Fichte`s Legacy in Logic
... logic of judgment deals only with general representations (i.e., not with intuitions), any judgment that is recognized in logic requires the synthesis [Synthesis] or combination [Verbindung] of at least two concepts. I shall refer to this as Kant’s synthetic construal of judgment. The traces of the ...
... logic of judgment deals only with general representations (i.e., not with intuitions), any judgment that is recognized in logic requires the synthesis [Synthesis] or combination [Verbindung] of at least two concepts. I shall refer to this as Kant’s synthetic construal of judgment. The traces of the ...
Notes on the Science of Logic
... There is one foundational matter, however, that we do not treat in this course: the justification of definitions of operators by proving the existence of functions satisfying given conditions (see NAL:7B-7). In fact what permits us to be rigorous without overwhelming you is that whenever a definitio ...
... There is one foundational matter, however, that we do not treat in this course: the justification of definitions of operators by proving the existence of functions satisfying given conditions (see NAL:7B-7). In fact what permits us to be rigorous without overwhelming you is that whenever a definitio ...
Propositional Discourse Logic
... the same as Frank then, at first, the situation may be unclear. But a moment of reflection shows that regardless of the actual subject matter, no one can be right and no one can be wrong. If Frank is right, then John is wrong, but then Paul is wrong so Frank must be wrong too. In a similar way all p ...
... the same as Frank then, at first, the situation may be unclear. But a moment of reflection shows that regardless of the actual subject matter, no one can be right and no one can be wrong. If Frank is right, then John is wrong, but then Paul is wrong so Frank must be wrong too. In a similar way all p ...
Propositional logic - Cheriton School of Computer Science
... We will introduce the connectives in an intuitive fashion, by describing their effect on declarative sentences. In doing so, we anticipate the semantics which we will use to decide if a sentence is true or false. However, it’s important to keep in mind that our proof system is not concerned with tru ...
... We will introduce the connectives in an intuitive fashion, by describing their effect on declarative sentences. In doing so, we anticipate the semantics which we will use to decide if a sentence is true or false. However, it’s important to keep in mind that our proof system is not concerned with tru ...
Modal Languages and Bounded Fragments of Predicate Logic
... 1. MODAL LOGIC AND CLASSICAL LOGIC Modal Logic is traditionally concerned with the intensional operators “possibly” and “necessary”, whose intuitive correspondence with the standard quantifiers “there exists” and “for all” comes out clearly in the usual Kripke semantics. This observation underlies t ...
... 1. MODAL LOGIC AND CLASSICAL LOGIC Modal Logic is traditionally concerned with the intensional operators “possibly” and “necessary”, whose intuitive correspondence with the standard quantifiers “there exists” and “for all” comes out clearly in the usual Kripke semantics. This observation underlies t ...
Propositions as [Types] - Research Showcase @ CMU
... According to one conception of the theory of types, propositions and types are identified: Propositions = Types . This idea is well-known under the slogan “Propositions as types”, and has been developed by Martin-Löf [ML84] and others [How80, Tai]. In this report we distinguish propositions and typ ...
... According to one conception of the theory of types, propositions and types are identified: Propositions = Types . This idea is well-known under the slogan “Propositions as types”, and has been developed by Martin-Löf [ML84] and others [How80, Tai]. In this report we distinguish propositions and typ ...
Consequence Operators for Defeasible - SeDiCI
... for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a con°uence point for many alternative logical frameworks. Di®erent formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasibl ...
... for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a con°uence point for many alternative logical frameworks. Di®erent formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasibl ...
Informal Proceedings of the 30th International Workshop on
... protocol for key exchange and then encryption with derived keys. For human users this is most visible as transport layer security (TLS) used by all web browsers. History has shown that developing such protocols is an error-prone process, and attacks have been found even after protocols were in wides ...
... protocol for key exchange and then encryption with derived keys. For human users this is most visible as transport layer security (TLS) used by all web browsers. History has shown that developing such protocols is an error-prone process, and attacks have been found even after protocols were in wides ...
No Syllogisms for the Numerical Syllogistic
... if `X is complete, then, trivially, so is X . The following questions now arise. Does there exist a finite set X of syllogistic rules in N † such that the direct derivation relation `X is sound and complete? If not, does there at least exist a finite set X of syllogistic rules in N † such that the ...
