Fichte`s Legacy in Logic
... To carry through the spirit of Kant’s project, and to make good on his own early promise not to take logic for granted, Fichte here insists that logical theory must be thoroughly reconstructed in the light of the new accounts of knowledge and subjectivity inaugurated by Kant’s critical investigation ...
... To carry through the spirit of Kant’s project, and to make good on his own early promise not to take logic for granted, Fichte here insists that logical theory must be thoroughly reconstructed in the light of the new accounts of knowledge and subjectivity inaugurated by Kant’s critical investigation ...
1Propositional Logic - Princeton University Press
... Other meanings (i.e., semantics) for implication are considered in Part 3 of this book. Definition. A wff A is satisfiable iff there exists an interpretation I such that V I [ A] = T . We also say “I makes A true” and “I satisfies A.” Definition. A wff A is unsatisfiable iff the wff is not satisfiab ...
... Other meanings (i.e., semantics) for implication are considered in Part 3 of this book. Definition. A wff A is satisfiable iff there exists an interpretation I such that V I [ A] = T . We also say “I makes A true” and “I satisfies A.” Definition. A wff A is unsatisfiable iff the wff is not satisfiab ...
Revisiting Preferences and Argumentation
... - the ordinary and assumption premises in A are exactly those in {A1 , . . . , An }; - the defeasible rules in A are exactly those in {A1 , . . . , An }; - the strict rules and axiom premises of A are a superset of the strict rules and axiom premises in {A1 , . . . , An }. Notice that if B defeats s ...
... - the ordinary and assumption premises in A are exactly those in {A1 , . . . , An }; - the defeasible rules in A are exactly those in {A1 , . . . , An }; - the strict rules and axiom premises of A are a superset of the strict rules and axiom premises in {A1 , . . . , An }. Notice that if B defeats s ...
Polarizing Double-Negation Translations
... Gödel-Gentzen negative translation (Definition 2.3 above) removes many negations from translations and the polarization we give in Section 5 will even more. If we want to follow the pattern of Theorem 1 to show equiprovability (in the absence of cut), we can no longer systematically move formulæ fr ...
... Gödel-Gentzen negative translation (Definition 2.3 above) removes many negations from translations and the polarization we give in Section 5 will even more. If we want to follow the pattern of Theorem 1 to show equiprovability (in the absence of cut), we can no longer systematically move formulæ fr ...
A game semantics for proof search: Preliminary results - LIX
... In the non-deterministic rewriting of neutral expressions, a switched expression does not rewrite. Such expressions represent expressions that are to be given to the other player to rewrite. To be more precise, we shall consider the question of whether or not the expression N can be rewritten to a s ...
... In the non-deterministic rewriting of neutral expressions, a switched expression does not rewrite. Such expressions represent expressions that are to be given to the other player to rewrite. To be more precise, we shall consider the question of whether or not the expression N can be rewritten to a s ...
CHAPTER 7 GENERAL PROOF SYSTEMS 1 Introduction
... proof system we choose not only axioms of the system, but also specific rules of inference. The choice of rules is often linked, as was the choice of axioms, with a given semantics. We want the rules to preserve the truthfulness of what we are proving, i.e. generating from axioms via the rules. Rule ...
... proof system we choose not only axioms of the system, but also specific rules of inference. The choice of rules is often linked, as was the choice of axioms, with a given semantics. We want the rules to preserve the truthfulness of what we are proving, i.e. generating from axioms via the rules. Rule ...
![overhead 12/proofs in predicate logic [ov]](http://s1.studyres.com/store/data/011612593_1-f0437b45ca3df4f633ddcc6197d427a6-300x300.png)
Bounded Proofs and Step Frames - Università degli Studi di Milano
... using formulae of modal complexity at most n. The bounded proof property is a kind of an analytic subformula property limiting the proof search space. This property holds for proof systems enjoying the subformula property (the latter is a property that usually follows from cut elimination). The bou ...
