MATHEMATICAL LOGIC FOR APPLICATIONS

... this study is the connection between Logic and the other areas of mathematics. There are areas of mathematics which are traditionally close to Logic. Such areas are: algebra, set theory, algorithm theory. For example, modern logic was defined originally in algebraic form (by Boole, De Morgan and Pei ...

... this study is the connection between Logic and the other areas of mathematics. There are areas of mathematics which are traditionally close to Logic. Such areas are: algebra, set theory, algorithm theory. For example, modern logic was defined originally in algebraic form (by Boole, De Morgan and Pei ...

Logic Program Based Updates

... body of a rule could be empty. We also allow the head of a rule to be empty. In this case, the rule with an empty head is called constraint. A term, atom, literal, or rule is ground if no variable occurs in it. An extended logic program Π is a collection of rules. Π is ground if each rule in Π is gr ...

... body of a rule could be empty. We also allow the head of a rule to be empty. In this case, the rule with an empty head is called constraint. A term, atom, literal, or rule is ground if no variable occurs in it. An extended logic program Π is a collection of rules. Π is ground if each rule in Π is gr ...

Computing Preferred Answer Sets by Meta

... B(r) ⊆ I implies H(r) ∩ I 6= ∅ for every r ∈ P . An interpretation X is an answer set for P if it is a minimal set (wrt. set inclusion) which is closed under P . (2) Let P I be the Gelfond-Lifschitz reduct of a program P w.r.t. I ⊆ BP , i.e., the program obtained from P by deleting ...

... B(r) ⊆ I implies H(r) ∩ I 6= ∅ for every r ∈ P . An interpretation X is an answer set for P if it is a minimal set (wrt. set inclusion) which is closed under P . (2) Let P I be the Gelfond-Lifschitz reduct of a program P w.r.t. I ⊆ BP , i.e., the program obtained from P by deleting ...

datalog - FORTH-ICS

... One way to think about this operator is that it applies rules on existing facts to get new facts according to the head of those rules. In general, for a recursive Datalog program, the same operator can be repeatedly applied on facts produced by previous applications of it. It is easy to see that the ...

... One way to think about this operator is that it applies rules on existing facts to get new facts according to the head of those rules. In general, for a recursive Datalog program, the same operator can be repeatedly applied on facts produced by previous applications of it. It is easy to see that the ...

Complex Preferences for Answer Set Optimization

... set optimization problem is a non-dominated answer set, that is, an answer set such that no strictly better answer set exists. Many AI problems have natural formulations as optimization problems (see for instance (Brewka 2004a) for a discussion of abduction and diagnosis, inconsistency handling and ...

... set optimization problem is a non-dominated answer set, that is, an answer set such that no strictly better answer set exists. Many AI problems have natural formulations as optimization problems (see for instance (Brewka 2004a) for a discussion of abduction and diagnosis, inconsistency handling and ...

KRR Lectures — Contents

... A problem domain is intractable if it is not possible for a (conventional) computer program to solve it in ‘reasonable’ time (and with ‘reasonable’ use of other resources such as memory). Certain classes of logical problem are not only intractable but also undecidable. This means that there is no pr ...

... A problem domain is intractable if it is not possible for a (conventional) computer program to solve it in ‘reasonable’ time (and with ‘reasonable’ use of other resources such as memory). Certain classes of logical problem are not only intractable but also undecidable. This means that there is no pr ...

Implementing Ordered Disjunction Using Answer Set Solvers for

... connective × representing ordered disjunction is allowed to appear in the head of rules only. A (propositional) LPOD thus consists of rules of the form C1 × · · · × Cn ← A1 , . . . , Am , not B1 , . . . , not Bk where the Ci , Aj and Bl are ground literals. The intuitive reading of the rule head is: ...

... connective × representing ordered disjunction is allowed to appear in the head of rules only. A (propositional) LPOD thus consists of rules of the form C1 × · · · × Cn ← A1 , . . . , Am , not B1 , . . . , not Bk where the Ci , Aj and Bl are ground literals. The intuitive reading of the rule head is: ...

thèse - IRIT

... As a result of this, ASP benefits from the integration of DB, KR and SAT techniques. It offers a concise problem representation, so provides rapid application development tools. Moreover, it handles of knowledge intensive applications including data, frame axioms, exceptions, defaults, closures, etc ...

... As a result of this, ASP benefits from the integration of DB, KR and SAT techniques. It offers a concise problem representation, so provides rapid application development tools. Moreover, it handles of knowledge intensive applications including data, frame axioms, exceptions, defaults, closures, etc ...

