Completeness - OSU Department of Mathematics
... • Whenever f is an n-ary function symbol h(f A (a1 , . . . , an )) = f B (h(a1 ), . . . , h(an )) for all a1 , . . . , an ∈ |A|. Notice that if = is in L, A and B respect equality and h is a homormorphism of A to B then h is 1-1 i.e. h is an embedding of A into B. When h is a homomorphism from A to ...
... • Whenever f is an n-ary function symbol h(f A (a1 , . . . , an )) = f B (h(a1 ), . . . , h(an )) for all a1 , . . . , an ∈ |A|. Notice that if = is in L, A and B respect equality and h is a homormorphism of A to B then h is 1-1 i.e. h is an embedding of A into B. When h is a homomorphism from A to ...
Set Theory and Logic
... Example 1.1.4. 3 ∈ /Q So far, we have been defining sets by describing them in words. We can also specify some sets by listing their elements. For example, define the set T by writing T = {a, b, c, d, e}. When defining a set by listing, always use the brackets {, }. Another set that we can define by ...
... Example 1.1.4. 3 ∈ /Q So far, we have been defining sets by describing them in words. We can also specify some sets by listing their elements. For example, define the set T by writing T = {a, b, c, d, e}. When defining a set by listing, always use the brackets {, }. Another set that we can define by ...
On the Distinctions between Semantics and Pragmatics
... meaning, we are interested in intensions only as far as they can be seen as an aid in determining situation independent linguistic meaning. The formal semantic notion of intension does not do this. It only provides a formal functional analysis of something, the determination of which has to be provi ...
... meaning, we are interested in intensions only as far as they can be seen as an aid in determining situation independent linguistic meaning. The formal semantic notion of intension does not do this. It only provides a formal functional analysis of something, the determination of which has to be provi ...
Full Text - Institute for Logic, Language and Computation
... connections must be found. This is not the case for the whole sentence (4); so (7) has another domain for the interpretation of pronouns than (4). For this reason, the statement made with (4) cannot be considered as just a conjunction of two independent statements: somehow the meaning of the first p ...
... connections must be found. This is not the case for the whole sentence (4); so (7) has another domain for the interpretation of pronouns than (4). For this reason, the statement made with (4) cannot be considered as just a conjunction of two independent statements: somehow the meaning of the first p ...
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 ...
Intuitionistic Type Theory - The collected works of Per Martin-Löf
... The principal problem that remained after Principia Mathematica was completed was, according to its authors, that of justifying the axiom of reducibility (or, as we would now say, the impredicative comprehension axiom). The ramified theory of types was predicative, but it was not sufficient for deri ...
... The principal problem that remained after Principia Mathematica was completed was, according to its authors, that of justifying the axiom of reducibility (or, as we would now say, the impredicative comprehension axiom). The ramified theory of types was predicative, but it was not sufficient for deri ...
Intuitionistic Type Theory
... The principal problem that remained after Principia Mathematica was completed was, according to its authors, that of justifying the axiom of reducibility (or, as we would now say, the impredicative comprehension axiom). The ramified theory of types was predicative, but it was not sufficient for deri ...
... The principal problem that remained after Principia Mathematica was completed was, according to its authors, that of justifying the axiom of reducibility (or, as we would now say, the impredicative comprehension axiom). The ramified theory of types was predicative, but it was not sufficient for deri ...
Suspension Across Domains - Jonathan Bobaljik
... Within the intermodular perspective of Distributed Morphology (Halle and Marantz 1993) various authors have raised the question of how the domains (e.g., cycles, phases) of one module (syntax, morphology, semantics) interact with those of others (see also Scheer 2008 and related work). In this short ...
... Within the intermodular perspective of Distributed Morphology (Halle and Marantz 1993) various authors have raised the question of how the domains (e.g., cycles, phases) of one module (syntax, morphology, semantics) interact with those of others (see also Scheer 2008 and related work). In this short ...
Notes on Classical Propositional Logic
... 1. Every axiom is a tautology. 2. Every rule is sound, which means that any boolean valuation that maps all the premises of a rule application to true must also map the conclusion of the rule to true. Then the axiom system is sound; it only proves tautologies. Proof It is easy to see that if the con ...
... 1. Every axiom is a tautology. 2. Every rule is sound, which means that any boolean valuation that maps all the premises of a rule application to true must also map the conclusion of the rule to true. Then the axiom system is sound; it only proves tautologies. Proof It is easy to see that if the con ...
Bounded Proofs and Step Frames - Università degli Studi di Milano
... members of Γ ). We need some care when replacing a logic L with an inference system Ax, because we want global consequence relation to be preserved, in the sense of Proposition 1(ii) below. To this aim, we need to use derivable rules: the rule (8) is derivable in a logic L iff {φ1 , . . . , φn } `L ...
... members of Γ ). We need some care when replacing a logic L with an inference system Ax, because we want global consequence relation to be preserved, in the sense of Proposition 1(ii) below. To this aim, we need to use derivable rules: the rule (8) is derivable in a logic L iff {φ1 , . . . , φn } `L ...
Reasoning about Action and Change
... We assume as given a set S = {s, t, ..., s0 , s00 , ...} of possible total states of the world. A proposition can be identified with the set of states in which it is true. An action α is a binary relation Rα on S, that is, a set of ordered pairs hs, ti of states where s is the initial state of some ...
... We assume as given a set S = {s, t, ..., s0 , s00 , ...} of possible total states of the world. A proposition can be identified with the set of states in which it is true. An action α is a binary relation Rα on S, that is, a set of ordered pairs hs, ti of states where s is the initial state of some ...
Points, lines and diamonds: a two-sorted modal logic for projective
... corresponding capital Greek letters; unless explicitly stated, we always assume that sets of formulas contain formulas of one sort only. We could and perhaps should have introduced boolean connectives in sorts as well; it seems however that no confusion is likely to arise with respect to the sort of ...
... corresponding capital Greek letters; unless explicitly stated, we always assume that sets of formulas contain formulas of one sort only. We could and perhaps should have introduced boolean connectives in sorts as well; it seems however that no confusion is likely to arise with respect to the sort of ...