The Closed World Assumption
... We view our program as a logical theory expressing knowledge about the world. In several situations, it is convenient to assume that the program contains complete information about certain kinds of logical statements. We can then make additional inferences about the world based on the assumed comple ...
... We view our program as a logical theory expressing knowledge about the world. In several situations, it is convenient to assume that the program contains complete information about certain kinds of logical statements. We can then make additional inferences about the world based on the assumed comple ...
An Axiomatization of G'3
... in the logics considered in this paper as explained in 2.3, gives an alternate interpretation to this notation: A formula F is a logical consequence of T , i.e. T `X F , if and only if `X (F1 ∧ · · · ∧ Fn ) → F for some formulas Fi ∈ T . We furthermore extend this notation, for any pair of theories ...
... in the logics considered in this paper as explained in 2.3, gives an alternate interpretation to this notation: A formula F is a logical consequence of T , i.e. T `X F , if and only if `X (F1 ∧ · · · ∧ Fn ) → F for some formulas Fi ∈ T . We furthermore extend this notation, for any pair of theories ...
Extending modal logic
... Theorem (Sahlqvist): If a frame class K is definable by Sahlqvist formulas, then a complete axiomatization of the modal logic of K is obtained by adding these formulas as axioms to the basic modal logic. ...
... Theorem (Sahlqvist): If a frame class K is definable by Sahlqvist formulas, then a complete axiomatization of the modal logic of K is obtained by adding these formulas as axioms to the basic modal logic. ...
Three Solutions to the Knower Paradox
... to Anderson’s solution. At the beginning of his discussion, Anderson adopts a notion of knowledge based on a formal notion of proof: the set K0 of the things known by James is recursively enumerable and contains Q, Robinson Arithmetic (as we will see in a moment, K0 has to contain Q, otherwise James ...
... to Anderson’s solution. At the beginning of his discussion, Anderson adopts a notion of knowledge based on a formal notion of proof: the set K0 of the things known by James is recursively enumerable and contains Q, Robinson Arithmetic (as we will see in a moment, K0 has to contain Q, otherwise James ...
SECOND-ORDER LOGIC, OR - University of Chicago Math
... pleases. It can be any cardinality.2 Call a first-order language with a set K of non-logical symbols L1K. If it has equality, call it L1K =. A set of symbols alone is insufficient for making a meaningful language; we also need to know how we can put those symbols together. Just as we cannot say in E ...
... pleases. It can be any cardinality.2 Call a first-order language with a set K of non-logical symbols L1K. If it has equality, call it L1K =. A set of symbols alone is insufficient for making a meaningful language; we also need to know how we can put those symbols together. Just as we cannot say in E ...
notes
... This is no accident. It turns out that all derivable type judgments ⊢ e : τ (with the empty environment to the left of the turnstile) give propositional tautologies. This is because the typing rules of λ→ correspond exactly to the proof rules of propositional intuitionistic logic. Intuitionistic log ...
... This is no accident. It turns out that all derivable type judgments ⊢ e : τ (with the empty environment to the left of the turnstile) give propositional tautologies. This is because the typing rules of λ→ correspond exactly to the proof rules of propositional intuitionistic logic. Intuitionistic log ...
Curry`s paradox, Lukasiewicz, and Field
... Lukasiewicz carries over to problem in understanding Field. Lukasiewicz’s early work on propositional many-valued logics was motivated by an antipathy to determinism, and in particular by the thought that the future is genuinely open. So, speaking of the future, some propositions are (already) true, ...
... Lukasiewicz carries over to problem in understanding Field. Lukasiewicz’s early work on propositional many-valued logics was motivated by an antipathy to determinism, and in particular by the thought that the future is genuinely open. So, speaking of the future, some propositions are (already) true, ...
A Proof of Cut-Elimination Theorem for U Logic.
... system, GBPC, is more suitable for the main aim of introducing the U logic; Which is finding a common base for BPL and B. To make the two systems more comparable, Ardeshir and Vaezian in [1], introduced a modified version of mentioned axiomatization, and called it GBPC*. They also excluded connectiv ...
... system, GBPC, is more suitable for the main aim of introducing the U logic; Which is finding a common base for BPL and B. To make the two systems more comparable, Ardeshir and Vaezian in [1], introduced a modified version of mentioned axiomatization, and called it GBPC*. They also excluded connectiv ...
