The Expressive Power of Modal Dependence Logic
... sentence of ML(6) if and only if K is downward closed and closed under team k-bisimulation, for some k ∈ N. Furthermore, we show that the expressive power of EMDL coincides with that of ML(>), thus answering the open problem from [3] mentioned above. In particular, we obtain as a corollary that the ...
... sentence of ML(6) if and only if K is downward closed and closed under team k-bisimulation, for some k ∈ N. Furthermore, we show that the expressive power of EMDL coincides with that of ML(>), thus answering the open problem from [3] mentioned above. In particular, we obtain as a corollary that the ...
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 ...
Default Reasoning in a Terminological Logic
... the contrary, it requires in general a DL theorem proving operation. This may clearly be seen by taking a look at our example: the relation between the precondition of rule (1) and the precondition of rule (3) has been determined by relying on the fact that Bird(x) is derivable from P enguin(x) thro ...
... the contrary, it requires in general a DL theorem proving operation. This may clearly be seen by taking a look at our example: the relation between the precondition of rule (1) and the precondition of rule (3) has been determined by relying on the fact that Bird(x) is derivable from P enguin(x) thro ...
Ramsey`s Theorem and Compactness
... weak version, called the axiom of dependent choice. However, if the axiom of dependent choice is false, it is possible for infinitary Ramsey’s theorem to be false as well. ...
... weak version, called the axiom of dependent choice. However, if the axiom of dependent choice is false, it is possible for infinitary Ramsey’s theorem to be false as well. ...
A Well-Founded Semantics for Logic Programs with Abstract
... While ASP assumes that solutions are given by answer sets, well-founded models (Van Gelder, Ross, and Schlipf 1991) have been found to be very useful as well. First, computing the well-founded model of a normal logic program is tractable. This compares to the NP-completeness of computing an answer s ...
... While ASP assumes that solutions are given by answer sets, well-founded models (Van Gelder, Ross, and Schlipf 1991) have been found to be very useful as well. First, computing the well-founded model of a normal logic program is tractable. This compares to the NP-completeness of computing an answer s ...
Ans - Logic Matters
... (d) Since terms cannot contain either ‘=’ or ‘<’, we can simply ask of an expression e: is it of the form e1 = e2 or e1 < e2 for some e1 and e2 ? It is a mechanical business to test if so. If ‘no’, then e isn’t an atomic wff. If ‘yes’, then e is an atomic wff iff both e1 and e2 are terms, and that’s ...
... (d) Since terms cannot contain either ‘=’ or ‘<’, we can simply ask of an expression e: is it of the form e1 = e2 or e1 < e2 for some e1 and e2 ? It is a mechanical business to test if so. If ‘no’, then e isn’t an atomic wff. If ‘yes’, then e is an atomic wff iff both e1 and e2 are terms, and that’s ...
Introduction to Logic for Computer Science
... be reduced to the manipulation of statements in symbolic logic? Logic enabled mathematicians to point out why an alleged proof is wrong, or where in the proof, the reasoning has been faulty. A large part of the credit for this achievement must go to the fact that by symbolising arguments rather than ...
... be reduced to the manipulation of statements in symbolic logic? Logic enabled mathematicians to point out why an alleged proof is wrong, or where in the proof, the reasoning has been faulty. A large part of the credit for this achievement must go to the fact that by symbolising arguments rather than ...
references
... Proof of G.Pall’s Theorem by means of traditional deductive methods of classical number theory takes about 6 pages of the close text [9,10]. By means of the superinduction method this theorem is proved as follows. In the considered case, the Theorem 2 states: IF there is a natural number, n*(1,2), w ...
... Proof of G.Pall’s Theorem by means of traditional deductive methods of classical number theory takes about 6 pages of the close text [9,10]. By means of the superinduction method this theorem is proved as follows. In the considered case, the Theorem 2 states: IF there is a natural number, n*(1,2), w ...
Infinity 1. Introduction
... by formulating the notion of compactness the properties of finite sets can be generalised to a useful class of infinite sets. Hence there is no separate theory of finite sets in topology: it is simply subsumed in the theory of compact sets. An advocate of actual infinity would draw a general moral f ...
... by formulating the notion of compactness the properties of finite sets can be generalised to a useful class of infinite sets. Hence there is no separate theory of finite sets in topology: it is simply subsumed in the theory of compact sets. An advocate of actual infinity would draw a general moral f ...
Guarded negation
... as a syntactic fragment of first-order logic, it is also natural to ask for syntactic explanations: what syntactic features of modal formulas (viewed as first-order formulas) are responsible for their good behavior? And can we generalize modal logic, preserving these features, while at the same tim ...
... as a syntactic fragment of first-order logic, it is also natural to ask for syntactic explanations: what syntactic features of modal formulas (viewed as first-order formulas) are responsible for their good behavior? And can we generalize modal logic, preserving these features, while at the same tim ...
CHAPTER 8 Hilbert Proof Systems, Formal Proofs, Deduction
... to denote that a formula A has a formal proof in H2 (from the set of logical axioms A1, A2, A3). We write Γ `H2 A to denote that a formula A has a formal proof in H2 from a set of formulas Γ (and the set of logical axioms A1, A2, A3). Observe that system H2 was obtained by adding axiom A3 to the sy ...
... to denote that a formula A has a formal proof in H2 (from the set of logical axioms A1, A2, A3). We write Γ `H2 A to denote that a formula A has a formal proof in H2 from a set of formulas Γ (and the set of logical axioms A1, A2, A3). Observe that system H2 was obtained by adding axiom A3 to the sy ...
A Resolution-Based Proof Method for Temporal Logics of
... This paper presents two logics, called KLn and BLn respectively, and gives resolutionbased proof methods for both. The logic KLn is a temporal logic of knowledge. That is, in addition to the usual connectives of linear discrete temporal logic [4], KLn contains an indexed set of unary modal connectiv ...
... This paper presents two logics, called KLn and BLn respectively, and gives resolutionbased proof methods for both. The logic KLn is a temporal logic of knowledge. That is, in addition to the usual connectives of linear discrete temporal logic [4], KLn contains an indexed set of unary modal connectiv ...
methods of proof
... is usually reserved for a statement that is considered at least somewhat important. A theorem may be the universal quantification of a conditional statement with one or more premises and a conclusion. We demonstrate that a theorem is true with a proof. A proof is a valid argument that establishes th ...
... is usually reserved for a statement that is considered at least somewhat important. A theorem may be the universal quantification of a conditional statement with one or more premises and a conclusion. We demonstrate that a theorem is true with a proof. A proof is a valid argument that establishes th ...