a-logic - Digital [email protected] State University

... paradox of the liar and related paradoxes were raised later. Other problems emerged as proponents tried to apply standard logic to the empirical sciences. These included the problems of contrary-to-fact conditionals, of dispositional predicates, of confirmation theory and of probabilities for condit ...

... paradox of the liar and related paradoxes were raised later. Other problems emerged as proponents tried to apply standard logic to the empirical sciences. These included the problems of contrary-to-fact conditionals, of dispositional predicates, of confirmation theory and of probabilities for condit ...

Predicate Logic

... Other forms of quantification Other Quantifiers The most important quantifiers are ∀ and ∃, but we could define many different quantifiers: “there is a unique”, “there are exactly two”, “there are no more than three”, “there are at least 100”, etc. A common one is the uniqueness quantifier, denoted ...

... Other forms of quantification Other Quantifiers The most important quantifiers are ∀ and ∃, but we could define many different quantifiers: “there is a unique”, “there are exactly two”, “there are no more than three”, “there are at least 100”, etc. A common one is the uniqueness quantifier, denoted ...

a semantic perspective - Institute for Logic, Language and

... chapters in this handbook. Thus the reader will find here definitions and discussions of all the basic tools needed in modal model theory (such as the standard translation, generated submodels, bounded morphisms, and so on). Basic results about these concepts are stated and some simple proofs are gi ...

... chapters in this handbook. Thus the reader will find here definitions and discussions of all the basic tools needed in modal model theory (such as the standard translation, generated submodels, bounded morphisms, and so on). Basic results about these concepts are stated and some simple proofs are gi ...

5 model theory of modal logic

... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a different perspective from that of classical model theory. In the classical picture, both first- and sec ...

... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a different perspective from that of classical model theory. In the classical picture, both first- and sec ...

Model Theory of Modal Logic, Chapter in: Handbook of Modal Logic

... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a diﬀerent perspective from that of classical model theory. In the classical picture, both ﬁrst- and secon ...

... second-order logic into which it can be naturally embedded. But, beside this ‘classical picture’, there are also many links with other logics, partly designed for other purposes or studied with a diﬀerent perspective from that of classical model theory. In the classical picture, both ﬁrst- and secon ...

SEQUENT SYSTEMS FOR MODAL LOGICS

... of relational terms. These terms may contain subterms representing the accessibility relation in possible-worlds models, so that semantic information is available at the same level as syntactic information. The derivation rules in relational proof systems manipulate finite sequences of relational fo ...

... of relational terms. These terms may contain subterms representing the accessibility relation in possible-worlds models, so that semantic information is available at the same level as syntactic information. The derivation rules in relational proof systems manipulate finite sequences of relational fo ...

Independence logic and tuple existence atoms

... M |=X ∃xφ iff for all s ∈ X , ∃m ∈ Dom(M) s.t. M |=s[m/x] φ; M |=X ∀xφ iff for all s ∈ X , ∀m ∈ Dom(M), M |=s[m/x] φ. ...

... M |=X ∃xφ iff for all s ∈ X , ∃m ∈ Dom(M) s.t. M |=s[m/x] φ; M |=X ∀xφ iff for all s ∈ X , ∀m ∈ Dom(M), M |=s[m/x] φ. ...

Artificial Intelligence

... • In fuzzy rules, the linguistic variable speed also has the range (the universe of discourse) between 0 and 220 km/h, but this range includes fuzzy sets, such as slow, medium and fast. The universe of discourse of the linguistic variable stopping_distance can be between 0 and 300 m and may include ...

... • In fuzzy rules, the linguistic variable speed also has the range (the universe of discourse) between 0 and 220 km/h, but this range includes fuzzy sets, such as slow, medium and fast. The universe of discourse of the linguistic variable stopping_distance can be between 0 and 300 m and may include ...

