Jacques Herbrand (1908 - 1931) Principal writings in logic
... Herbrand domain D(F,p): an arbitrary item, and values for f and g (and any other function signs in R) iterated up to p times. Herbrand (validity) expansion: disjunction of instances of Herbrand functional form over D(F,p): ...
... Herbrand domain D(F,p): an arbitrary item, and values for f and g (and any other function signs in R) iterated up to p times. Herbrand (validity) expansion: disjunction of instances of Herbrand functional form over D(F,p): ...
Logic - UNM Computer Science
... circuits. In this section, we will show how a NAND gate can be implemented using transistors. The underlying principle also extends to the more modern CMOS technology. A transistor is a semiconductor device invented in 1947 by William Shockley, John Bardeen, and Walter Brattain at AT&T’s Bell Labs, ...
... circuits. In this section, we will show how a NAND gate can be implemented using transistors. The underlying principle also extends to the more modern CMOS technology. A transistor is a semiconductor device invented in 1947 by William Shockley, John Bardeen, and Walter Brattain at AT&T’s Bell Labs, ...
Artificial Intelligence techniques: An introduction to their use for
... problem, a pattern matcher and a rule applier. The pattern matcher refers to the working memory to decide which rules are relevant, then the rule applier chooses what rule to apply. New information created by the action (then-) part of the rule applied is added to the working memory and the match-se ...
... problem, a pattern matcher and a rule applier. The pattern matcher refers to the working memory to decide which rules are relevant, then the rule applier chooses what rule to apply. New information created by the action (then-) part of the rule applied is added to the working memory and the match-se ...
Justification logic with approximate conditional probabilities
... Justification logic [5] is a variant of modal logic that ‘unfolds’ the 2-modality into justification terms, i.e., justification logics replaces modal formulas 2α with formulas of the form t:α where t is a justification term. The first justification logic, the Logic of Proofs, was developed by Artemo ...
... Justification logic [5] is a variant of modal logic that ‘unfolds’ the 2-modality into justification terms, i.e., justification logics replaces modal formulas 2α with formulas of the form t:α where t is a justification term. The first justification logic, the Logic of Proofs, was developed by Artemo ...
Propositional Logic: Why? soning Starts with George Boole around 1850
... We saw some examples in the context of propositional logic, e.g. the non existence of Superman In propositional logic, at least in principle, if there are finitely many propositional variables involved, logical consequence can be checked by means of truth tables (cumbersome) We also saw alternatives, ...
... We saw some examples in the context of propositional logic, e.g. the non existence of Superman In propositional logic, at least in principle, if there are finitely many propositional variables involved, logical consequence can be checked by means of truth tables (cumbersome) We also saw alternatives, ...
TEMPORAL LOGIC
... Proposition A can be viewed as timeless, since it is true in past, present, and future. In contrast, the propositions B and C have a temporalized aspect and refer to the implicit time condition “now”. Consequently temporal logic applies to time-related universes of discourse where behaviors and cour ...
... Proposition A can be viewed as timeless, since it is true in past, present, and future. In contrast, the propositions B and C have a temporalized aspect and refer to the implicit time condition “now”. Consequently temporal logic applies to time-related universes of discourse where behaviors and cour ...
First-Order Predicate Logic (2) - Department of Computer Science
... the case for finite F coincides with querying relational database instances and can be done very efficiently. It is also the underlying problem of model checking approaches to program verification: F is a representation of a program and one wants to know whether a property expressed by G is true. • ...
... the case for finite F coincides with querying relational database instances and can be done very efficiently. It is also the underlying problem of model checking approaches to program verification: F is a representation of a program and one wants to know whether a property expressed by G is true. • ...
Philosophy 240: Symbolic Logic
... P He has provided a formal construction in an artificial language. P Does it capture our ordinary notion? P “It seems to me obvious that the only rational approach to [questions about the correct notion of truth] would be the following: We should reconcile ourselves with the fact that we are confron ...
... P He has provided a formal construction in an artificial language. P Does it capture our ordinary notion? P “It seems to me obvious that the only rational approach to [questions about the correct notion of truth] would be the following: We should reconcile ourselves with the fact that we are confron ...
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 ...
Chapter 1: The Foundations: Logic and Proofs
... The biconditional statement pq is true when p and q have the same truth value, and is false otherwise. Biconditional statements are also called bi-implications. ...
... The biconditional statement pq is true when p and q have the same truth value, and is false otherwise. Biconditional statements are also called bi-implications. ...
Is the Liar Sentence Both True and False? - NYU Philosophy
... degree of belief in it; say a degree of belief over a certain threshold T , which may depend on context but must be greater than 12 . (Degrees of belief are assumed to be real numbers in the interval [0, 1].) To the same degree of approximation, rejecting A is having a low degree of belief in it: on ...
