On modal logics of group belief
... of doxastic mental states, acceptances have only been examined since [57] and since [17]. Some authors (e.g. [16]) claim that acceptance implies belief (at least to some minimal degree as argued in [59]). On the contrary, in [57] acceptance is considered to be stronger than belief. Although belief a ...
... of doxastic mental states, acceptances have only been examined since [57] and since [17]. Some authors (e.g. [16]) claim that acceptance implies belief (at least to some minimal degree as argued in [59]). On the contrary, in [57] acceptance is considered to be stronger than belief. Although belief a ...
logic for computer science - Institute for Computing and Information
... Gottlob Frege, a German mathematician working in relative obscurity. Frege aimed to derive all of mathematics from logical principles, in other words pure reason, together with some self-evident truths about sets. (Such as 'sets are identical if they have the same members' or 'every property determi ...
... Gottlob Frege, a German mathematician working in relative obscurity. Frege aimed to derive all of mathematics from logical principles, in other words pure reason, together with some self-evident truths about sets. (Such as 'sets are identical if they have the same members' or 'every property determi ...
A really temporal logic
... TPTL, employs a novel quantifier construct for referencing time: the freeze quantifier variable to the time of the local temporal context. TPTL is both a natural language for specification and a suitable present a tableau-based decision procedure and a model-checking ...
... TPTL, employs a novel quantifier construct for referencing time: the freeze quantifier variable to the time of the local temporal context. TPTL is both a natural language for specification and a suitable present a tableau-based decision procedure and a model-checking ...
On presenting monotonicity and on EA=>AE (pdf file)
... We seek a uniform way of substantiating steps like the above one. Rather than rely directly on all the individual monotonicity properties (1)–(3), it is easier to rely on inference rules (6) and (7), which can be used to substantiate all such weakening/strengthening steps. We suggest the use of “Mo ...
... We seek a uniform way of substantiating steps like the above one. Rather than rely directly on all the individual monotonicity properties (1)–(3), it is easier to rely on inference rules (6) and (7), which can be used to substantiate all such weakening/strengthening steps. We suggest the use of “Mo ...
A Logical Expression of Reasoning
... reasoning taken in greater generality, including some complex aspects not usually treated in the AI literature, such as what Hempel has called “the problem of inductive inconsistencies”, and the problem of reasoning by considering the plausibility of multiple alternative scenarios. What is presented ...
... reasoning taken in greater generality, including some complex aspects not usually treated in the AI literature, such as what Hempel has called “the problem of inductive inconsistencies”, and the problem of reasoning by considering the plausibility of multiple alternative scenarios. What is presented ...
Note 2 - inst.eecs.berkeley.edu
... many values of x that we did not test! To be certain that the statement is true, we must provide a rigorous proof. So what is a proof? A proof is a finite sequence of steps, called logical deductions, which establishes the truth of a desired statement. In particular, the power of a proof lies in the ...
... many values of x that we did not test! To be certain that the statement is true, we must provide a rigorous proof. So what is a proof? A proof is a finite sequence of steps, called logical deductions, which establishes the truth of a desired statement. In particular, the power of a proof lies in the ...
Argument construction and reinstatement in logics for
... Arguments based on ordered theories, such as those depicted in the Tweety and Nixon examples, can conflict with one another; and it is at first tempting to think of two arguments as conflicting just in case they contain complementary literals as conclusions. This notion of conflict fails to account, ...
... Arguments based on ordered theories, such as those depicted in the Tweety and Nixon examples, can conflict with one another; and it is at first tempting to think of two arguments as conflicting just in case they contain complementary literals as conclusions. This notion of conflict fails to account, ...
An Automata Theoretic Decision Procedure for the Propositional Mu
... For example, occurrences of pX. X and vX.X merely trigger re-evaluation of themselves via the fixpoint property, while pX. (A ) X and vX. (A ) X can generate infinite sequences of reoccurrences along a chain of A edges. The presence or absence of nonterminating evaluations distinguishes least from g ...
... For example, occurrences of pX. X and vX.X merely trigger re-evaluation of themselves via the fixpoint property, while pX. (A ) X and vX. (A ) X can generate infinite sequences of reoccurrences along a chain of A edges. The presence or absence of nonterminating evaluations distinguishes least from g ...
Introduction to Logic
... without changing its value. In Aristotle this meant simply that the pairs he determined could be exchanged. The intuition might have been that they “essentially mean the same”. In a more abstract, and later formulation, one would say that “not to affect a proposition” is “not to change its truth val ...
... without changing its value. In Aristotle this meant simply that the pairs he determined could be exchanged. The intuition might have been that they “essentially mean the same”. In a more abstract, and later formulation, one would say that “not to affect a proposition” is “not to change its truth val ...
Intuitionistic and Modal Logic
... in the informal, not formal sense. • Platonism. Most famous modern representatives: Frege, Gödel. View that mathematical objects have independent existence outside of spacetime, that mathematical truths are independent of us. At the time mixed with logicism, Frege’s idea that mathematics is no more ...
... in the informal, not formal sense. • Platonism. Most famous modern representatives: Frege, Gödel. View that mathematical objects have independent existence outside of spacetime, that mathematical truths are independent of us. At the time mixed with logicism, Frege’s idea that mathematics is no more ...
The equational theory of N, 0, 1, +, ×, ↑ is decidable, but not finitely
... school are complete for showing all arithmetic equations valid for the natural numbers. The answer to this question has occupied many prestigious mathematicians over half a century, that gave the answer for various subsystems, the most intriguing one being the one involving a constant for the number ...
... school are complete for showing all arithmetic equations valid for the natural numbers. The answer to this question has occupied many prestigious mathematicians over half a century, that gave the answer for various subsystems, the most intriguing one being the one involving a constant for the number ...
Chapter 2
... In Chapter 2, we deal with proofs for things that aren’t universally true but only apply within a certain context – graph theory, number theory, the animal kingdom, etc. To prove theorems of this sort we can add facts from the context that act as hypotheses. ...
... In Chapter 2, we deal with proofs for things that aren’t universally true but only apply within a certain context – graph theory, number theory, the animal kingdom, etc. To prove theorems of this sort we can add facts from the context that act as hypotheses. ...
YABLO WITHOUT GODEL
... By proving paradoxes from very weak assumption one can hope to reveal what is really needed to arrive at a contradiction and what the source of paradox is. Arithmetic provides us with very strong tools that are not required to arrive at the paradox. In particular, it provides us with the diagonal le ...
... By proving paradoxes from very weak assumption one can hope to reveal what is really needed to arrive at a contradiction and what the source of paradox is. Arithmetic provides us with very strong tools that are not required to arrive at the paradox. In particular, it provides us with the diagonal le ...
Examples of Natural Deduction
... • But in the logic problems I am using terms that include a negation: – cannot be wearing ...
... • But in the logic problems I am using terms that include a negation: – cannot be wearing ...
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” ...
Lecture notes #2: Proofs - EECS: www
... Intuitively, the concept of proof should already be familiar. We all like to assert things, and few of us like to say things that turn out to be false. A proof provides a means for guaranteeing such claims. Proofs in mathematics and computer science require a precisely stated proposition to be prove ...
... Intuitively, the concept of proof should already be familiar. We all like to assert things, and few of us like to say things that turn out to be false. A proof provides a means for guaranteeing such claims. Proofs in mathematics and computer science require a precisely stated proposition to be prove ...
