marked in red takes care of that. • If we read ?{p , q} as an alternative question, it may be observed that the answers p and q do not have the same status as the answer ¬p ∧ ¬q. • Already for the pola ...

... • Since the interrogative ?{p , q} is to be a question, is has to be non-informative. The disjunct marked in red takes care of that. • If we read ?{p , q} as an alternative question, it may be observed that the answers p and q do not have the same status as the answer ¬p ∧ ¬q. • Already for the pola ...

1992-Ideal Introspective Belief

... Any set I’ from Cl that satisfies these conditions, and is closed under tautological consequence, will be called Cl-stable (or simply stable) for the premises I’. The definition and term “stable set” are from Stalnaker [13]. The beliefs are stable in the sense that an agent has perfect knowledge of ...

... Any set I’ from Cl that satisfies these conditions, and is closed under tautological consequence, will be called Cl-stable (or simply stable) for the premises I’. The definition and term “stable set” are from Stalnaker [13]. The beliefs are stable in the sense that an agent has perfect knowledge of ...

Remarks on Second-Order Consequence

... A large amount of set-theoretical propositions which are known to be independent of the usual set theory ZFC (Zermelo-Fraenkel with the axiom of choice) are precisely about the contents of the power set operation. The most discussed among these is Cantor's Continuum Hypothesis (CH) according to whic ...

... A large amount of set-theoretical propositions which are known to be independent of the usual set theory ZFC (Zermelo-Fraenkel with the axiom of choice) are precisely about the contents of the power set operation. The most discussed among these is Cantor's Continuum Hypothesis (CH) according to whic ...