The disjunction introduction rule: Syntactic and semantics
... example, Braine and O´Brien (1998b) assign it a limited role in the basic model linked to primary skills of the mental logic theory, and Braine and O´Brien (1998c) acknowledge that they thought of the possibility of introducing some restrictions to this rule. Nonetheless, this new problem can be eas ...
... example, Braine and O´Brien (1998b) assign it a limited role in the basic model linked to primary skills of the mental logic theory, and Braine and O´Brien (1998c) acknowledge that they thought of the possibility of introducing some restrictions to this rule. Nonetheless, this new problem can be eas ...
03_Artificial_Intelligence-PredicateLogic
... • There are many deductive systems for predicate logic that are sound (only deriving correct results) and complete (able to derive any logically valid implication) • The logical consequence relation in predicate logic is only semidecidable • This lecture focused on three core aspects of the predicat ...
... • There are many deductive systems for predicate logic that are sound (only deriving correct results) and complete (able to derive any logically valid implication) • The logical consequence relation in predicate logic is only semidecidable • This lecture focused on three core aspects of the predicat ...
Predicate Logic
... of discourse over which all quantifiers range; manysorted first-order logic allows variables to have different sorts, which have different domains • The characteristic feature of first-order logic is that individuals can be quantified, but not predicates; secondorder logic extends first-order logic ...
... of discourse over which all quantifiers range; manysorted first-order logic allows variables to have different sorts, which have different domains • The characteristic feature of first-order logic is that individuals can be quantified, but not predicates; secondorder logic extends first-order logic ...
Predicate logic
... • There are many deductive systems for predicate logic that are sound (only deriving correct results) and complete (able to derive any logically valid implication) • The logical consequence relation in predicate logic is only semidecidable • This lecture focused on three core aspects of the predicat ...
... • There are many deductive systems for predicate logic that are sound (only deriving correct results) and complete (able to derive any logically valid implication) • The logical consequence relation in predicate logic is only semidecidable • This lecture focused on three core aspects of the predicat ...
03_Artificial_Intelligence-PredicateLogic
... • There are many deductive systems for predicate logic that are sound (only deriving correct results) and complete (able to derive any logically valid implication) • The logical consequence relation in predicate logic is only semidecidable • This lecture focused on three core aspects of the predicat ...
... • There are many deductive systems for predicate logic that are sound (only deriving correct results) and complete (able to derive any logically valid implication) • The logical consequence relation in predicate logic is only semidecidable • This lecture focused on three core aspects of the predicat ...
IS COMMON KNOWLEDGE OF RATIONALITY SLUGGISH? 1
... denote this event by [S ′ ]. Knowledge is introduced by operators Ki for each player i, such that for any event E, Ki E is the event that i knows E.5 We skip the details of the construction of the state space, which is documented in numerous publications.6 Recall the following two properties of know ...
... denote this event by [S ′ ]. Knowledge is introduced by operators Ki for each player i, such that for any event E, Ki E is the event that i knows E.5 We skip the details of the construction of the state space, which is documented in numerous publications.6 Recall the following two properties of know ...
Chapter 2
... connected if it has more than one vertex. A forest is a graph that consists of a set of trees. Given a forest, removal of one edge increases the number of connected components by exactly one. An example of a tree is the set of all descendants of a particular person, where (p, p ) is an edge if p i ...
... connected if it has more than one vertex. A forest is a graph that consists of a set of trees. Given a forest, removal of one edge increases the number of connected components by exactly one. An example of a tree is the set of all descendants of a particular person, where (p, p ) is an edge if p i ...
Predicate logic - Teaching-WIKI
... • There are many deductive systems for predicate logic that are sound (only deriving correct results) and complete (able to derive any logically valid implication) • The logical consequence relation in predicate logic is only semidecidable • This lecture focused on three core aspects of the predicat ...
... • There are many deductive systems for predicate logic that are sound (only deriving correct results) and complete (able to derive any logically valid implication) • The logical consequence relation in predicate logic is only semidecidable • This lecture focused on three core aspects of the predicat ...
Predicate logic
... • There are many deductive systems for predicate logic that are sound (only deriving correct results) and complete (able to derive any logically valid implication) • The logical consequence relation in predicate logic is only semidecidable • This lecture focused on three core aspects of the predicat ...
