slides

... If there are infinitely many possible values for X the meaning of this expression cannot be represented using a propositional formula. In AG, the meaning of aggregate expressions is captured using an infinitary propositional formula. The definition is based on the semantics for propositional aggrega ...

... If there are infinitely many possible values for X the meaning of this expression cannot be represented using a propositional formula. In AG, the meaning of aggregate expressions is captured using an infinitary propositional formula. The definition is based on the semantics for propositional aggrega ...

Bilattices and the Semantics of Logic Programming

... kind of truth value space, to allow treating confidence factors as truth values [20]. And in [10], sets of possible worlds in a Kripke model were considered, as something like evidence factors. What do these approaches have in common? There must be enough machinery to ensure the existence of fixed p ...

... kind of truth value space, to allow treating confidence factors as truth values [20]. And in [10], sets of possible worlds in a Kripke model were considered, as something like evidence factors. What do these approaches have in common? There must be enough machinery to ensure the existence of fixed p ...

07.1-Reasoning

... • Our agent starts in 1,1 and feels no stench. By the rule Modus Ponens and the built in knowledge in it’s KB, it can conclude that 1,2 and 2,1 do not have a wumpus. • Now by the rule And-Elimination we can see that 1,2 doesn’t contain a wumpus and neither does 2,1. • If our agent now moves to 2,1 i ...

... • Our agent starts in 1,1 and feels no stench. By the rule Modus Ponens and the built in knowledge in it’s KB, it can conclude that 1,2 and 2,1 do not have a wumpus. • Now by the rule And-Elimination we can see that 1,2 doesn’t contain a wumpus and neither does 2,1. • If our agent now moves to 2,1 i ...

The Omnitude Determiner and Emplacement for the Square of

... TOM: "Subject false" sounds more like an insult than comfort. I don't think Lord Strawson would have agreed that all sentences with an S- P+ profile are false, because you've made your point only with singular subjects, not with universally quantified statements, such as ...

... TOM: "Subject false" sounds more like an insult than comfort. I don't think Lord Strawson would have agreed that all sentences with an S- P+ profile are false, because you've made your point only with singular subjects, not with universally quantified statements, such as

From Syllogism to Common Sense Normal Modal Logic

... ‣ These systems are however mutually incompatible, and no base logic was given of which the other logics are extensions of. ‣ The modal logic K is such a base logic, named after SAUL KRIPKE, and which serves as a minimal logic for the class of all its (normal) extensions - defined next via a Hilbert ...

... ‣ These systems are however mutually incompatible, and no base logic was given of which the other logics are extensions of. ‣ The modal logic K is such a base logic, named after SAUL KRIPKE, and which serves as a minimal logic for the class of all its (normal) extensions - defined next via a Hilbert ...

Modal Logic - Web Services Overview

... • Semantics is given in terms of Kripke Structures (also known as possible worlds structures) • Due to American logician Saul Kripke, City University of NY • A Kripke Structure is (W, R) – W is a set of possible worlds – R : W W is an binary accessibility relation over W – This relation tells us h ...

... • Semantics is given in terms of Kripke Structures (also known as possible worlds structures) • Due to American logician Saul Kripke, City University of NY • A Kripke Structure is (W, R) – W is a set of possible worlds – R : W W is an binary accessibility relation over W – This relation tells us h ...

Logic

... A simple example Let P(x) be the statement “x spends more than five hours every weekday in class,” where the universe of discourse for x is the set of students in a class. Express each of the following quantifications in English: ∃x, P(x) : “There is a student who spends more than five hours each w ...

... A simple example Let P(x) be the statement “x spends more than five hours every weekday in class,” where the universe of discourse for x is the set of students in a class. Express each of the following quantifications in English: ∃x, P(x) : “There is a student who spends more than five hours each w ...