The Journal of Functional and Logic Programming The MIT Press

... systems where the various domains are built over disjoint signatures and their constraints are processed by different, specialized solvers. In these systems, predicate or function symbols in one signature are applicable, with few exceptions, only to (nonvariable) terms entirely built with symbols fr ...

... systems where the various domains are built over disjoint signatures and their constraints are processed by different, specialized solvers. In these systems, predicate or function symbols in one signature are applicable, with few exceptions, only to (nonvariable) terms entirely built with symbols fr ...

The History of Categorical Logic

... concerning the foundations of mathematics and the very nature of mathematical knowledge are inescapable. In particular, issues related to abstraction and the nature of mathematical objects emerges naturally from categorical logic. This paper covers the period that can be qualified as the birth and t ...

... concerning the foundations of mathematics and the very nature of mathematical knowledge are inescapable. In particular, issues related to abstraction and the nature of mathematical objects emerges naturally from categorical logic. This paper covers the period that can be qualified as the birth and t ...

Dialectica Interpretations A Categorical Analysis

... When Gödel finally1 published his functional interpretation in the journal Dialectica, hence the name “Dialectica Interpretation”, in 1958, it was as a contribution to Hilbert’s program. The Dialectica interpretation reduces consistency of Heyting arithmetic (and combined with the double negation tr ...

... When Gödel finally1 published his functional interpretation in the journal Dialectica, hence the name “Dialectica Interpretation”, in 1958, it was as a contribution to Hilbert’s program. The Dialectica interpretation reduces consistency of Heyting arithmetic (and combined with the double negation tr ...

A joint logic of problems and propositions, a modified BHK

... Atomic formulas: problem symbols, propositional symbols (possibly depending on variables that all range over the same domain of discourse) and the constant ⊥ Formulas are of two types: problems (denoted by Greek letters) and propositions (denoted by Roman letters) Classical connectives: propositions ...

... Atomic formulas: problem symbols, propositional symbols (possibly depending on variables that all range over the same domain of discourse) and the constant ⊥ Formulas are of two types: problems (denoted by Greek letters) and propositions (denoted by Roman letters) Classical connectives: propositions ...

Logic in Nonmonotonic Reasoning

... knowledge bases, when such hierarchies have been allowed to have exceptions. The theory of reasoning in such taxonomies has been called nonmonotonic inheritance (see [Horty, 1994] for an overview). The guiding principle in resolving potential conflicts in such hierarchies was a specificity principl ...

... knowledge bases, when such hierarchies have been allowed to have exceptions. The theory of reasoning in such taxonomies has been called nonmonotonic inheritance (see [Horty, 1994] for an overview). The guiding principle in resolving potential conflicts in such hierarchies was a specificity principl ...

thèse - IRIT

... (E-S) as an extension of disjunctive logic programming by epistemic notions. The underlying idea of E-S is to correctly reason about incomplete information, especially in situations when there are multiple answer sets. Related to this aim, he has proposed the world view semantics because the previou ...

... (E-S) as an extension of disjunctive logic programming by epistemic notions. The underlying idea of E-S is to correctly reason about incomplete information, especially in situations when there are multiple answer sets. Related to this aim, he has proposed the world view semantics because the previou ...

A Logical Framework for Default Reasoning

... syntax, semantics and a proof procedure and have theorems of soundness and completeness for this logic. 2. An alternative is to say that there is nothing wrong with classical logic; we should not expect reasoning to be just deduction from our knowledge. Circumscription [McCarthy86] can be seen in th ...

... syntax, semantics and a proof procedure and have theorems of soundness and completeness for this logic. 2. An alternative is to say that there is nothing wrong with classical logic; we should not expect reasoning to be just deduction from our knowledge. Circumscription [McCarthy86] can be seen in th ...

AN EARLY HISTORY OF MATHEMATICAL LOGIC AND

... theoretical strain began with Bernard Bolzano’s Paradoxes of the Infinite and was influenced by problems in the use of the infinite in mathematics. A cursory inspection of this work will show a heavy influence on the subject of logic from Britain. Of the first two chapters C.S. Peirce is the only no ...

