Failures of Categoricity and Compositionality for
... The news is not all good for the modest inferentialist. The meaning generated by Garson’s method for disjunction has a pair of undesirable properties. It is not categorical in the sense above of not uniquely extending an assignment of semantic values to the atomic sentences of a language and it is n ...
... The news is not all good for the modest inferentialist. The meaning generated by Garson’s method for disjunction has a pair of undesirable properties. It is not categorical in the sense above of not uniquely extending an assignment of semantic values to the atomic sentences of a language and it is n ...
The Relative Expressiveness of Abstract Argumentation and Logic
... that language L2 is strictly more expressive than L1 , we additionally have to present a knowledge base K from L2 of which we prove that L1 cannot express the model set of K. For both methods, we can make use of several recent works on the formalisms we study here. First of all, Brewka, Dunne, and W ...
... that language L2 is strictly more expressive than L1 , we additionally have to present a knowledge base K from L2 of which we prove that L1 cannot express the model set of K. For both methods, we can make use of several recent works on the formalisms we study here. First of all, Brewka, Dunne, and W ...
On Equivalent Transformations of Infinitary Formulas under the
... originally as a tool for proving a theorem about the logic FO(ID), has been used also to prove a new generalization of Fages’ theorem [4]. One of the reasons why stable models of infinitary formulas are important is that they are closely related to aggregates in answer set programming (ASP). The sem ...
... originally as a tool for proving a theorem about the logic FO(ID), has been used also to prove a new generalization of Fages’ theorem [4]. One of the reasons why stable models of infinitary formulas are important is that they are closely related to aggregates in answer set programming (ASP). The sem ...
Reducing Propositional Theories in Equilibrium Logic to
... the bodies and heads of rules, they do not support embedded implications; so for example one cannot write in nlp a rule with a conditional body, such as p ← (q ← r). In fact several authors have suggested the usefulness of embedded implications for knowledge representation (see eg [3,8,23]) but prop ...
... the bodies and heads of rules, they do not support embedded implications; so for example one cannot write in nlp a rule with a conditional body, such as p ← (q ← r). In fact several authors have suggested the usefulness of embedded implications for knowledge representation (see eg [3,8,23]) but prop ...
4. Propositional Logic Using truth tables
... Problems: Use the truth table method to solve the following problems: 1. Decide whether p0→p1 is equivalent to ¬(p1→p0) or not. 2. Decide whether ¬p0 ∨p1 is equivalent to ¬(p0 ∧p1) or not. ...
... Problems: Use the truth table method to solve the following problems: 1. Decide whether p0→p1 is equivalent to ¬(p1→p0) or not. 2. Decide whether ¬p0 ∨p1 is equivalent to ¬(p0 ∧p1) or not. ...
Modal Logic
... engineer the basic framework to fit the following readings of ϕ: • It is necessarily true that ϕ • It will always be true that ϕ • Agent A knows ϕ. We know that ♦ϕ ≡ ¬¬ϕ, so the reading of ♦ϕ in each situation is given automatically by that of ϕ: • It is not necessarily true that not ϕ ≡ It is po ...
... engineer the basic framework to fit the following readings of ϕ: • It is necessarily true that ϕ • It will always be true that ϕ • Agent A knows ϕ. We know that ♦ϕ ≡ ¬¬ϕ, so the reading of ♦ϕ in each situation is given automatically by that of ϕ: • It is not necessarily true that not ϕ ≡ It is po ...
On the continuity of Gelfond-Lifschitz operator and other applications
... P is the least fixed point of a continuous operator TP representing 1-step Horn clause logic deduction ([L89]). That is, for any set I ⊆ At, we let TP (I) equal the set of all p ∈ At such that there is a clause C = p ← q1 , . . . , qm in P and q1 , . . . , qm ∈ I. Then TP has a least fixed point FSP ...
... P is the least fixed point of a continuous operator TP representing 1-step Horn clause logic deduction ([L89]). That is, for any set I ⊆ At, we let TP (I) equal the set of all p ∈ At such that there is a clause C = p ← q1 , . . . , qm in P and q1 , . . . , qm ∈ I. Then TP has a least fixed point FSP ...
Temporal Equilibrium Logic: a first approach
... a temporal equilibrium model. Assume, on the contrary, that Ti is the unique state containing p, so Tk = ∅ for all k 6= i. Then, the only possible smaller interpretation would be {H, T } with Hk = Tk = ∅ for k 6= i and Hi = ∅, but t u this is not a THT model of ♦p, as p would not occur in H. Example ...
