02_Artificial_Intelligence-PropositionalLogic
... • A valid sentence or tautology is a sentence that is True under all interpretations, no matter what the world is actually like or how the semantics are defined (example: “It’s raining or it’s not raining”) • An inconsistent sentence or contradiction is a sentence that is False under all interpretat ...
... • A valid sentence or tautology is a sentence that is True under all interpretations, no matter what the world is actually like or how the semantics are defined (example: “It’s raining or it’s not raining”) • An inconsistent sentence or contradiction is a sentence that is False under all interpretat ...
Aristotle`s particularisation
... We begin by noting that, in a first order language, the formula ‘[(∃x)P (x)]’ is an abbreviation for the formula ‘[¬(∀x)¬P (x)]’9 . The commonly accepted interpretation of this formula appeals—generally tacitly, but sometimes explicitly10 —to Aristotle’s particularisation. This is a fundamental tene ...
... We begin by noting that, in a first order language, the formula ‘[(∃x)P (x)]’ is an abbreviation for the formula ‘[¬(∀x)¬P (x)]’9 . The commonly accepted interpretation of this formula appeals—generally tacitly, but sometimes explicitly10 —to Aristotle’s particularisation. This is a fundamental tene ...
Relative normalization
... proof-language of T is complex: it contains proof-variables, proof-terms, as well as the terms of the theory T (that appear in proof-terms). Moreover, we need to express usual syntactic operations, such as α-conversion, substitution, etc. For that let us consider a language of trees L generated by a ...
... proof-language of T is complex: it contains proof-variables, proof-terms, as well as the terms of the theory T (that appear in proof-terms). Moreover, we need to express usual syntactic operations, such as α-conversion, substitution, etc. For that let us consider a language of trees L generated by a ...
cl-ch9
... (For the empty language L ∅ , there are no nonlogical symbols to be assigned denotations, but an interpretation must still specify a domain, and that specification makes a difference as to truth for closed formulas involving =. For instance, ∃x∃y ∼ x = y will be true if the domain has at least two d ...
... (For the empty language L ∅ , there are no nonlogical symbols to be assigned denotations, but an interpretation must still specify a domain, and that specification makes a difference as to truth for closed formulas involving =. For instance, ∃x∃y ∼ x = y will be true if the domain has at least two d ...
7 LOGICAL AGENTS
... actions do—is hidden inside the domain-specific code of the R ESULT function. It can be used to predict the outcome of actions but not to deduce that two tiles cannot occupy the same space or that states with odd parity cannot be reached from states with even parity. The atomic representations used ...
... actions do—is hidden inside the domain-specific code of the R ESULT function. It can be used to predict the outcome of actions but not to deduce that two tiles cannot occupy the same space or that states with odd parity cannot be reached from states with even parity. The atomic representations used ...
PRESERVATION THEOREMS IN LUKASIEWICZ MODEL THEORY
... Keisler in [2]. We particularize their work by considering [0, 1]L (the unit interval equipped with the Lukasiewicz t-norm) as the value space. Note that as the Lukasiewicz t-norm induces continuous connectives, the Chang and Keisler requirement of continuity of connectives is satisfied. We also use ...
... Keisler in [2]. We particularize their work by considering [0, 1]L (the unit interval equipped with the Lukasiewicz t-norm) as the value space. Note that as the Lukasiewicz t-norm induces continuous connectives, the Chang and Keisler requirement of continuity of connectives is satisfied. We also use ...
slides1
... ¬A is treated as A ⇒ ⊥ where ⊥ is a sentence without proof. A proof of ∀ξ.A is a function f that maps each point a in the domain of definition to a proof f (a) of A[a/ξ]. A proof of ∃ξ.A is a pair (a, p) where a is in the domain of definition and p is a proof of A[a/ξ]. Bow-Yaw Wang (Academia Sinica ...
... ¬A is treated as A ⇒ ⊥ where ⊥ is a sentence without proof. A proof of ∀ξ.A is a function f that maps each point a in the domain of definition to a proof f (a) of A[a/ξ]. A proof of ∃ξ.A is a pair (a, p) where a is in the domain of definition and p is a proof of A[a/ξ]. Bow-Yaw Wang (Academia Sinica ...
Précis of Propositions - SHANTI Pages
... propositions are sets of possible worlds maintains that that thesis cannot be combined, without incurring new and serious problems, with any standard account of the nature of possible worlds. In fact, this chapter argues that the best account of the nature of possible worlds rules out the thesis tha ...
... propositions are sets of possible worlds maintains that that thesis cannot be combined, without incurring new and serious problems, with any standard account of the nature of possible worlds. In fact, this chapter argues that the best account of the nature of possible worlds rules out the thesis tha ...
Handout
... probably to develop an (empirical) semantic theory of the language of ordinary mathematical discourse--or as philosophers sometimes call it, mathematese. The reason semantics can be seen as more central than ontology to what philosophers of mathematics are doing is that while ontological theories ar ...
... probably to develop an (empirical) semantic theory of the language of ordinary mathematical discourse--or as philosophers sometimes call it, mathematese. The reason semantics can be seen as more central than ontology to what philosophers of mathematics are doing is that while ontological theories ar ...