... if `X is complete, then, trivially, so is X . The following questions now arise. Does there exist a finite set X of syllogistic rules in N † such that the direct derivation relation `X is sound and complete? If not, does there at least exist a finite set X of syllogistic rules in N † such that the ...
Keep Changing Your Beliefs, Aiming for the Truth
... introduced this distinction in the context of belief revision, and investigated the connection between repeated updates and finite identifiability. Of course, the interested case in Formal Learning Theory is the infinite one, corresponding to e.g. learning a natural language and connected to the pro ...
... introduced this distinction in the context of belief revision, and investigated the connection between repeated updates and finite identifiability. Of course, the interested case in Formal Learning Theory is the infinite one, corresponding to e.g. learning a natural language and connected to the pro ...
BASIC COUNTING - Mathematical sciences
... • Set Theory: Informally we define a set as a collection of objects. The resulting theory of how one can operate on sets is known as naïve set theory. It is naïve because the informal definition leads to subtle paradoxes. A more careful definition of set removes these paradoxes and leaves the conclu ...
... • Set Theory: Informally we define a set as a collection of objects. The resulting theory of how one can operate on sets is known as naïve set theory. It is naïve because the informal definition leads to subtle paradoxes. A more careful definition of set removes these paradoxes and leaves the conclu ...
God, the Devil, and Gödel
... the second ingredient: a philosophical view concerning what constitutes mathematics and what constitutes proof. Il would suffice to identify provability with derivability in some particular formal system, and mathematics with the body of propositions expressible in that system, with ‘expressible’ su ...
... the second ingredient: a philosophical view concerning what constitutes mathematics and what constitutes proof. Il would suffice to identify provability with derivability in some particular formal system, and mathematics with the body of propositions expressible in that system, with ‘expressible’ su ...
Logic in the Finite - CIS @ UPenn
... 3 De nability and Complexity In light of all these contrasts, one might legitimately wonder what nite model theory could be. The following sections attempt to answer this question by giving a feeling for some of the techniques, results, and open problems of the subject. For the most part, we will ...
... 3 De nability and Complexity In light of all these contrasts, one might legitimately wonder what nite model theory could be. The following sections attempt to answer this question by giving a feeling for some of the techniques, results, and open problems of the subject. For the most part, we will ...
Discrete Mathematics: Chapter 2, Predicate Logic
... using only words, something that was done prior to the seventeenth century! The vocabulary of Predicate Logic generalizes and extends that of mathematical theories. PL takes to the extreme the modern mathematical tendency to use symbolic representation. Formulating a sentence by means of PL complete ...
... using only words, something that was done prior to the seventeenth century! The vocabulary of Predicate Logic generalizes and extends that of mathematical theories. PL takes to the extreme the modern mathematical tendency to use symbolic representation. Formulating a sentence by means of PL complete ...
Sequent Combinators: A Hilbert System for the Lambda
... Department of Computer Science, University of Edinburgh The King’s Buildings, Edinburgh, EH9 3JZ, United Kingdom Fax: (+44) (131) 667-7209 Abstract This paper introduces a Hilbert system for lambda calculus called sequent combinators. Sequent combinators address many of the problems of Hilbert syste ...
... Department of Computer Science, University of Edinburgh The King’s Buildings, Edinburgh, EH9 3JZ, United Kingdom Fax: (+44) (131) 667-7209 Abstract This paper introduces a Hilbert system for lambda calculus called sequent combinators. Sequent combinators address many of the problems of Hilbert syste ...
F - Teaching-WIKI
... • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sentence that is True under all interpretations, no matter what the world is actually like or how the semantics are defined (ex ...
... • A model for a KB is a “possible world” (assignment of truth values to propositional symbols) in which each sentence in the KB is True • A valid sentence or tautology is a sentence that is True under all interpretations, no matter what the world is actually like or how the semantics are defined (ex ...
Introduction to Linear Logic
... Basic Research In Computer Science, Centre of the Danish National Research Foundation. ...
... Basic Research In Computer Science, Centre of the Danish National Research Foundation. ...
Group knowledge is not always distributed (neither is it always implicit)
... they would be able to conclude w. This example also illustrates the relevance of communication with respect to this kind of group knowledge: the scientists should somehow transfer their knowledge through communication in order to make the underlying implicit knowledge explicit. In this paper, we try ...
... they would be able to conclude w. This example also illustrates the relevance of communication with respect to this kind of group knowledge: the scientists should somehow transfer their knowledge through communication in order to make the underlying implicit knowledge explicit. In this paper, we try ...