... a temporal equilibrium model. Assume, on the contrary, that Ti is the unique state containing p, so Tk = ∅ for all k 6= i. Then, the only possible smaller interpretation would be {H, T } with Hk = Tk = ∅ for k 6= i and Hi = ∅, but t u this is not a THT model of ♦p, as p would not occur in H. Example ...
From Turner`s Logic of Universal Causation to the Logic of GK
... To date, there have been embeddings from default logic [13] and autoepistemic logic [12] to the logic of GK [4], as well as from general logic programs [2, 3] to logic of GK [5]. Among others, these embeddings shed new lights on nonmonotonic reasoning, and have led to an interesting characterization ...
... To date, there have been embeddings from default logic [13] and autoepistemic logic [12] to the logic of GK [4], as well as from general logic programs [2, 3] to logic of GK [5]. Among others, these embeddings shed new lights on nonmonotonic reasoning, and have led to an interesting characterization ...
A Logical Characterisation of Ordered Disjunction
... for introducing an extension called disjunctive LPOD (DLPOD) that combines ordered and regular disjunctions. Other ASP extensions like CR-Prolog, have also incorporated the use of ordered disjunctions [1]. The semantics of an LPOD is defined in two steps. First, the program with ordered disjunctions ...
... for introducing an extension called disjunctive LPOD (DLPOD) that combines ordered and regular disjunctions. Other ASP extensions like CR-Prolog, have also incorporated the use of ordered disjunctions [1]. The semantics of an LPOD is defined in two steps. First, the program with ordered disjunctions ...
A Probabilistic Extension of the Stable Model
... Logic programs under the stable model semantics (Gelfond and Lifschitz 1988) is the language of Answer Set Programming (ASP). Many useful knowledge representation constructs have been introduced in ASP, and several efficient ASP solvers are available. However, like many other logical approaches, ASP ...
... Logic programs under the stable model semantics (Gelfond and Lifschitz 1988) is the language of Answer Set Programming (ASP). Many useful knowledge representation constructs have been introduced in ASP, and several efficient ASP solvers are available. However, like many other logical approaches, ASP ...
Notes on Propositional Logic
... and q evaluates to T , and F otherwise. Therefore, we say “p and q”. This operator is called conjunction, and traditionally, the symbol ∧ is used to denote it. p ∧ q := op2 (p, q) op8 : The operator application op8 (p, q) evaluates to T when p evaluates to T or q evaluates to T , and F otherwise. Th ...
... and q evaluates to T , and F otherwise. Therefore, we say “p and q”. This operator is called conjunction, and traditionally, the symbol ∧ is used to denote it. p ∧ q := op2 (p, q) op8 : The operator application op8 (p, q) evaluates to T when p evaluates to T or q evaluates to T , and F otherwise. Th ...
from Converse PDL - School of Computer Science
... the converse programs from a CPDL formula, but adds enough information so as not to destroy its original meaning with respect to satisfiability, validity, and logical implication. Notably the resulting PDL formula is polynomially related to the original one. This encoding on the one hand helps to be ...
... the converse programs from a CPDL formula, but adds enough information so as not to destroy its original meaning with respect to satisfiability, validity, and logical implication. Notably the resulting PDL formula is polynomially related to the original one. This encoding on the one hand helps to be ...
A Logical Characterisation of Ordered Disjunction
... survey), one that has recently received much attention is the formalism of Logic Programs with Ordered Disjunction (LPOD) [3], probably due to its simplicity and expressiveness. This approach essentially consists of introducing a new operator ‘×’ standing for ordered disjunction (with its correspond ...
... survey), one that has recently received much attention is the formalism of Logic Programs with Ordered Disjunction (LPOD) [3], probably due to its simplicity and expressiveness. This approach essentially consists of introducing a new operator ‘×’ standing for ordered disjunction (with its correspond ...
Propositional Logic .
... Recall the question: what is the minimal set of operators necessary? A: Through such equivalences all Boolean operators can be written with a single operator (NAND). ...
... Recall the question: what is the minimal set of operators necessary? A: Through such equivalences all Boolean operators can be written with a single operator (NAND). ...
Logic - Decision Procedures
... Recall the question: what is the minimal set of operators necessary? A: Through such equivalences all Boolean operators can be written with a single operator (NAND). ...
... Recall the question: what is the minimal set of operators necessary? A: Through such equivalences all Boolean operators can be written with a single operator (NAND). ...