Fine`s Theorem on First-Order Complete Modal Logics

... step of allowing languages to have arbitrarily large sets of variables, from which arbitrarily large canonical frames can be built for any given logic. The above body of work by Fine can be seen as part of a second wave of research that flowed from the publication by Kripke [41] of his seminal work ...

... step of allowing languages to have arbitrarily large sets of variables, from which arbitrarily large canonical frames can be built for any given logic. The above body of work by Fine can be seen as part of a second wave of research that flowed from the publication by Kripke [41] of his seminal work ...

Lecture - 04 (Logic Knowledge Base)

... behavior or performance. • Can often be teased out of a competent performer (task analyst, knowledge engineer) • E.g. processing applications in an insurance company, the range of outcomes for the underwriters’ work took three basic forms: (1) they could approve the policy application, (2) they coul ...

... behavior or performance. • Can often be teased out of a competent performer (task analyst, knowledge engineer) • E.g. processing applications in an insurance company, the range of outcomes for the underwriters’ work took three basic forms: (1) they could approve the policy application, (2) they coul ...

The Emergence of First

... First-order logic—stripped of all infinitary operations—emerged only with Hilbert in (1917), where it remained a subsystem of logic, and with Skolem in (1923), who treated it as all of logic. During the nineteenth and early twentieth centuries, there was no generally accepted classification of the d ...

... First-order logic—stripped of all infinitary operations—emerged only with Hilbert in (1917), where it remained a subsystem of logic, and with Skolem in (1923), who treated it as all of logic. During the nineteenth and early twentieth centuries, there was no generally accepted classification of the d ...

Proof theory for modal logic

... An axiom system for modal logic can be an extension of intuitionistic or classical propositional logic. In the latter, the notions of necessity and possibility are interdefinable by the equivalence 2A ⊃⊂ ¬3¬A. It is seen that necessity and possibility behave analogously to the quantifiers: In one in ...

... An axiom system for modal logic can be an extension of intuitionistic or classical propositional logic. In the latter, the notions of necessity and possibility are interdefinable by the equivalence 2A ⊃⊂ ¬3¬A. It is seen that necessity and possibility behave analogously to the quantifiers: In one in ...

The Expressive Power of Modal Dependence Logic

... With the aim to import dependences and team semantics to modal logic Väänänen [17] introduced modal dependence logic MDL. In the context of modal logic a team is just a set of states in a Kripke model. Modal dependence logic extends standard modal logic with team semantics by modal dependence atoms, ...

... With the aim to import dependences and team semantics to modal logic Väänänen [17] introduced modal dependence logic MDL. In the context of modal logic a team is just a set of states in a Kripke model. Modal dependence logic extends standard modal logic with team semantics by modal dependence atoms, ...

Chapter 2 Propositional Logic

... is studied by philosophers, mathematicians and computer scientists. Logic appears in different areas of computer science, such as programming, circuits, artificial intelligence and databases. It is useful to represent knowledge precisely and to help extract information. This last sentence may not be ...

... is studied by philosophers, mathematicians and computer scientists. Logic appears in different areas of computer science, such as programming, circuits, artificial intelligence and databases. It is useful to represent knowledge precisely and to help extract information. This last sentence may not be ...

Let me begin by reminding you of a number of passages ranging

... gesture toward what really does indicate the essence of logic—the assertoric force with which a sentence is uttered. Frege writes: How is it then that this word ‘true’, though it seems devoid of content, cannot be dispensed with? Would it not be possible, at least in laying the foundations of logic, ...

... gesture toward what really does indicate the essence of logic—the assertoric force with which a sentence is uttered. Frege writes: How is it then that this word ‘true’, though it seems devoid of content, cannot be dispensed with? Would it not be possible, at least in laying the foundations of logic, ...

Strong Completeness for Iteration

... A monad morphism from (T, η, µ) to (T 0 , η 0 , µ0 ) is a natural transformation ρ : T ⇒ T 0 which respects the monad structure meaning that: ρ ◦ η = η 0 and ρ ◦ µ = µ0 ◦ ρT 0 ◦ T ρ. Since ρ is natural the last equation is equivalent to ρ ◦ µ = µ0 ◦ T 0 ρ ◦ ρT . Monads and monad morphisms together f ...