Applications of Preferences using Answer Set Programming

... In order to specify a preference ordering among the answer sets of a program with respect to an ordered list of atoms, we propose to use double negation in each atom of the ordered rule that represents the mentioned list of atoms. Formally, an atom with double negation corresponds to a negated negat ...

... In order to specify a preference ordering among the answer sets of a program with respect to an ordered list of atoms, we propose to use double negation in each atom of the ordered rule that represents the mentioned list of atoms. Formally, an atom with double negation corresponds to a negated negat ...

Refinement Modal Logic

... model restrictions were not sufficient to simulate informative events, and they introduced refinement trees for this purpose — a precursor of the dynamic epistemic logics developed later (for an overview, see [57]). This usage of refinement as a more general operation than model restriction is simil ...

... model restrictions were not sufficient to simulate informative events, and they introduced refinement trees for this purpose — a precursor of the dynamic epistemic logics developed later (for an overview, see [57]). This usage of refinement as a more general operation than model restriction is simil ...

FLP Semantics Without Circular Justifications for General Logic

... rules of the form H ← B, where H and B are arbitrary first-order formulas. Normal logic programs can be viewed as a special form of general logic programs, where the negation not is identified with ¬, each rule head H with an atom, and each rule body B with a conjunction of literals. Answer sets of ...

... rules of the form H ← B, where H and B are arbitrary first-order formulas. Normal logic programs can be viewed as a special form of general logic programs, where the negation not is identified with ¬, each rule head H with an atom, and each rule body B with a conjunction of literals. Answer sets of ...

Inferring preferred extensions by Pstable semantics

... The problem of characterizing abstract argumentation semantics does not only depend of the codification but also in the logic programming semantics. In fact, to find a suitable logic programming semantic is as important as to find a suitable codification for characterizing a particular abstract arg ...

... The problem of characterizing abstract argumentation semantics does not only depend of the codification but also in the logic programming semantics. In fact, to find a suitable logic programming semantic is as important as to find a suitable codification for characterizing a particular abstract arg ...

Answer Sets for Logic Programs with Arbitrary Abstract Constraint

... The first explicit definition of answer sets for positive programs with arbitrary c-atoms (i.e., programs without the negation-as-failure operator)—called programs with set constraints or SC-programs—has been introduced in the work of Marek and Remmel (2004). In this work answer sets for programs wi ...

... The first explicit definition of answer sets for positive programs with arbitrary c-atoms (i.e., programs without the negation-as-failure operator)—called programs with set constraints or SC-programs—has been introduced in the work of Marek and Remmel (2004). In this work answer sets for programs wi ...

Reasoning in Argumentation Frameworks Using Quantified

... true under any interpretation, then Φ is valid. Observe that a closed QBF is either valid or unsatisfiable, because closed QBFs are either true under each interpretation or false under each interpretation. Hence, for closed QBFs, there is no need to refer to particular interpretations. Two sets of Q ...

... true under any interpretation, then Φ is valid. Observe that a closed QBF is either valid or unsatisfiable, because closed QBFs are either true under each interpretation or false under each interpretation. Hence, for closed QBFs, there is no need to refer to particular interpretations. Two sets of Q ...

Disproving False Conjectures

... derivation that is known to exist. Often, however, interim conjectures are not necessarily known to be derivable. These situations arise frequently in systems where induction principles are not axiomatized but encoded via special elimination rules. In many inductive theorem provers, therefore, failu ...

... derivation that is known to exist. Often, however, interim conjectures are not necessarily known to be derivable. These situations arise frequently in systems where induction principles are not axiomatized but encoded via special elimination rules. In many inductive theorem provers, therefore, failu ...

Logic Programming with Defaults and Argumentation Theories*

... framework for defeasible reasoning that abstracts the intuitions about defeasibility into what we call argumentation theories. Then we develop a simple semantics for this framework and study its properties. The semantics is based on well-founded models [15]; due to space limitations, stable models [ ...

... framework for defeasible reasoning that abstracts the intuitions about defeasibility into what we call argumentation theories. Then we develop a simple semantics for this framework and study its properties. The semantics is based on well-founded models [15]; due to space limitations, stable models [ ...

Complete Workshop Proceedings

... PD Dr. Pascal Hitzler is assistant professor and project leader at the Institute for Applied Informatics and Formal Description Methods (AIFB) of the University of Karlsruhe in Germany. Beforehand, he graduated in Mathematics at Tübingen University, did his dissertation at the National University of ...