... theoretical strain began with Bernard Bolzano’s Paradoxes of the Infinite and was influenced by problems in the use of the infinite in mathematics. A cursory inspection of this work will show a heavy influence on the subject of logic from Britain. Of the first two chapters C.S. Peirce is the only no ...

PDF - University of Kent

... The Laws of Form (LoF) were developed by George Spencer-Brown (1972) as a way of representing graphically the laws of logic, and in particular the propositional calculus or Boolean algebra. They provide an extremely elegant and parsimonious form of representation for both the algebra and the arithme ...

... The Laws of Form (LoF) were developed by George Spencer-Brown (1972) as a way of representing graphically the laws of logic, and in particular the propositional calculus or Boolean algebra. They provide an extremely elegant and parsimonious form of representation for both the algebra and the arithme ...

Formale Methoden der Softwaretechnik Formal methods of software

... The problem with this proof is step 8. In this step we have used step 3, a step that occurs within an earlier subproof. But it turns out that this sort of justification—one that reaches back inside a subproof that has already ended—is not legitimate. To understand why it’s not legitimate, we need to ...

... The problem with this proof is step 8. In this step we have used step 3, a step that occurs within an earlier subproof. But it turns out that this sort of justification—one that reaches back inside a subproof that has already ended—is not legitimate. To understand why it’s not legitimate, we need to ...

The Foundations

... xn + yn = zn ---- Fermat’s last theorem 6. “Every even number > 2 is the sum of two prime numbers.” ---Goldbach’s conjecture (1742) ...

... xn + yn = zn ---- Fermat’s last theorem 6. “Every even number > 2 is the sum of two prime numbers.” ---Goldbach’s conjecture (1742) ...

relevance logic - Consequently.org

... and to a lesser extent on [Meyer, 1966], both of which are very much recommended to the reader for their wise heresy from logical tradition. Thus logical tradition (think of [Quine, 1953]) makes much of the grammatical distinction between ‘if, then’ (a connective), and ‘implies’ or its rough synonym ...

... and to a lesser extent on [Meyer, 1966], both of which are very much recommended to the reader for their wise heresy from logical tradition. Thus logical tradition (think of [Quine, 1953]) makes much of the grammatical distinction between ‘if, then’ (a connective), and ‘implies’ or its rough synonym ...

Understanding SPKI/SDSI Using First-Order Logic

... program. Since the semantics of a policy is defined by classical logical implication, this approach allows FOL formulas to be understood as meaningful queries against a policy. We prove that the FOL semantics is equivalent to the string rewriting semantics used by SDSI designers, for all queries ass ...

... program. Since the semantics of a policy is defined by classical logical implication, this approach allows FOL formulas to be understood as meaningful queries against a policy. We prove that the FOL semantics is equivalent to the string rewriting semantics used by SDSI designers, for all queries ass ...

Programming in Logic Without Logic Programming

... 0 of the state Si to which the fluent belongs. The unstamped fluent atom p(t1, …, tn) is the same atom without this timestamp. Event predicates represent events contributing to the transition from one state to the next. The last argument of a timestamped event atom e(t1, …, tn, i) is a time paramete ...

... 0 of the state Si to which the fluent belongs. The unstamped fluent atom p(t1, …, tn) is the same atom without this timestamp. Event predicates represent events contributing to the transition from one state to the next. The last argument of a timestamped event atom e(t1, …, tn, i) is a time paramete ...

A Judgmental Reconstruction of Modal Logic

... of introduction rules for logical connectives which allow us to conclude when propositions are true. They are complemented by elimination rules which allow us to obtain further knowledge from the knowledge of compound propositions. The elimination rules for a connective should be locally sound and c ...

... of introduction rules for logical connectives which allow us to conclude when propositions are true. They are complemented by elimination rules which allow us to obtain further knowledge from the knowledge of compound propositions. The elimination rules for a connective should be locally sound and c ...

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.