... A monad morphism from (T, η, µ) to (T 0 , η 0 , µ0 ) is a natural transformation ρ : T ⇒ T 0 which respects the monad structure meaning that: ρ ◦ η = η 0 and ρ ◦ µ = µ0 ◦ ρT 0 ◦ T ρ. Since ρ is natural the last equation is equivalent to ρ ◦ µ = µ0 ◦ T 0 ρ ◦ ρT . Monads and monad morphisms together f ...

On the Notion of Coherence in Fuzzy Answer Set Semantics

... I(∼ p) > ∼ I(p) or I(∼ p) and ∼ I(p) are incomparable elements in L. In both cases a non-coherent interpretation implies a contradiction with the negation meta-rule. Is this contradiction given by an excess of information? Certainly. The contrapositive of Proposition 1 tells us that by adding inform ...

... I(∼ p) > ∼ I(p) or I(∼ p) and ∼ I(p) are incomparable elements in L. In both cases a non-coherent interpretation implies a contradiction with the negation meta-rule. Is this contradiction given by an excess of information? Certainly. The contrapositive of Proposition 1 tells us that by adding inform ...

INTERMEDIATE LOGIC – Glossary of key terms

... A rule of digital logic that can be used to simplify a proposition (see Appendix D). AND gate Lesson 32, page 266 A logic gate that performs the logical operation conjunction. Antecedent Lesson 4, page 27 In a conditional if p then q, the antecedent is the proposition represented by the p. Argument ...

... A rule of digital logic that can be used to simplify a proposition (see Appendix D). AND gate Lesson 32, page 266 A logic gate that performs the logical operation conjunction. Antecedent Lesson 4, page 27 In a conditional if p then q, the antecedent is the proposition represented by the p. Argument ...

Suszko`s Thesis, Inferential Many-Valuedness, and the

... universe of interpretation into two subsets of elements: distinguished ...

... universe of interpretation into two subsets of elements: distinguished ...

Verification Conditions Are Code - Electronics and Computer Science

... Also note that this property is very familiar from the study of program semantics, for example in the theory of predicate transformers, where this result would follow directly from the associativity of function composition. Working directly with program semantics is a model-theoretic approach, howev ...

... Also note that this property is very familiar from the study of program semantics, for example in the theory of predicate transformers, where this result would follow directly from the associativity of function composition. Working directly with program semantics is a model-theoretic approach, howev ...

Quantifiers

... validity, we should be able to make this into a test for FO invalidity as follows: Have the procedure test for validity. If it is valid, then eventually the procedure will say it is valid (e.g. it says “Yes, it’s valid”), and hence we will know (because the procedure is sound) that it is not invalid ...

... validity, we should be able to make this into a test for FO invalidity as follows: Have the procedure test for validity. If it is valid, then eventually the procedure will say it is valid (e.g. it says “Yes, it’s valid”), and hence we will know (because the procedure is sound) that it is not invalid ...

Lecture 2

... • A proposition can be interpreted as being either true or false. For example: • “Henry VIII had one son and Cleopatra had two” • We wish to translate English propositions to Boolean expressions because: – English is ambiguous, computers require logical clarity. – We can automate, analyse, reason ab ...

... • A proposition can be interpreted as being either true or false. For example: • “Henry VIII had one son and Cleopatra had two” • We wish to translate English propositions to Boolean expressions because: – English is ambiguous, computers require logical clarity. – We can automate, analyse, reason ab ...

relevant reasoning as the logical basis of

... extensional notion of material implication (denoted by → in this paper) which is defined as A→B =df ¬(A∧¬B) or A→B =df ¬A∨B. However, the material implication is just a truth-function of its antecedent and consequent but not requires that there must exist a necessarily relevant and/or conditional re ...