... using formulae of modal complexity at most n. The bounded proof property is a kind of an analytic subformula property limiting the proof search space. This property holds for proof systems enjoying the subformula property (the latter is a property that usually follows from cut elimination). The bou ...
Logic Programming, Functional Programming, and Inductive
... interpreted as an iterated inductive definition (via some treatment of finite failure.) Such databases are called stratified or free from recursive negation [44]. The main stream of (sound) research into negation [34] uses the mathematics of fixedpoints, ordinals, and inductive definitions, not that ...
... interpreted as an iterated inductive definition (via some treatment of finite failure.) Such databases are called stratified or free from recursive negation [44]. The main stream of (sound) research into negation [34] uses the mathematics of fixedpoints, ordinals, and inductive definitions, not that ...
A proof
... using rules of inference, with the final step showing that q must also be true. • A direct proof shows that a conditional statement pq is true by showing that if p is true then q must also be true. • In a direct proof, we assume that p is true and use axioms, definitions, and previously proven theo ...
... using rules of inference, with the final step showing that q must also be true. • A direct proof shows that a conditional statement pq is true by showing that if p is true then q must also be true. • In a direct proof, we assume that p is true and use axioms, definitions, and previously proven theo ...
Second-Order Logic of Paradox
... the familiar “truth tables” of Kleene’s (strong) 3-valued logic [9, §64], but whereas for Kleene (thinking of the “middle value” as truth-valuelessness) only the top value (True) is designated, for Priest the top two values are both designated. As Priest might say: a formula which is both true and f ...
... the familiar “truth tables” of Kleene’s (strong) 3-valued logic [9, §64], but whereas for Kleene (thinking of the “middle value” as truth-valuelessness) only the top value (True) is designated, for Priest the top two values are both designated. As Priest might say: a formula which is both true and f ...
Propositional Logic - Department of Computer Science
... We want an algorithm that checks whether a given propositional formula is satisfiable. In other words, for a given P , we search for an interpretation I such that I(P ) = 1. If this search is successful, then the output of the algorithm should be • “yes, P is satisfiable”. If no such interpretation ...
... We want an algorithm that checks whether a given propositional formula is satisfiable. In other words, for a given P , we search for an interpretation I such that I(P ) = 1. If this search is successful, then the output of the algorithm should be • “yes, P is satisfiable”. If no such interpretation ...
Temporal Here and There - Computational Cognition Lab
... and a pair of connections with other logics based on HT [5] are known. In this paper we deal with two problems that remained open in THT. The first problem consists in determining whether modal operators are interdefinable or not while the second problem corresponds to the definition of a sound an comp ...
... and a pair of connections with other logics based on HT [5] are known. In this paper we deal with two problems that remained open in THT. The first problem consists in determining whether modal operators are interdefinable or not while the second problem corresponds to the definition of a sound an comp ...
Verification Conditions Are Code - Electronics and Computer Science
... a single substitution to a set of conditions (or more typically terms) to give a single common instance. A single substitution is a natural notion in the context of declarative programming languages, which are referentially transparent. Imperative languages are not referentially transparent, so it i ...
... a single substitution to a set of conditions (or more typically terms) to give a single common instance. A single substitution is a natural notion in the context of declarative programming languages, which are referentially transparent. Imperative languages are not referentially transparent, so it i ...
Divide and congruence applied to eta-bisimulation
... Labelled transition systems can be distinguished from each other by a wide range of semantic equivalences, based on e.g. branching structure or decorated versions of execution sequences. Van Glabbeek [8] classified equivalences for processes that take into account the internal action τ . Here we foc ...
... Labelled transition systems can be distinguished from each other by a wide range of semantic equivalences, based on e.g. branching structure or decorated versions of execution sequences. Van Glabbeek [8] classified equivalences for processes that take into account the internal action τ . Here we foc ...
Inquiry
An inquiry is any process that has the aim of augmenting knowledge, resolving doubt, or solving a problem. A theory of inquiry is an account of the various types of inquiry and a treatment of the ways that each type of inquiry achieves its aim.