On the Complexity of the Equational Theory of Relational Action
... in Eq(RACTA) (resp. Eq(RACTL)); see section 2. Then, Π10 −completeness of the former theory does not directly provide any information on the complexity of the latter. In section 3, we prove that Eq(RACTA) and Eq(RACTL) are Π10 −hard. The argument is similar to that in [9] which yields Π10 −hardness ...
... in Eq(RACTA) (resp. Eq(RACTL)); see section 2. Then, Π10 −completeness of the former theory does not directly provide any information on the complexity of the latter. In section 3, we prove that Eq(RACTA) and Eq(RACTL) are Π10 −hard. The argument is similar to that in [9] which yields Π10 −hardness ...
PDF - University of Kent
... A valid syllogism is a type of argument that is valid because of its form alone – i.e., because of the particular relationships between the terms and the propositions in it, regardless of the content of the propositions or the truth of the premises. Thus the form of a syllogism is that the conjuncti ...
... A valid syllogism is a type of argument that is valid because of its form alone – i.e., because of the particular relationships between the terms and the propositions in it, regardless of the content of the propositions or the truth of the premises. Thus the form of a syllogism is that the conjuncti ...
AGM Postulates in Arbitrary Logics: Initial Results and - FORTH-ICS
... state that it forces a contraction operator to remove too little information from the KB. However, it is generally acceptable that the recovery postulate cannot be dropped unless replaced by some other constraint, such as filtering ([8]), that would somehow express the Principle of Minimal Change. A ...
... state that it forces a contraction operator to remove too little information from the KB. However, it is generally acceptable that the recovery postulate cannot be dropped unless replaced by some other constraint, such as filtering ([8]), that would somehow express the Principle of Minimal Change. A ...
possible-worlds semantics for modal notions conceived as predicates
... restricts the expressive power of the language in a dramatic way because it rules out quantification in the following sense: There is no direct formalisation of a sentence like “All tautologies of propositional logic are necessary”. Proponents of the operator approach have proposed several strategie ...
... restricts the expressive power of the language in a dramatic way because it rules out quantification in the following sense: There is no direct formalisation of a sentence like “All tautologies of propositional logic are necessary”. Proponents of the operator approach have proposed several strategie ...
Let ав бд гжеиз © § § § § "! be a Boolean algebra, where ¥ for some
... is a set, and are binary operations on called disjunction and conjunctions, respectively, is a unary operation, called the complementation operation, and are two special elements of , with such that the usual axioms of Boolean algebras are satisfied as given in [15] or [6]. Boolean functions are tho ...
... is a set, and are binary operations on called disjunction and conjunctions, respectively, is a unary operation, called the complementation operation, and are two special elements of , with such that the usual axioms of Boolean algebras are satisfied as given in [15] or [6]. Boolean functions are tho ...
Interactive Theorem Proving in Coq and the Curry
... • Identifiers: The simplest form of an expression is an identifier x. If (x : A) ∈ E ∪ Γ then x has a type A. This typing rule is usually presented ...
... • Identifiers: The simplest form of an expression is an identifier x. If (x : A) ∈ E ∪ Γ then x has a type A. This typing rule is usually presented ...
The Omnitude Determiner and Emplacement for the Square of
... their logic in natural languages like everyone else, but the portion of logic they took from it was selected and tooled for its utility in deriving mathematical statements, improving proofs, establishing relations between classes and between sets. Logicists selected a logic for their purpose. Howeve ...
... their logic in natural languages like everyone else, but the portion of logic they took from it was selected and tooled for its utility in deriving mathematical statements, improving proofs, establishing relations between classes and between sets. Logicists selected a logic for their purpose. Howeve ...
Hilbert Type Deductive System for Sentential Logic, Completeness
... Proof: The following is a proof of α→α α→[(α→α)→α], {α→[(α→α)→ α]}→{[α→(α→α)]→(α→α)], (α→(α→α))→(α→α), α→(α→α), α→α The first wff is an instance of Axiom (i), the second––of Axiom (ii), the third is inferred from the first two via modus ponens, the fourth is an instance of Axiom (i) and the fifth i ...
... Proof: The following is a proof of α→α α→[(α→α)→α], {α→[(α→α)→ α]}→{[α→(α→α)]→(α→α)], (α→(α→α))→(α→α), α→(α→α), α→α The first wff is an instance of Axiom (i), the second––of Axiom (ii), the third is inferred from the first two via modus ponens, the fourth is an instance of Axiom (i) and the fifth i ...
Uniform satisfiability in PSPACE for local temporal logics over
... of processes involved in this action. Here, two actions are dependent if they share a common process and conversely any dependence alphabet can be described with this more concrete view based on processes. The uniform satisfiability problem was studied in [7] for general modalities that can be descr ...
... of processes involved in this action. Here, two actions are dependent if they share a common process and conversely any dependence alphabet can be described with this more concrete view based on processes. The uniform satisfiability problem was studied in [7] for general modalities that can be descr ...
The Logic of Compound Statements
... called proposition forms or formulas built from propositional variables (atoms), which represent simple propositions and symbols representing logical connectives Proposition or propositional variables: p, q,… each can be true or false Examples: p=“Socrates is mortal” q=“Plato is mortal” ...
... called proposition forms or formulas built from propositional variables (atoms), which represent simple propositions and symbols representing logical connectives Proposition or propositional variables: p, q,… each can be true or false Examples: p=“Socrates is mortal” q=“Plato is mortal” ...