Autoepistemic Logic and Introspective Circumscription
... Thus, technically, the two systems appear to be quite different, and introspective circumscription, the younger and less known of the two, may have important advantages. The ease with which it handles quantification and equality is, in particular, of interest to logic programming. Since autoepistemi ...
... Thus, technically, the two systems appear to be quite different, and introspective circumscription, the younger and less known of the two, may have important advantages. The ease with which it handles quantification and equality is, in particular, of interest to logic programming. Since autoepistemi ...
Revised October 2009
... variables in a full, first-order context. In several cases, assumptions such as standard names (SNA) are being relaxed and issues involving programming in open domains are being addressed. A stable model semantics for first-order structures and languages was defined in the framework of equilibrium l ...
... variables in a full, first-order context. In several cases, assumptions such as standard names (SNA) are being relaxed and issues involving programming in open domains are being addressed. A stable model semantics for first-order structures and languages was defined in the framework of equilibrium l ...
A Revised Concept of Safety for General Answer Set Programs
... CSD2007-00022, and the Junta de Andalucia project P6-FQM-02049. ...
... CSD2007-00022, and the Junta de Andalucia project P6-FQM-02049. ...
Definition - Rogelio Davila
... statements from previously obtained ones. Def. An axiomatic system consists of a set of axioms (or axioms schemata) and a set of inference rules. Def. In an axiomatic system, valid statements produced by the system are called theorems. ...
... statements from previously obtained ones. Def. An axiomatic system consists of a set of axioms (or axioms schemata) and a set of inference rules. Def. In an axiomatic system, valid statements produced by the system are called theorems. ...
Assumption Sets for Extended Logic Programs
... H ⊆ H 0 . A model M of a program Π is said to be a minimal model of Π, if it is minimal under the ≤-ordering among all models of Π. Definition 3 An N 2-model hH, T i of Π is said to be an equilibrium model of Π iff it is minimal and H = T . Thus an equilibrium model is a model hH, T i in which H = T ...
... H ⊆ H 0 . A model M of a program Π is said to be a minimal model of Π, if it is minimal under the ≤-ordering among all models of Π. Definition 3 An N 2-model hH, T i of Π is said to be an equilibrium model of Π iff it is minimal and H = T . Thus an equilibrium model is a model hH, T i in which H = T ...
74.419 Artificial Intelligence 2002 Description Logics
... Richard A. Frost, Introduction to Knowledge-Base Systems, Collins, 1986 (out of print) Comments: one of my favourite books; contains (almost) everything you need w.r.t. foundations of classical and non-classical logic; very compact, comprehensive and relatively easy to understand. Allan Ramsay, Form ...
... Richard A. Frost, Introduction to Knowledge-Base Systems, Collins, 1986 (out of print) Comments: one of my favourite books; contains (almost) everything you need w.r.t. foundations of classical and non-classical logic; very compact, comprehensive and relatively easy to understand. Allan Ramsay, Form ...
Propositional Logic First Order Logic
... Truth tables define the semantics (=meaning) of the operators Convention: 0 = false, 1 = true p q ...
... Truth tables define the semantics (=meaning) of the operators Convention: 0 = false, 1 = true p q ...
Full version - Villanova Computer Science
... There are various deductive systems for classical propositional logic. They can be divided into two major classes: Hilbert-style and Gentzen-style. Hilbert-style systems are axiom-based while Gentzen-style systems are rule-based. Gentzen-style systems have a number of advantages, including existence ...
... There are various deductive systems for classical propositional logic. They can be divided into two major classes: Hilbert-style and Gentzen-style. Hilbert-style systems are axiom-based while Gentzen-style systems are rule-based. Gentzen-style systems have a number of advantages, including existence ...
Ch1 - COW :: Ceng
... Extend I to all formulas: 1. I(T) = 1 and I() = 0. 2. I(A1 ... An) = 1 if and only if I(Ai) = 1 for all i. 3. I(A1 ... An) = 1 if and only if I(Ai) = 1 for some i. 4. I(A) = 1 if and only if I(A) = 0. 5. I(A B) = 1 if and only if I(A) = 0 or I(B) = 1. 6. I(A B) = 1 if and only if I(A) ...
... Extend I to all formulas: 1. I(T) = 1 and I() = 0. 2. I(A1 ... An) = 1 if and only if I(Ai) = 1 for all i. 3. I(A1 ... An) = 1 if and only if I(Ai) = 1 for some i. 4. I(A) = 1 if and only if I(A) = 0. 5. I(A B) = 1 if and only if I(A) = 0 or I(B) = 1. 6. I(A B) = 1 if and only if I(A) ...