... degree of belief in it; say a degree of belief over a certain threshold T , which may depend on context but must be greater than 12 . (Degrees of belief are assumed to be real numbers in the interval [0, 1].) To the same degree of approximation, rejecting A is having a low degree of belief in it: on ...
Intrusion Detection using Fuzzy Clustering and Artificial Neural
... numbers. 3. For every training example, forward propagate the input through the network: a. Each hidden node receives the weighted summation of the inputs and bias ...
... numbers. 3. For every training example, forward propagate the input through the network: a. Each hidden node receives the weighted summation of the inputs and bias ...
symbolic logic and logic processing
... Artificial Intelligence is a blend of three main academic disciplines namely psychology (cognitive science), philosophy (mind) and computer science with further strands from mathematics, logic and linguistics. The aim of AI is broad: to get below the surface of human behaviour; to discover the proce ...
... Artificial Intelligence is a blend of three main academic disciplines namely psychology (cognitive science), philosophy (mind) and computer science with further strands from mathematics, logic and linguistics. The aim of AI is broad: to get below the surface of human behaviour; to discover the proce ...
Artificial intelligence applications in the intensive care unit
... language, which in turn presupposed that the required data were available in a relational database. Using an OLAP, an administrator could answer the question at whim using natural language rather than a specifically designed computer program. The administrator might then follow-up (or “drill down” i ...
... language, which in turn presupposed that the required data were available in a relational database. Using an OLAP, an administrator could answer the question at whim using natural language rather than a specifically designed computer program. The administrator might then follow-up (or “drill down” i ...
completeness theorem for a first order linear
... system for PLTL was given in [8], while its rst order extension, FOLTL, was presented in [13]. There are many complete axiomatizations of di erent rst order temporal logics. For example, some kinds of such logics with F and P operators over various classes of time ows were axiomatized in [9], whi ...
... system for PLTL was given in [8], while its rst order extension, FOLTL, was presented in [13]. There are many complete axiomatizations of di erent rst order temporal logics. For example, some kinds of such logics with F and P operators over various classes of time ows were axiomatized in [9], whi ...
A Framework for Comparing Alternative Formalisms for
... has grown for applicable methodologies for reasoning under uncertainty. of a proof In this paper, we discuss the ramifications showing that the axioms of probability theory follow logically from a set of simple properties. We shall reformulate the work of R.T. Cox, a physicist interested in reasonin ...
... has grown for applicable methodologies for reasoning under uncertainty. of a proof In this paper, we discuss the ramifications showing that the axioms of probability theory follow logically from a set of simple properties. We shall reformulate the work of R.T. Cox, a physicist interested in reasonin ...
Full-Text PDF
... Interpretability [1–3] and accuracy [4] are the two important features of a fuzzy system developed for a specific application. The term ‘interpretability’ describes the capability of a model that allows a human being to understand its behavior by inspecting its functioning or its rule base. On the o ...
... Interpretability [1–3] and accuracy [4] are the two important features of a fuzzy system developed for a specific application. The term ‘interpretability’ describes the capability of a model that allows a human being to understand its behavior by inspecting its functioning or its rule base. On the o ...
First-order logic;
... Representation: Understand the relationships between different representations of the same information or idea. I ...
... Representation: Understand the relationships between different representations of the same information or idea. I ...
Mathematical Logic Deciding logical consequence Complexity of
... syntax: a precisely defined symbolic language with procedures for transforming symbolic statements into other statements, based solely on their form. No intuition or interpretation is needed, merely applications of agreed upon rules to a set of agreed upon ...
... syntax: a precisely defined symbolic language with procedures for transforming symbolic statements into other statements, based solely on their form. No intuition or interpretation is needed, merely applications of agreed upon rules to a set of agreed upon ...
Analysis of the paraconsistency in some logics
... 1. We will say that the formulas A, B are equivalent if one implies the other and viceversa, that is: A ` B and B ` A; 2. In a similar way, the theories Γ and ∆ are equivalent if: ( ∀A ∈ Γ : ∆ ` A ) y ( ∀B ∈ ∆ : Γ ` B ). From the previous definition, we obtain the following property. Proposition 4. ...
... 1. We will say that the formulas A, B are equivalent if one implies the other and viceversa, that is: A ` B and B ` A; 2. In a similar way, the theories Γ and ∆ are equivalent if: ( ∀A ∈ Γ : ∆ ` A ) y ( ∀B ∈ ∆ : Γ ` B ). From the previous definition, we obtain the following property. Proposition 4. ...
Fuzzy logic
Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1. By contrast, in Boolean logic, the truth values of variables may only be 0 or 1. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false. Furthermore, when linguistic variables are used, these degrees may be managed by specific functions.The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Zadeh. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. Fuzzy logic had however been studied since the 1920s, as infinite-valued logic—notably by Łukasiewicz and Tarski.