CSI 2101 / Rules of Inference (§1.5)
... Definition: An integer n is even iff ∃ integer k such that n = 2k Definition: An integer n is odd iff ∃ integer k such that n = 2k+1 Definition: Let k and n be integers. We say that k divides n (and write k | n) if and only if there exists an integer a such that n = ka. Definition: An integer n is p ...
... Definition: An integer n is even iff ∃ integer k such that n = 2k Definition: An integer n is odd iff ∃ integer k such that n = 2k+1 Definition: Let k and n be integers. We say that k divides n (and write k | n) if and only if there exists an integer a such that n = ka. Definition: An integer n is p ...
071 Embeddings
... For technical explanation of this term see Monk [1976] chapters 13 to 16, and Tarski, Mostowski and Robinson ...
... For technical explanation of this term see Monk [1976] chapters 13 to 16, and Tarski, Mostowski and Robinson ...
Studying Sequent Systems via Non-deterministic Multiple
... 3. We formulate the two kinds of three-valued valuation semantics inside the well-studied framework of (three-valued) Nmatrices, exploiting some known general properties of Nmatrices. 4. In [8], it seems that the two dual kinds of three-valued valuation semantics cannot be combined. However, in this ...
... 3. We formulate the two kinds of three-valued valuation semantics inside the well-studied framework of (three-valued) Nmatrices, exploiting some known general properties of Nmatrices. 4. In [8], it seems that the two dual kinds of three-valued valuation semantics cannot be combined. However, in this ...
Chapter 6: The Deductive Characterization of Logic
... straightforward; in intro logic, the semantic characterization of SL is given in terms of truth tables, whereas the deductive characterization of SL is given in terms of derivations in a natural deduction system. Whereas truth tables are easy to describe in a logically and mathematically rigorous ma ...
... straightforward; in intro logic, the semantic characterization of SL is given in terms of truth tables, whereas the deductive characterization of SL is given in terms of derivations in a natural deduction system. Whereas truth tables are easy to describe in a logically and mathematically rigorous ma ...
Acts of Commanding and Changing Obligations
... A word about my choice of monadic deontic operators here may be in order. Monadic deontic logics are known to be inadequate to deal with conditional obligations and R. M. Chisholm’s contrary-to-duty paradox; dyadic deontic logics are better in this respect. But there are still other problems which a ...
... A word about my choice of monadic deontic operators here may be in order. Monadic deontic logics are known to be inadequate to deal with conditional obligations and R. M. Chisholm’s contrary-to-duty paradox; dyadic deontic logics are better in this respect. But there are still other problems which a ...
PROBLEM SOLVING THROUGH FIRST-ORDER LOGIC
... The first-order theory is well known among mathematicians and computer scientists. It is a suitable formal representation for expressing knowledge and theorems. Although it is very popular and clear way, the problem of automated theorem proving is not so simple. If you want to enjoy the power of log ...
... The first-order theory is well known among mathematicians and computer scientists. It is a suitable formal representation for expressing knowledge and theorems. Although it is very popular and clear way, the problem of automated theorem proving is not so simple. If you want to enjoy the power of log ...
High True vs. Low True Logic
... • A set of logic gates is complete if it can implement any boolean function. – Must be able to implement AND, OR, NOT function to be complete The 7400 gate is complete all by itself!!!! AND ...
... • A set of logic gates is complete if it can implement any boolean function. – Must be able to implement AND, OR, NOT function to be complete The 7400 gate is complete all by itself!!!! AND ...
Decision procedures in Algebra and Logic
... Algebraic structure positive definite. See Birkhoff and MacLane (1979: 369). • Graded vector space: a vector space such that the members of M have a direct sum decomposition. See graded algebra below. Four binary operations. • Algebra over a field: An algebra over a ring except that R is a field in ...
... Algebraic structure positive definite. See Birkhoff and MacLane (1979: 369). • Graded vector space: a vector space such that the members of M have a direct sum decomposition. See graded algebra below. Four binary operations. • Algebra over a field: An algebra over a ring except that R is a field in ...
SLD-Resolution And Logic Programming (PROLOG)
... where we can assume without loss of generality that Cn = (A ∨ B). By the induction hypothesis, each axiom of T1 is labeled with a set of clauses of the form {L1 , ..., Ln } ∪ J, where each literal Li is in Ci for i = 1, ..., n − 1, and either Ln = A if A consists of a single literal, or Ln belongs t ...
... where we can assume without loss of generality that Cn = (A ∨ B). By the induction hypothesis, each axiom of T1 is labeled with a set of clauses of the form {L1 , ..., Ln } ∪ J, where each literal Li is in Ci for i = 1, ..., n − 1, and either Ln = A if A consists of a single literal, or Ln belongs t ...
Continuous first order logic and local stability
... continuity moduli. Appendix B deals with the case of a formula which is stable in a single model of a theory. ...
... continuity moduli. Appendix B deals with the case of a formula which is stable in a single model of a theory. ...
Modal Logics of Submaximal and Nodec Spaces 1 Introduction
... examples see Lemma 3.1 below. We also recall that a space X is called an I-space if ddX = ∅. It is pointed out in [3] that for a space X the following three conditions are equivalent: (i) X is an I-space; (ii) X is nodec and (weakly) scattered; (iii) X is submaximal and (weakly) scattered. Examples ...
... examples see Lemma 3.1 below. We also recall that a space X is called an I-space if ddX = ∅. It is pointed out in [3] that for a space X the following three conditions are equivalent: (i) X is an I-space; (ii) X is nodec and (weakly) scattered; (iii) X is submaximal and (weakly) scattered. Examples ...