... PD Dr. Pascal Hitzler is assistant professor and project leader at the Institute for Applied Informatics and Formal Description Methods (AIFB) of the University of Karlsruhe in Germany. Beforehand, he graduated in Mathematics at Tübingen University, did his dissertation at the National University of ...

Reductio ad Absurdum Argumentation in Normal Logic

... as a means to achieve it. This is the main motivation of the work we present in this paper: by taking the Argumentation perspective we intend to show methods of identifying and finding a 2-valued complete Model for any NLP. The approach is unifying in the sense that it allows us to find the Stable M ...

... as a means to achieve it. This is the main motivation of the work we present in this paper: by taking the Argumentation perspective we intend to show methods of identifying and finding a 2-valued complete Model for any NLP. The approach is unifying in the sense that it allows us to find the Stable M ...

Properties of maximal cliques of a pair-wise compatibility graph for three nonmonotonic reasoning system

... atom, and (4) 2 is emptied by the following transformation: facts are transformed into prerequisite-free, justification-free rules (or in the sense of logic programs, bodiless rules) and horn clauses are transformed into justification-free rules (or rules without ‘not’s in the logic program sense). ...

... atom, and (4) 2 is emptied by the following transformation: facts are transformed into prerequisite-free, justification-free rules (or in the sense of logic programs, bodiless rules) and horn clauses are transformed into justification-free rules (or rules without ‘not’s in the logic program sense). ...

Equivalence for the G3'-stable models semantics

... Two programs P1 and P2 are said to be strongly G03 -stable equivalent, if for every program P , the programs P1 ∪ P and P2 ∪ P are G03 -stable equivalent, i.e. they have the same G03 -stable models. The notion of strongly equivalent logic programs is interesting since, given two sets of rules that ...

... Two programs P1 and P2 are said to be strongly G03 -stable equivalent, if for every program P , the programs P1 ∪ P and P2 ∪ P are G03 -stable equivalent, i.e. they have the same G03 -stable models. The notion of strongly equivalent logic programs is interesting since, given two sets of rules that ...

Bilattices and the Semantics of Logic Programming

... and [1], can be developed, based on Belnap’s logic (see [4] for a version). But we need not stop here. Van Emden has proposed using real numbers in [0, 1] as quantitative truth values [20]. How should such a truth value space be modified if programs are distributed? Similar issues arise for any choi ...

... and [1], can be developed, based on Belnap’s logic (see [4] for a version). But we need not stop here. Van Emden has proposed using real numbers in [0, 1] as quantitative truth values [20]. How should such a truth value space be modified if programs are distributed? Similar issues arise for any choi ...

Contextual Reasoning - Homepages of UvA/FNWI staff

... by configurations of the connections in a network of interconnected nodes. Networks of this kind are often called neural networks, as they are intended ...

... by configurations of the connections in a network of interconnected nodes. Networks of this kind are often called neural networks, as they are intended ...

Translation of Aggregate Programs to Normal Logic Programs

... programs are, respectively, definite and stratified logic programs. Consequently these two classes of programs have a single partial stable model which is twovalued and is also the well-founded model. Our definition of stratification is more general than the existing one and covers a strictly larger ...

... programs are, respectively, definite and stratified logic programs. Consequently these two classes of programs have a single partial stable model which is twovalued and is also the well-founded model. Our definition of stratification is more general than the existing one and covers a strictly larger ...

Document

... of three usual operators: the negation operator ¬ (unary), the conjunction operator ∧ (binary) and the disjunction operator ∨ (binary), each of them being used to connect formulae (the variables themselves are atomic formulae). Insofar as a propositional formula is built in an inductive way (since t ...

... of three usual operators: the negation operator ¬ (unary), the conjunction operator ∧ (binary) and the disjunction operator ∨ (binary), each of them being used to connect formulae (the variables themselves are atomic formulae). Insofar as a propositional formula is built in an inductive way (since t ...

A Deduction Method Complete for Refutation and Finite Satis ability

... it satis es, and will therefore be denoted by ( ). If is a set ( nite set, resp.) of formulas and ( ) a term model of , there might be constants ( nitely many constants, resp.) in which do not occur in . These constants are assumed to be interpreted over the special constant c0 which without loss of ...

... it satis es, and will therefore be denoted by ( ). If is a set ( nite set, resp.) of formulas and ( ) a term model of , there might be constants ( nitely many constants, resp.) in which do not occur in . These constants are assumed to be interpreted over the special constant c0 which without loss of ...