... extensional notion of material implication (denoted by → in this paper) which is defined as A→B =df ¬(A∧¬B) or A→B =df ¬A∨B. However, the material implication is just a truth-function of its antecedent and consequent but not requires that there must exist a necessarily relevant and/or conditional re ...

Paper - Department of Computer Science and Information Systems

... set of equations axiomatising the variety of Boolean algebras with operators and additional equations corresponding the axioms of L. A closely related algorithmic problem for L is the admissibility problem for inference rules: given an inference rule ϕ1 , . . . , ϕn /ϕ, decide whether it is admissib ...

... set of equations axiomatising the variety of Boolean algebras with operators and additional equations corresponding the axioms of L. A closely related algorithmic problem for L is the admissibility problem for inference rules: given an inference rule ϕ1 , . . . , ϕn /ϕ, decide whether it is admissib ...

ICS 353: Design and Analysis of Algorithms

... Translating English Sentences into Logical Expressions • Q 16 page 18: For each of these sentences, determine whether an inclusive or an exclusive or is intended. Explain your answer a. Experience with C++ or Java is required b. Lunch includes soup or salad c. To enter the country, you need a passpo ...

... Translating English Sentences into Logical Expressions • Q 16 page 18: For each of these sentences, determine whether an inclusive or an exclusive or is intended. Explain your answer a. Experience with C++ or Java is required b. Lunch includes soup or salad c. To enter the country, you need a passpo ...

Equivalence of the information structure with unawareness to the

... All tautologies of propositional logic are also axioms of the logic of awareness. Additional theorems can be derived from the axioms and previous theorems using rules of inference. The rules of inference in the logic of awareness are the same as in traditional modal logic, but the rule (RN) is appli ...

... All tautologies of propositional logic are also axioms of the logic of awareness. Additional theorems can be derived from the axioms and previous theorems using rules of inference. The rules of inference in the logic of awareness are the same as in traditional modal logic, but the rule (RN) is appli ...

Willard Van Orman Quine (/kwaɪn/; June 25, 1908 – December 25, 2000) (known to intimates as ""Van"") was an American philosopher and logician in the analytic tradition, recognized as ""one of the most influential philosophers of the twentieth century."" From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor of philosophy and a teacher of logic and set theory, and finally as a professor emeritus who published or revised several books in retirement. He filled the Edgar Pierce Chair of Philosophy at Harvard from 1956 to 1978. A recent poll conducted among analytic philosophers named Quine as the fifth most important philosopher of the past two centuries. He won the first Schock Prize in Logic and Philosophy in 1993 for ""his systematical and penetrating discussions of how learning of language and communication are based on socially available evidence and of the consequences of this for theories on knowledge and linguistic meaning."" In 1996 he was awarded the Kyoto Prize in Arts and Philosophy for his ""outstanding contributions to the progress of philosophy in the 20th century by proposing numerous theories based on keen insights in logic, epistemology, philosophy of science and philosophy of language.""Quine falls squarely into the analytic philosophy tradition while also being the main proponent of the view that philosophy is not conceptual analysis but the abstract branch of the empirical sciences. His major writings include ""Two Dogmas of Empiricism"" (1951), which attacked the distinction between analytic and synthetic propositions and advocated a form of semantic holism, and Word and Object (1960), which further developed these positions and introduced Quine's famous indeterminacy of translation thesis, advocating a behaviorist theory of meaning. He also developed an influential naturalized epistemology that tried to provide ""an improved scientific explanation of how we have developed elaborate scientific theories on the basis of meager sensory input."" He is also important in philosophy of science for his ""systematic attempt to understand science from within the resources of science itself"" and for his conception of philosophy as continuous with science. This led to his famous quip that ""philosophy of science is philosophy enough."" In philosophy of mathematics, he and his Harvard colleague Hilary Putnam developed the ""Quine–Putnam indispensability thesis,"" an argument for the reality of mathematical entities.