... • There are many deductive systems for predicate logic that are sound (only deriving correct results) and complete (able to derive any logically valid implication) • The logical consequence relation in predicate logic is only semidecidable • This lecture focused on three core aspects of the predicat ...
KnotandTonk 1 Preliminaries
... with more than two truth-values, which nonetheless characterise classical sentential logic. Call these many-valued truth-tables for classical sentential logic. Consequently, the classical inference rules for the connectives ¬, ∧, ∨ and → fail to pin down the twovalued truth-tables uniquely (up to is ...
... with more than two truth-values, which nonetheless characterise classical sentential logic. Call these many-valued truth-tables for classical sentential logic. Consequently, the classical inference rules for the connectives ¬, ∧, ∨ and → fail to pin down the twovalued truth-tables uniquely (up to is ...
PDF
... 1 Intuitionistic Logic and Constructive Mathematics It turns out that there is there is a deep connection between the type systems we have been exploring for the lambda calculus, and proof systems for a variety of logic known as intuitionistic logic. Intuitionistic logic is the basis of constructive ...
... 1 Intuitionistic Logic and Constructive Mathematics It turns out that there is there is a deep connection between the type systems we have been exploring for the lambda calculus, and proof systems for a variety of logic known as intuitionistic logic. Intuitionistic logic is the basis of constructive ...
Propositions as types
... 1 Intuitionistic Logic and Constructive Mathematics It turns out that there is there is a deep connection between the type systems we have been exploring for the lambda calculus, and proof systems for a variety of logic known as intuitionistic logic. Intuitionistic logic is the basis of constructive ...
... 1 Intuitionistic Logic and Constructive Mathematics It turns out that there is there is a deep connection between the type systems we have been exploring for the lambda calculus, and proof systems for a variety of logic known as intuitionistic logic. Intuitionistic logic is the basis of constructive ...
RR-01-02
... formulas in table 1 and axioms in table 2 for representing the specific problem domain of interest and for controlling deduction, and uses McCarthy’s 1986 [11] predicate circumscription 3 with forced separation as modelpreference criterion. The language of the calculus is defined in table 1. Let S1 ...
... formulas in table 1 and axioms in table 2 for representing the specific problem domain of interest and for controlling deduction, and uses McCarthy’s 1986 [11] predicate circumscription 3 with forced separation as modelpreference criterion. The language of the calculus is defined in table 1. Let S1 ...
A logical basis for quantum evolution and entanglement
... A natural step in this program is to use the logic underlying monoidal categories as a syntactic framework for analyzing such quantum systems. But more than that is possible. While a logic does come with a syntax, it also has a builtin notion of dynamics, given by the cut-elimination procedure. In i ...
... A natural step in this program is to use the logic underlying monoidal categories as a syntactic framework for analyzing such quantum systems. But more than that is possible. While a logic does come with a syntax, it also has a builtin notion of dynamics, given by the cut-elimination procedure. In i ...
this PDF file
... in the ≤k ordering in every model. We feel that this notion of necessary approximation carries some interest given the pivotal role of the approximation (or ‘knowledge’) ordering in the semantics of programming languages. The main purpose of this paper is a simple one. We want to add one more doubli ...
... in the ≤k ordering in every model. We feel that this notion of necessary approximation carries some interest given the pivotal role of the approximation (or ‘knowledge’) ordering in the semantics of programming languages. The main purpose of this paper is a simple one. We want to add one more doubli ...
Introduction to Theoretical Computer Science, lesson 3
... Plato and teacher of Alexander the Great. He wrote on diverse subjects, including physics, metaphysics, poetry (including theater), biology and zoology, logic, rhetoric, politics, government, and ethics. Along with Socrates and Plato, Aristotle was one of the most influential of the ancient Greek ph ...
... Plato and teacher of Alexander the Great. He wrote on diverse subjects, including physics, metaphysics, poetry (including theater), biology and zoology, logic, rhetoric, politics, government, and ethics. Along with Socrates and Plato, Aristotle was one of the most influential of the ancient Greek ph ...
Jesús Mosterín
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Jesús Mosterín (born 1941) is a leading Spanish philosopher and a thinker of broad spectrum, often at the frontier between science and philosophy.