Many-Valued Models
... it says (namely that it is false) is true. So it is true if and only if it is false. A possible reaction to a paradox like this is to add a third truth-value for “both true and false”. A philosophical application of three-valued logics to the discussion of paradoxes was proposed by the Russian logic ...
... it says (namely that it is false) is true. So it is true if and only if it is false. A possible reaction to a paradox like this is to add a third truth-value for “both true and false”. A philosophical application of three-valued logics to the discussion of paradoxes was proposed by the Russian logic ...
On the Complexity of Linking Deductive and Abstract Argument
... important, and of course by relaxing this constraint we admit into our analysis some scenarios that do not seem to have any useful interpretation; but of course this does not invalidate the results we present. Let A(∆) denote the set of arguments over ∆. If α is an argument, then we denote the suppo ...
... important, and of course by relaxing this constraint we admit into our analysis some scenarios that do not seem to have any useful interpretation; but of course this does not invalidate the results we present. Let A(∆) denote the set of arguments over ∆. If α is an argument, then we denote the suppo ...
Modus Ponens Defended
... It is commonly thought that logically valid arguments play some kind of special normative role in our epistemic practices. From the first-person standpoint of deliberation and the related second-person standpoint of advice—which is an attempt to aid in another’s deliberation—logically valid argument ...
... It is commonly thought that logically valid arguments play some kind of special normative role in our epistemic practices. From the first-person standpoint of deliberation and the related second-person standpoint of advice—which is an attempt to aid in another’s deliberation—logically valid argument ...
On the Construction of Analytic Sequent Calculi for Sub
... a) sub-classical logic. Various important and useful non-classical logics can be formalized in this way, with the most prominent example being intuitionistic logic. In general, the resulting logics come at first with no semantics. They might be also unusable for computational purposes, since the new ...
... a) sub-classical logic. Various important and useful non-classical logics can be formalized in this way, with the most prominent example being intuitionistic logic. In general, the resulting logics come at first with no semantics. They might be also unusable for computational purposes, since the new ...
Logic for Computer Science. Lecture Notes
... the one to be proved valid: if α is an axiom, or is already proved, then the proof is finished, otherwise select (nondeterministically) a set of axioms or previously proved theorems and then apply a nondeterministically chosen applicable derivation rule. Accept the thus obtained conclusion as the new ...
... the one to be proved valid: if α is an axiom, or is already proved, then the proof is finished, otherwise select (nondeterministically) a set of axioms or previously proved theorems and then apply a nondeterministically chosen applicable derivation rule. Accept the thus obtained conclusion as the new ...
An Overview of Intuitionistic and Linear Logic
... Kronecker, perhaps the first ‘constructivist’, famously proclaimed that only the natural numbers are “God-given”, the rest have to be explained in terms of natural numbers. There are several branches in constructivism, each with a varying degree of preference towards constructive concepts and method ...
... Kronecker, perhaps the first ‘constructivist’, famously proclaimed that only the natural numbers are “God-given”, the rest have to be explained in terms of natural numbers. There are several branches in constructivism, each with a varying degree of preference towards constructive concepts and method ...
A causal approach to nonmonotonic reasoning
... lated causal approaches to representing actions and change have been suggested in [23,36, 38], to mention only a few. From the point of view of the present study, the causal reasoning constitutes an important conceptual shift in the general framework of explanatory nonmonotonic reasoning, since it i ...
... lated causal approaches to representing actions and change have been suggested in [23,36, 38], to mention only a few. From the point of view of the present study, the causal reasoning constitutes an important conceptual shift in the general framework of explanatory nonmonotonic reasoning, since it i ...
Logical Arguments - Computer Science, Stony Brook University
... • All statements in an argument, except the final one, are called premises • The final statement is called the conclusion • The key fact about a valid argument is that the truth of the conclusion must necessarily follow from the truth of the premises • One way to determine the validity of an argume ...
... • All statements in an argument, except the final one, are called premises • The final statement is called the conclusion • The key fact about a valid argument is that the truth of the conclusion must necessarily follow from the truth of the premises • One way to determine the validity of an argume ...
Reasoning about Complex Actions with Incomplete Knowledge: A
... explicit representation is needed if we want to model an agent which is capable of reasoning and acting on the basis of its (dis)beliefs. In particular, an agent might want to take actions to acquire new knowledge on the world, if its knowledge is incomplete. These knowledge producing actions are us ...
... explicit representation is needed if we want to model an agent which is capable of reasoning and acting on the basis of its (dis)beliefs. In particular, an agent might want to take actions to acquire new knowledge on the world, if its knowledge is incomplete. These knowledge producing actions are us ...
Classical First-Order Logic Introduction
... propositional logic, but also the symbols ∃ and ∀ for “there exists” and “for all”, along with various symbols to represent variables, constants, functions, and relations. ...
... propositional logic, but also the symbols ∃ and ∀ for “there exists” and “for all”, along with various symbols to represent variables, constants, functions, and relations. ...
Intuitionistic Type Theory - The collected works of Per Martin-Löf
... by which its elements are constructed. However, the weakness of this definition is clear: 1010 , for instance, though not obtainable with the given rules, is clearly an element of N, since we know that we can bring it to the form a0 for some a ∈ N. We thus have to distinguish the elements which have ...
... by which its elements are constructed. However, the weakness of this definition is clear: 1010 , for instance, though not obtainable with the given rules, is clearly an element of N, since we know that we can bring it to the form a0 for some a ∈ N. We thus have to distinguish the elements which have ...
Intuitionistic Type Theory
... by which its elements are constructed. However, the weakness of this definition is clear: 1010 , for instance, though not obtainable with the given rules, is clearly an element of N, since we know that we can bring it to the form a0 for some a ∈ N. We thus have to distinguish the elements which have ...
... by which its elements are constructed. However, the weakness of this definition is clear: 1010 , for instance, though not obtainable with the given rules, is clearly an element of N, since we know that we can bring it to the form a0 for some a ∈ N. We thus have to distinguish the elements which have ...
Almost-certain eventualities and abstract probabilities in quantitative
... almost certainly: no matter where the system is started, the state s will evenually be H, and will eventually be T , provided 0 < p < 1. An abstract probability is one which — like p above — is known only to be neither 0 nor 1: beyond that, its precise value is immaterial for the conclusions that ar ...
... almost certainly: no matter where the system is started, the state s will evenually be H, and will eventually be T , provided 0 < p < 1. An abstract probability is one which — like p above — is known only to be neither 0 nor 1: beyond that, its precise value is immaterial for the conclusions that ar ...
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.