Independence logic and tuple existence atoms
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
... Definition R relation, ~x , ~y , ~z tuples of attributes. Then R |= ~x ~y | ~z if and only if, for all r , r 0 ∈ R such that r (~x ) = r 0 (~x ) there exists a r 00 ∈ R such that r 00 (~x ~y ) = r (~x ~y ) and r 00 (~x ~z ) = r (~x ~z ). Huge literature on the topic; If ~x ~y ~z contains all attri ...
proof terms for classical derivations
... Variables annotate assumptions, and the term constructors of pairing and λ-abstraction correspond to the introduction of conjunctions and conditionals respectively. Now the terms corresponding to the proofs bear the marks of the different proof behaviour. The first proof took an assumption p to p ∧ ...
... Variables annotate assumptions, and the term constructors of pairing and λ-abstraction correspond to the introduction of conjunctions and conditionals respectively. Now the terms corresponding to the proofs bear the marks of the different proof behaviour. The first proof took an assumption p to p ∧ ...
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 ...
logic, programming and prolog (2ed)
... predicate logic including notions like language, interpretation, model, logical consequence, logical inference, soundness and completeness. The final section introduces the concept of substitution which is needed in subsequent chapters. Chapter 2 introduces the restricted language of definite progra ...
... predicate logic including notions like language, interpretation, model, logical consequence, logical inference, soundness and completeness. The final section introduces the concept of substitution which is needed in subsequent chapters. Chapter 2 introduces the restricted language of definite progra ...
Harmony, Normality and Stability
... he gives two quite different ways of spelling it out formally. One is connected to the notion of a conservative extension. Let L1 be a logic with language L1 , a deductive system R1 and a consequence relation `L1 ; let L2 be a logic with language L2 and a deductive system R2 extending L1 by new symb ...
... he gives two quite different ways of spelling it out formally. One is connected to the notion of a conservative extension. Let L1 be a logic with language L1 , a deductive system R1 and a consequence relation `L1 ; let L2 be a logic with language L2 and a deductive system R2 extending L1 by new symb ...
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 ...
Classical Propositional Logic
... These are relatively new questions. Throughout the history of logic, soundness was an intuitive notion, and asked rule-by-rule; the assumption seems to have been that a logical system is sound if and only if all its rules are sound. ...
... These are relatively new questions. Throughout the history of logic, soundness was an intuitive notion, and asked rule-by-rule; the assumption seems to have been that a logical system is sound if and only if all its rules are sound. ...
LPF and MPLω — A Logical Comparison of VDM SL and COLD-K
... This allows a large class of recursive and inductive definitions of functions and predicates to be expressed as formulae of MPLω . This was first sketched in [KR89, Section 4] and later worked out in detail by Renardel de Lavalette in [Ren89]. If A is a formula, then the term ιx : S (A) can be forme ...
... This allows a large class of recursive and inductive definitions of functions and predicates to be expressed as formulae of MPLω . This was first sketched in [KR89, Section 4] and later worked out in detail by Renardel de Lavalette in [Ren89]. If A is a formula, then the term ιx : S (A) can be forme ...
MATH20302 Propositional Logic
... Remark: Following the usual convention in mathematics we will use symbols such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). ...
... Remark: Following the usual convention in mathematics we will use symbols such as p, q, respectively s, t, not just for individual propositional variables, respectively propositional terms, but also as variables ranging over propositional variables, resp. propositional terms, (as we did just above). ...