Essentials Of Symbolic Logic
... special logical notation is not peculiar to modern logic. Aristotle, the ancient founder of the subject, used variables to facilitate his own work. Although the difference in this respect between modern and classical logic is not one of kind but of degree, the difference in degree is tremendous. The ...
... special logical notation is not peculiar to modern logic. Aristotle, the ancient founder of the subject, used variables to facilitate his own work. Although the difference in this respect between modern and classical logic is not one of kind but of degree, the difference in degree is tremendous. The ...
Classical first-order predicate logic This is a powerful extension of
... A formula with free variables is neither true nor false in a structure M , because the free variables have no meaning in M . It’s like asking ‘is x = 7 true?’ We get stuck trying to evaluate a predicate formula in a structure in the same way as a propositional one, because the structure does not fix ...
... A formula with free variables is neither true nor false in a structure M , because the free variables have no meaning in M . It’s like asking ‘is x = 7 true?’ We get stuck trying to evaluate a predicate formula in a structure in the same way as a propositional one, because the structure does not fix ...
Lecture slides
... Testing an Argument Form 1. Identify the premises and conclusions. 2. Construct a truth table showing the truth values of all the premises and the conclusion. 3. If the truth table contains a row in which all premises are true and the conclusion is false, then the argument form is invalid. If every ...
... Testing an Argument Form 1. Identify the premises and conclusions. 2. Construct a truth table showing the truth values of all the premises and the conclusion. 3. If the truth table contains a row in which all premises are true and the conclusion is false, then the argument form is invalid. If every ...
On the Notion of Coherence in Fuzzy Answer Set Semantics
... negation in the context of residuated logic programming is provided in terms of the notion of coherence as a generalization in the fuzzy framework of the concept of consistence. Then, fuzzy answer sets for general residuated logic programs are defined as a suitable generalization of the Gelfond-Lifs ...
... negation in the context of residuated logic programming is provided in terms of the notion of coherence as a generalization in the fuzzy framework of the concept of consistence. Then, fuzzy answer sets for general residuated logic programs are defined as a suitable generalization of the Gelfond-Lifs ...
Document
... : Show that for all A M(P), every interpretation I: I |= P implies I |= A. Let us consider Herbrand interpretation IH = {A | A ground atom and I |= A}. Then, I |= P I |= A ← B1, ... , Bn for all A ← B1, ... , Bn ground(P) if I |= B1, ... , Bn then I |= A for all A ← B1, ... , Bn ground(P) ...
... : Show that for all A M(P), every interpretation I: I |= P implies I |= A. Let us consider Herbrand interpretation IH = {A | A ground atom and I |= A}. Then, I |= P I |= A ← B1, ... , Bn for all A ← B1, ... , Bn ground(P) if I |= B1, ... , Bn then I |= A for all A ← B1, ... , Bn ground(P) ...
Least and greatest fixed points in Ludics, CSL 2015, Berlin.
... µX. (↑1)⊕(↑X) is the type of natural numbers, and νY. ↑((↑Nat)⊗Y ) is the type of infinite streams of natural numbers. Fixed points can also be interleaved, which corresponds to mutual (co)inductive definitions. For example, µX. T ⊗(νY. ↑((↑1)⊕((↑X)⊗Y ))) is the type of arbitrarily branching well-fo ...
... µX. (↑1)⊕(↑X) is the type of natural numbers, and νY. ↑((↑Nat)⊗Y ) is the type of infinite streams of natural numbers. Fixed points can also be interleaved, which corresponds to mutual (co)inductive definitions. For example, µX. T ⊗(νY. ↑((↑1)⊕((↑X)⊗Y ))) is the type of arbitrarily branching well-fo ...
full text (.pdf)
... used to reduce partial correctness assertions to static assertions about the underlying domain of computation. In this paper we show that this propositional fragment, which we call propositional Hoare logic (PHL), is subsumed by Kleene algebra with tests (KAT), an equational algebraic system introdu ...
... used to reduce partial correctness assertions to static assertions about the underlying domain of computation. In this paper we show that this propositional fragment, which we call propositional Hoare logic (PHL), is subsumed by Kleene algebra with tests (KAT), an equational algebraic system introdu ...
Jesús Mosterín
Jesús Mosterín (born 1941) is a leading Spanish philosopher and a thinker of broad spectrum, often at the frontier between science and philosophy.